Fluid Mechanics Fundamentals

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FLUID MECHANICS AND MACHINERY
II B.E., III Sem., ME
Jun’12 – Nov’12
UNIT - I - INTRODUCTION
Part - A
1.1) What is a fluid? How are fluids classified?
1.2) Define fluid. Give examples. [AU, Nov / Dec - 2010]
1.3) How fluids are classified? [AU, Nov / Dec - 2008, May / June - 2012]
1.4) Distinguish between solid and fluid. [AU, May / June - 2006]
1.5) Differentiate between solids and liquids. [AU, May / June - 2007]
1.6) Discuss the importance of ideal fluid. [AU, April / May - 2011]
1.7) What is a real fluid? [AU, April / May - 2003]
1.8) Define Newtonian and Non – Newtonian fluids. [AU, Nov / Dec - 2008]
1.9) What are Non – Newtonian fluids? Give example. [AU, Nov / Dec - 2009]
1.10) Differentiate between Newtonian and Non – Newtonian fluids.
[AU, Nov / Dec - 2007]
1.11) What is the difference between an ideal and a real fluid?
1.12) Differentiate between liquids and gases.
1.13) Define Pascal’s law. [AU, Nov / Dec – 2005, 2008]
1.14) Define the term density.
1.15) Define mass density and weight density. [AU, Nov / Dec - 2007]
1.16) Distinguish between the mass density and weight density.
[AU, May / June - 2009]
1.17) Define the term specific volume and express its units. [AU, April / May - 2011]
1.18) Define specific weight.
1.19) Define specific weight and density. [AU, May / June - 2012]
1.20) Define the term specific gravity.
1.21) What is specific weight and specific gravity of a fluid? [AU, April / May - 2010]
1.22) What is specific gravity? How is it related to density? [AU, April / May - 2008]
1.23) What do you mean by the term viscosity?

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1.24) What is viscosity? What is the cause of it in liquids and in gases?
[AU, Nov / Dec - 2005]
1.25) Define Viscosity and give its unit. [AU, Nov / Dec - 2003]
1.26) State the Newton's law of viscosity.
[AU, April / May, Nov / Dec - 2005, May / June - 2007]
1.27) Define Newton’s law of viscosity and write the relationship between shear stress
and velocity gradient? [AU, Nov / Dec - 2006]
1.28) What is viscosity and give its units? [AU, April / May - 2011]
1.29) Define coefficient of viscosity. [AU, April / May - 2005]
1.30) Define kinematic viscosity. [AU, Nov / Dec - 2009]
1.31) Define kinematic and dynamic viscosity. [AU, May / June - 2006]
1.32) Mention the significance of kinematic viscosity. [AU, Nov / Dec - 2011]
1.33) What is dynamic viscosity? What are its units?
1.34) Define dynamic viscosity. [AU, Nov / Dec - 2008, May / June - 2012]
1.35) Define the terms kinematic viscosity and give its dimensions.
[AU, May / June - 2009]
1.36) What is kinematic viscosity? What are its units?
1.37) Write the units and dimensions for kinematic and dynamic viscosity.
[AU, Nov / Dec - 2005]
1.38) What are the units and dimensions for kinematic and dynamic viscosity of a fluid?
[AU, Nov / Dec - 2006]
1.39) Differentiate between kinematic and dynamic viscosity.
[AU, May / June - 2007, Nov / Dec – 2008, 2011]
1.40) How does the dynamic viscosity of liquids and gases vary with temperature?
[AU, Nov / Dec - 2007, April / May - 2008]
1.41) What are the variations of viscosity with temperature for fluids?
[AU, Nov / Dec - 2009]
1.42) What is the effect of temperature on viscosity of water and that of air?
1.43) Why is it necessary in winter to use lighter oil for automobiles than insummer?
To what property does the term lighter refer? [AU, Nov / Dec - 2010]
1.44) Define the term pressure. What are its units? [AU, Nov / Dec - 2005]

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1.45) Give the dimensions of the following physical quantities
[AU, April / May - 2003]
a) Pressure b) surface tension
c) Dynamic viscosity d) kinematic viscosity
1.46) Define eddy viscosity. How it differs from molecular viscosity?
[AU, Nov / Dec - 2010]
1.47) Define surface tension. [AU, May / June - 2006]
1.48) Define surface tension and expression its unit. [AU, April / May - 2011]
1.49) Define capillarity. [AU, Nov / Dec - 2005, May / June - 2006]
1.50) What is the difference between cohesion and adhesion?
1.51) Define the term vapour pressure.
1.52) What is meant by vapour pressure of a fluid? [AU, April / May - 2010]
1.53) What are the types of pressure measuring devices?
1.54) What do you understand by terms:
i) Isothermal process ii) adiabatic process
1.55) What do you mean by capillarity? [AU, Nov / Dec - 2009]
1.56) Explain the phenomenon of capillarity.
1.57) Define surface tension.
1.58) What is compressibility of fluid?
1.59) Define compressibility of the fluid.
[AU, Nov / Dec – 2008, May / June - 2009]
1.60) Define compressibility and viscosity of a fluid. [AU, April / May - 2005]
1.61) Define coefficient of compressibility. What is its value for ideal gases?
[AU, Nov / Dec - 2010]
1.62) List the components of total head in a steady, in compressible irrotational flow.
[AU, Nov / Dec - 2009]
1.63) Define the bulk modulus of fluid. [AU, Nov / Dec - 2008]
1.64) Define - compressibility and bulk modulus. [AU, Nov / Dec – 2011]
1.65) Write short notes on thyxotropic fluid.
1.66) What is Thyxotrphic fluid? [AU, Nov / Dec - 2003]
1.67) One poise’s equal to __________Pa.s.

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1.68) Give the types of fluid flow.
1.69) Define steady flow and give an example.
1.70) Define unsteady flow and give an example.
1.71) Differentiate between the steady and unsteady flow. [AU, May / June - 2006]
1.72) When is the flow regarded as unsteady? Give an example for unsteady flow.
1.73) Define uniform flow and give an example.
1.74) Define non uniform flow and give an example.
1.75) Differentiate between steady flow and uniform flow. [AU, Nov / Dec - 2007]
1.76) Define laminar and turbulent flow and give an example.
1.77) Differentiate between laminar and turbulent flow.
[AU, Nov / Dec – 2005, 2008]
1.78) Distinguish between Laminar and Turbulent flow. [AU, April / May - 2010]
1.79) State the criteria for laminar flow. [AU, Nov / Dec - 2008]
1.80) State the characteristics of laminar flow. [AU, April / May - 2010]
1.81) Define compressible and incompressible flow and give an example.
1.82) Define rotational and irrotational flow and give an example.
1.83) Distinguish between rotation and circularity in fluid flow.
1.84) Define stream line. What do stream lines indicate? [AU, Nov / Dec - 2007]
1.85) Define streamline and path line in fluid flow. [AU, Nov / Dec - 2005]
1.86) What is stream line and path line in fluid flow? [AU, April / May - 2010]
1.87) What is a streamline? [AU, Nov / Dec - 2010]
1.88) Define streak line. [AU, April / May - 2008]
1.89) Define stream function. [AU, April / May – 2010, May / June - 2012]
1.90) Define control volume.
1.91) What is meant by continuum? [AU, Nov / Dec - 2008]
1.92) Define continuity equation.
1.93) Write down the equation of continuity. [AU, Nov / Dec –2008, 2009]
1.94) State the continuity equation in one dimensional form?
[AU, May / June - 2012]

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1.95) State the general continuity equation for a 3 - D incompressible fluid flow.
[AU, May / June - 2007]
1.96) State the continuity equation for the case of a general 3-D flow.
[AU, Nov / Dec - 2007]
1.97) State the equation of continuity in 3dimensional incompressible flow.
[AU, Nov / Dec - 2005]
1.98) State the assumptions made in deriving continuity equation.
[AU, Nov / Dec - 2011]
1.99) Define Euler's equation of motion.
1.100) Write the Euler's equation. [AU, April / May - 2011]
1.101) What is Euler’s equation of motion? [AU, Nov / Dec - 2008]
1.102) Define Bernoulli's equation.
1.103) Write the Bernoulli’s equation in terms of head. Explain each term.
[AU, Nov / Dec - 2007]
1.104) What are the basic assumptions made is deriving Bernoulli’s theorem?
[AU, Nov / Dec - 2005]
1.105) List the assumptions which are made while deriving Bernoulli’s equation.
[AU, May / June - 2012]
1.106) State at least two assumptions of Bernoulli’s equation.
[AU, May / June - 2009]
1.107) What are the three major assumptions made in the derivation of the Bernoulli’s
equation? [AU, April / May - 2008]
1.108) State Bernoulli’s theorem as applicable to fluid flow. [AU, Nov / Dec - 2003]
1.109) Give the assumptions made in deriving Bernoulli’s equation.
1.110) What are the applications of Bernoulli’s theorem? [AU, April / May - 2010]
1.111) Give the application of Bernoulli’s equation.
1.112) List the types of flow measuring devices fitted in a pipe flow, which uses the
principle of Bernoulli’s equation. [AU, May / June - 2012]
1.113) Mention the uses of manometer. [AU, Nov / Dec - 2009]
1.114) State the use of venturimeter. [AU, May / June - 2006]
1.115) Define momentum principle.

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1.116) Define impulse momentum equation.
1.117) Write the impulse momentum equation. [AU, May / June - 2007]
1.118) What do you understand by impulse momentum equation?
1.119) State the momentum equation. When can it applied. [AU, May / June - 2009]
1.120) State the usefulness of momentum equation as applicable to fluid flow
phenomenon. [AU, May / June - 2007]
1.121) Define discharge (or) rate of flow.
1.122) Discuss the momentum flux. [AU, April / May - 2011]
1.123) Find the continuity equation, when the fluid is incompressible and densities are
equal.
1.124) Define moment of momentum equation.
1.125) Explain classification of fluids based on viscosity.
1.126) State and prove Euler's equation of motion. Obtain Bernoulli's equation from
Euler's equation.
1.127) State and prove Bernoulli's equation. What are the limitations of the Bernoulli's
equation?
1.128) State the momentum equation. How will you apply momentum equation for
determining the force exerted by a flowing liquid on a pipe bend?
1.129) Give the equation of continuity. Obtain an expression for continuity equation
forathree - dimensional flow.
1.130) Calculate the density of one litre petrol of specific gravity 0.7?
1.131) A soap bubble is formed when the inside pressure is 5 N/m2
above the
atmospheric pressure. If surface tension in the soap bubble is 0.0125 N/m, find the
diameter of the bubble formed. [AU, April / May - 2010]
1.132) The converging pipe with inlet and outlet diameters of 200 mm and 150 mm
carries the oil whose specific gravity is 0.8. The velocity of oil at the entry is 2.5
m/s, find the velocity at the exit of the pipe and oil flow rate in kg/sec.

7
1.133) Find the height through which the water rises by the capillary action in a 2mm
bore if the surface tension at the prevailing temperature is0.075 g/cm.
1.134) Find the height of a mountain where the atmospheric pressure is 730mm of Hg
at normal conditions. [AU, Nov / Dec - 2009]
1.135) Suppose the small air bubbles in a glass of tap water may be on the order of50 μ
m in diameter. What is the pressure inside these bubbles? [AU, Nov / Dec - 2010]
1.136) An open tank contains water up to depth of 2.85m and above it an oil of specific
gravity 0.92 for the depth of 2.1m. Calculate the pressures at the interface of two
liquids and at the bottom of the tank. [AU, April / May - 2011]
1.137) Two horizontal plates are placed 12.5mm apart, the space between them is being
filled with oil of viscosity 14 poise. Calculate the shear stress in the oil if the upper
plate is moved with the velocity of 2.5m/s. Define specific weight.
[AU, May / June - 2012]
1.138) Calculate the height of capillary rise for water in a glass tube of diameter 1mm.
[AU, May / June - 2012]
PART - B
1.139) State and prove Pascal's law. [AU, May / June, Nov / Dec - 2007]
1.140) What is Hydrostatic law? Derive an expression to show the same.
[AU, Nov / Dec - 2009]
1.141) Explain the properties of hydraulic fluid. [AU, Nov / Dec - 2009]
1.142) Discuss the equation of continuity. Obtain an expression for continuity equation
in three dimensional forms. [AU, April / May - 2011]
1.143) Explain in detail the Newton's law of viscosity. Briefly classify the fluids based
on the density and viscosity. Give the limitations of applicability of Newton's law of
viscosity. [AU, April / May - 2011]
1.144) State the effect of temperature and pressure on viscosity.
[AU, May / June - 2009]
1.145) Explain the term specific gravity, density, compressibility and vapour pressure.
[AU, May / June - 2009]

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1.146) Explain the terms Specific weight, Density, Absolute pressure and Gauge
pressure. [AU, April / May - 2011]
1.147) Define Surface tension and also compressibility of a fluid?
[AU, Nov / Dec - 2006]
1.148) Explain the phenomenon surface tension and capillarity.
1.149) What is compressibility of fluids? Give the relationship between compressibility
and bulk modulus [AU, Nov / Dec - 2009]
1.150) Prove that the relationship between surface tension and pressure inside the
droplet of liquid in excess of outside pressure is given by P = 4σ/d.
[AU, April / May –2010, 2011, Nov / Dec - 2008]
1.151) Explain the following
 Capillarity
 Surface tension
 Compressibility
 Kinematic viscosity [AU, May / June - 2012]
1.152) Derive the energy equation and state the assumptions made while deriving the
equation. [AU, Nov / Dec - 2010]
1.153) Derive from the first principles, the Euler’s equation of motion for a steady flow
along a stream line. Hence derive Bernoulli’ equation. State the various assumptions
involved in the above derivation. [AU, May / June - 2009]
1.154) Derive from basic principle the Euler’s equation of motion in 2D flow in X-Y
coordinate system and reduce the equation to get Bernoulli’s equation for
unidirectional stream lined flow. [AU, April / May - 2005]
1.155) State Euler’s equation of motion, in the differential form. Derive Bernoulli’s
equation from the above for the cases of an ideal fluid flow.
[AU, May / June - 2007]
1.156) State the law of conservation of man and derive the equation of continuity in
Cartesian coordinates for an incompressible fluid. Would it alter if the flow were
unsteady, highly viscous and compressible? [AU, April / May - 2011]

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1.157) Derive the equation of continuity for one dimensional flow.
1.158) Derive the continuity equation for 3 dimensional flow in Cartesian coordinates.
[AU, May / June - 2006]
1.159) Derive the continuity equation of differential form. Discuss weathers equation is
valid for a steady flow or unsteady flow, viscous or in viscid flow, compressible or
incompressible flow. [AU, April / May - 2003]
1.160) Derive continuity equation from basic principles. [AU, Nov / Dec - 2009]
1.161) Derive Bernoulli’s equation along with assumptions made.
[AU, May / June - 2007]
1.162) State Bernoulli’s theorem for steady flow of an in compressible fluid.
[AU, Nov / Dec – 2004, 2005, April / May - 2010]
1.163) State Bernoulli’s theorem for steady flow of an in compressible fluid. Derive an
expression for Bernoulli equation and state the assumptions made.
[AU, May / June - 2009]
1.164) State the assumptions in the derivation of Bernoulli’s equation.
[AU, May / June, Nov / Dec - 2007]
1.165) Derive an expression for Bernoulli’s equation for a fluid flow.
1.166) Derive Bernoulli’s equation from the first principles? State the assumptions
made while deriving Bernoulli’s equation. [AU, May / June - 2012]
1.167) Derive from basic principle the Euler’s equation of motion in Cartesian co –
ordinates system and deduce the equation to Bernoulli’s theorem steady irrotational
flow. [AU, April / May - 2004]
1.168) Develop the Euler equation of motion and then derive the onedimensional form
of Bernoulli’s equation. [AU, Nov / Dec - 2011]
1.169) Show that for a perfect gas the bulk modulus of elasticity equals its pressure for
 An isothermal process
 γ times the pressure for an isentropic process
1.170) State and derive impulse momentum equation. [AU, April / May - 2005]

10
1.171) Derive momentum equation for a steady flow. [AU, May / June - 2012]
1.172) Derive the linear momentum equation using the control volume approach and
determine the force exerted by the fluid flowing through a pipe bend.
[AU, Nov / Dec - 2011]
1.173) Draw the sectional view of Pitot’s tube and write its concept to measure velocity
of fluid flow? [AU, April / May - 2005]
PROBLEMS
1.174) A soap bubble is 60mm in diameter. If the surface tension of the soap film is
0.012 N/m. Find the excess pressure inside the bubble and also derive the expression
used in this problem. [AU, Nov / Dec - 2009]
1.175) A liquid weighs 7.25N per litre. Calculate the specific weight, density and
specific gravity of the liquid.
1.176) One litre of crude oil weighs 9.6N. Calculate its specific weight, density and
specific gravity. [AU, Nov / Dec - 2008]
1.177) Determine the viscosity of a liquid having a kinematic viscosity 6 stokes and
specific gravity 1.9. [AU, Nov / Dec - 2008, April / May - 2010]
1.178) Determine the mass density; specific volume and specific weight of liquid whose
specific gravity 0.85. [AU, April / May - 2010]
1.179) If the volume of a balloon is to reach a sphere of 8m diameter at an altitude where
the pressure is 0.2 bar and temperature -40°C. Determine the mass hydrogen to be
charged into the balloon and volume and diameter at ground level. Where the
pressure is 1bar and temperature is 25°C. [AU, Nov / Dec - 2009]
1.180) A pipe of 30 cm diameter carrying 0.25 m3
/s water. The pipe is bentby 135° from
the horizontal anti-clockwise. The pressure of waterflowing through the pipe is 400
kN. Find the magnitude anddirection of the resultant force on the bend.
[AU, Nov / Dec - 2011]
1.181) A liquid has a specific gravity of 0.72. Find its density and specific weight. Find
also the weight per litre of the liquid.
1.182) A 1.9mm diameter tube is inserted into an unknown liquid whose density is
960kg/m3, and it is observed that the liquid raise 5mm in the tube, making a contact

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angle of 15°. Determine the surface tension of the liquid.
1.183) A 0.3m diameter pipe carrying oil at 1.5m/s velocity suddenly expands to 0.6m
diameter pipe. Determine the discharge and velocity in 0.6m diameter pipe.
[AU, May / June - 2012]
1.184) Explain surface tension. Water at 20°C (σ = 0.0.73N/m, γ = 9.8kN/m3
and angle
of contact = 0°) rises through a tube due to capillary action. Find the tube diameter
requires, if the capillary rise is less than 1mm. [AU, Nov / Dec - 2010]
1.185) A Newtonian fluid is filled in the clearance between a shaft and a concentric
sleeve. The sleeve attains a speed of 50cm/s, when a force of 40N is applied to the
sleeve parallel to the shaft. Determine the speed of the shaft, if a force of 200N is
applied. [AU, Nov / Dec - 2006]
1.186) An oil film thickness 10mm is used for lubrication between the square parallel
plate of size 0.9 m * 0.9 m, in which the upper plate moves at 2m/s requires a force
of 100 N to maintain this speed. Determine the
 Dynamic viscosity of the oil in poise and
 Kinematic viscosity of the oil in stokes.
The specific gravity of the oil is 0.95. [AU, Nov / Dec – 2003]
1.187) The space between two square flat parallel plates is filled with oil. Each side of
the plate is 60cm. The thickness of the oil film is 12.5mm. The upper plate, which
moves at 2.5 meter per sec,requires a force of 98.1N to maintain the speed.
Determine the
 Dynamic viscosity of the oil in poise and
 Kinematic viscosity of the oil in stokes.
The specific gravity of the oil is 0.95.
1.188) What is the bulk modulus of elasticity of a liquid which is compressed in a
cylinder from a volume of 0.0125m3
at 80N/cm2
pressure to a volume of 0.0124m3
at pressure 150N/cm2
[AU, Nov / Dec - 2004]
1.189) Determine the bulk modulus of elasticity of elasticity of a liquid, if the pressure
of the liquid is increased from 7MN/m2
to 13MN/m2
, the volume of liquid decreases
by 0.15%. [AU, May / June - 2009]

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1.190) The measuring instruments fitted inside an airplane indicate the pressure 1.032
*105
Pa, temperature T0 = 288 K and density ρ0 = 1.285 kg/m3
at takeoff. If a standard
temperature lapse rate of 0.0065° K/m is assumed, at what elevation is the plane
when a pressure of 0.53*105
recorded? Neglect the variations of acceleration due
gravity with the altitude and take airport elevation as 600m.
A person must breathe a constant mass rate of air to maintain his metabolic
process. If he inhales 20 times per minute at the airport level of 600m, what would
you except his breathing rate at the calculated altitude of the plane?
[AU, May / June - 2009]
1.191) The space between two square parallel plates is filled with oil. Each side of the
plate is 75 cm. The thickness of oil film is 10 mm. The upper plate which moves at
3 m/s requires a force of 100 N to maintain the speed. Determine the
 Dynamic viscosity of the oil
 Kinematic viscosity of the oil, if the specific gravity of the oil is 0.9.
1.192) A rectangular plate of size 25cm* 50zm and weighing at 245.3 N slides down at
30° inclined surface with uniform velocity of 2m/s. If the uniform 2mm gap between
the plates is inclined surface filled with oil. Determine the viscosity of the oil.
1.193) A space between two parallel plates 5mm apart, is filled with crude oil of specific
gravity 0.9. A force of 2N is require to drag the upper plate at a constant velocity of
0.8m/s. the lower plate is stationary. The area of upper plate is 0.09m2
. Determine
the dynamic viscosity in poise and kinematic viscosity of oil in strokes.
[AU, May / June - 2009]
1.194) The space between two large flat and parallel walls 25mm apart is filled with
liquid of absolute viscosity 0.7 Pa.sec. Within this space a thin flat plate 250mm *
250mm is towed at a velocity of 150mm/s at a distance of 6mm from one wall, the
plate and its movement being parallel to the walls. Assuming linear variations of
velocity between the plates and the walls, determine the force exerted by the liquid
on the plate. [AU, May / June - 2012]
1.195) A jet issuing at a velocity of 25 m/s is directed at 35° to the horizontal. Calculate
the height cleared by the jet at 28 m from the discharge location? Also determine the

13
maximum height the jet will clear and the corresponding horizontal location.
[AU, Nov / Dec - 2011]
1.196) A flat plate of area 0.125m2
is pulled at 0.25 m/secwith respect to another parallel
plate 1mm distant from it, the space between the plates containing water of viscosity
0.001Ns/ m2
. Find the force necessary to maintain this velocity. Find also the power
required.
1.197) Lateral stability of a long shaft 150 mm in diameter is obtained by means of a
250 mm stationary bearing having an internal diameter of 150.25 mm. If the space
between bearing and shaft is filled with a lubricant having a viscosity 0.245 N s/m2
,
what power will be required to overcome the viscous resistance when the shaft is
rotated at a constant rate of 180 rpm? [AU, Nov / Dec - 2010]
1.198) Find the kinematic viscosity of water whose specific gravity is 0.95 and viscosity
is0.0011Ns/m2
.
1.199) The dynamic viscosity of oil, used for lubrication between a shaft and sleeve
is6poise. The shaft is of diameter 0.4m and rotates at 190 rpm. Calculate the power
lost in the bearing for a sleeve length of 90mm. The thickness of the oil film is
1.5mm. [AU, Nov / Dec - 2007, May / June - 2012]
1.200) A 200 mm diameter shaft slides through a sleeve, 200.5 mm in diameter and 400
mm long, at a velocity of 30 cm/s. The viscosity of the oil filling the annular space
is m = 0.1125 NS/ m2
. Find resistance to the motion.
[A.U. Nov / Dec - 2008]
1.201) A 0.5m shaft rotates in a sleeve under lubrication with viscosity 5 Poise at
200rpm. Calculate the power lost for a length of 100mm if the thickness of the oil is
1mm. [AU, Nov / Dec - 2009]
1.202) Calculate the gauge pressure and absolute pressure within (i) a droplet of water
0.4cm in diameter (ii) a jet of water 0.4cm in diameter. Assume the surface tension
of water as 0.03N/m and the atmospheric pressure as 101.3kN/m2
.
1.203) What do you mean by surface tension? If the pressure difference between the
inside and outside of air bubble of diameter, 0.01 mm is 29.2kPa, what will be the
surface tension at air water interface? Derive an expression for the surface tension in

14
the air bubble and from it, deduce the result for the given conditions.
[AU, Nov / Dec - 2005]
1.204) A 1.9-mm - diameter tube is inserted into an unknown liquid whose density is
960 kg/ m3
, and it is observed that the liquid rises 5 mm in the tube, making a contact
angle of 15°. Determine the surface tension of the liquid.
1.205) At the depth of 2km in ocean the pressure is 82401kN/m2
. Assume the specific
gravity at the surface as 10055 N/m3
and the average bulk modulus of elasticity is
2.354 * 109
N/m2
for the pressure range. Determine the change in specific volume
between the surface and 2km depth and also determine the specific weight at the
depth? [AU, April / May - 2004]
1.206) At the depth of 8km from the surface of the ocean, the pressure is stated to be
82MN/m2
. Determine the mass density, weight density and specific volume of water
at this depth. Take density at the surface ρ = 1025kg/m3
and bulk modulus K =
2350MPa for indicated pressure range. [AU, May / June - 2009]
1.207) 8 km below the surface of ocean pressure is 81.75MPa. Determine the density
of sea water at this depth if the density at the surface is 1025 kg/m3
and the average
bulk modulus of elasticity is 2.34GPa. [AU, May / June - 2012]
1.208) Calculate the capillary rise in glass tube of 3 mm diameter when immersed in
mercury; take the surface tension and the angle of contact of mercury as 0.52 N/m
and 130° respectively. Also determine the minimum size of the glass tube, if it is
immersed in water, given that the surface tension of water is 0.0725 N/m and
capillary rise in the tube is not to exceed 0.5mm. [AU, Nov / Dec - 2003]
1.209) The capillary rise in a glass tube is not to exceed 0.2mm of water. Determine its
minimum size, given that the surface tension for water in contact with air =
0.0725N/m. [AU, Nov / Dec - 2007, May / June - 2012]
1.210) Calculate the capillary effect in millimeters in a glass tube of 4mm diameter
when immersed in(i) water and (ii) mercury. The temperature of the liquid is 20°C
and the values of surface tension of water and mercury at 20°C in contact with air
are 0.0735 N/m and 0.51 N/m respectively. The contact angle for water u = 0° and

15
for mercury u = 130°. Take specific weight of water at 20°C as equal to 9780 N/m3
.
[AU, Nov / Dec - 2007]
1.211) Derive an expression for the capillary rise at a liquid in a capillarytube of radius
r having surface tension σ and contact angle θ . Ifthe plates are of glass, what will be
the capillary rise of waterhaving σ = 0.073 N/m, θ = 0°? Take r = 1mm.
[AU, Nov / Dec - 2011]
1.212) A pipe containing water at 180kN/m2 pressure is connected to differential gauge
to another pipe 1.6m lower than the first pipe and containing water at high pressure.
If the difference in height of 2 mercury columns of the gauge is equal to 90mm, what
is the pressure in the lower pipe? [AU, Nov / Dec - 2008]
1.213) Determine the minimum size of glass tubing that can be used to measure water
level. If the capillary rise in the tube is not exceed 2.5mm. Assume surface tension
of water in contact with air as 0.0746 N/m. [AU, Nov / Dec - 2004]
1.214) Calculate the capillary effect in millimeters in a glass tube of 4 mm diameter,
when immersed in (i) waterand (ii) mercury. The temperature of the liquid is 20°C
and the values of surface tension of water and mercury at 20°C in contact with air
are 0.0735 N/m and 0.51 N/m respectively. The contact angle for water u = 0 and
for mercury u = 130°. Take specific weight of water at 20°C as equal to 9790N/ m3
.
[AU, Nov / Dec – 2005, 2007]
1.215) A Capillary tube having inside diameter 6 mm is dipped in CCl4at 20o C. Find
the rise of CCl4 in the tube if surface tension is 2.67 N/m and Specific gravity is
1.594 and contact angle u is 60° and specific weight of water at 20° C is 9981 N/m3
.
[AU, Nov / Dec - 2008]
1.216) Two pipes A & B are connected to a U – tube manometer containing mercury of
density 13,600kg/m3
. Pipe A carries a liquid of density 1250kg/m3
and a liquid of
density 800kg/m3
flows through a pipe B, The center of pipe A is 80mm above the
pipe B. The difference of mercury level manometer is 200mm and the mercury
surface on pipe A side is 100mm below the center. Find the difference of pressure
between the two connected points of the pipes. [AU, Nov / Dec - 2010]

16
1.217) A simple U tube manometer containing mercury is connected to a pipe in which
a fluid of specific gravity 0.8 and having vacuum pressure is flowing. The other end
of the manometer is open to atmosphere. Find the vacuum pressure in the pipe, if the
difference of mercury level in the two limbs is 40cm and the height of the fluid in
the left from the center pipe is 15cm below. Draw the sketch for the above problem.
[AU, April / May - 2011, May / June - 2012]
1.218) A U-tube is made of two capillaries of diameter 1.0 mm and 1.5 mmrespectively.
The tube is kept vertically and partially filled withwater of surface tension 0.0736
N/m and zero contact angles.Calculate the difference in the levels of the menisci
caused by thecapillary. [AU, Nov / Dec - 2010]
1.219) The barometric pressure at sea level is 760 mm of mercury while that on a
mountain top is 735 mm. If the density of air is assumed constant at 1.2 kg/m3
,
what is the elevation of the mountain top? [AU, Nov / Dec - 2007]
1.220) The barometric pressure at the top and bottom of a mountain are 734mm and
760mm of mercury respectively. Assuming that the average density of air =
1.15kg/m3, calculate the height of the mountain. [AU, Nov / Dec - 2009]
1.221) The maximum blood pressure in the upper arm of a healthy person is about 120
mmHg. If a vertical tube open to the atmosphere is connected to the vein in the arm
of the person, determine how high the blood will rise in the tube. Take the density
of the blood to be 1050 kg/ m3
. [AU, April / May - 2008]
1.222) When a pressure of 20.7 MN/m2
is applied to 100 litres of a liquid, its volume
decreases by one litre. Find the bulk modulus of the liquid and identify this liquid.
[AU, Nov / Dec - 2007]
1.223) Determine the minimum size of the glass tubing that can be used to measure
water level. If the capillary rise in the tube is not to exceed 2.5mm. Assume surface
tension of water in contact with air as 0.0746 N/m [AU, April / May - 2004]
1.224) A cylinder of 0.6m3
in volume contains air at 50oC and 0.3N/mm2
absolute
pressure. The air is compressed to 0.3m3
. Find the (i) pressure inside the cylinder
assuming isothermal process and(ii) pressure and temperature assuming adiabatic
process. Take k = 1.4.

17
1.225) A 30cm diameter pipe, conveying water, branches into two pipes of diameters
20cm and 15cm respectively. If the average velocity in the 30cm diameter pipe is
2.5m/sec, find the discharge in this pipe. Also determine the velocity in the 15cm
diameter pipe if the average velocity in the 20cm diameter pipe is 2m/sec.
1.226) Water flows through a pipe AB 1.2m diameter at 3m/second then passes through
a pipe BC 1.5m diameter. At C, the pipe branches. Branch CD is 0.8m in diameter
and carries one - third of the flow in AB. The flow velocity in branch CE is 2.5m/sec.
Find the volume rate of flow in AB, the velocity in BC, the velocity in CD and the
diameter of CE.
1.227) Water is flowing through a pipe having diameters 20cm and 10cm at sections 1
and 2 respectively. The rate of flow, through the pipe is 35litre/sec. The section 1 is
6m above datum and section 2 is 4m above datum. If the pressure at section 1 is
39.24N/cm2
, find the intensity of pressure at section 2. [AU, Nov / Dec - 2008]
1.228) Water is flowing through a taper pipe of length 100m having diameters 600mm
at the upper end and 300mm at the lower end, at the rate of 50 litres/ sec. The pipe
has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher
level is 19.62 N/cm2
.
1.229) A pipe of diameter 400mm carries water at a velocity of 25m/sec. The pressures
at the points A and B are given as 29.43N/cm2
and 22.563 N/cm2
respectively, while
the datum head at A and B are 28m and 30m. Find the loss of head between A and
B.
1.230) A drainage pipe is tapered in a section running with full of water. The pipe
diameters at the inlet and exit are 1000 mm and 50 mm respectively. The water
surface is 2 m above the center of the inlet and exit is 3 m above the free surface of
the water. The pressure at the exit is250 mm of Hg vacuum. The friction loss
between the inlet and exit of the pipe is 1/10 of the velocity head at the exit.
Determine the discharge through the pipe. [AU, April / May - 2010]
1.231) A pipeline 60 cm in diameter bifurcates at a Y-junction into two branches 40 cm
and 30 cm in diameter. If the rate of flow in the main pipe is 1.5 m3
/s, and the mean

18
velocity of flow in the 30 cm pipe is 7.5 m/s, determine the rate of flow in the 40 cm
pipe. [AU, Nov / Dec - 2010]
1.232) A pipeline of 175 mm diameter branches into two pipes which delivers the water
at atmospheric pressure. The diameter of the branch 1 which is at 35° counter-
clockwise to the pipe axis is 75mm. and the velocity at outlet is 15 m/s. The branch
2 is at 15° with the pipe center line in the clockwise direction has a diameter of 100
mm. The outlet velocity is 15 m/s. The pipes lie in a horizontal plane. Determine the
magnitude and direction of the forces on the pipes.
[AU, Nov / Dec - 2011]
1.233) A 45° reducing bend is connected in a pipe line, the diameters at the inlet and
outlet of the bend being 600mm and 300mm respectively. Find the force exerted by
water on the bend if the intensity of pressure at the inlet to the bend is 8.829N/cm2
and rate of flow of water is600 litre / sec.
1.234) Gasoline (specific gravity = 0.8) is flowing upwards through a vertical pipe line
which tapers from300mm to 150mm diameter. A gasoline mercury differential
manometer is connected between 300 mm and 150 mm pipe sections to measure the
rate of flow. The distance between the manometer tappings is 1meter and the gauge
heading is 500 mm of mercury. Find the(i) differential gauge reading in terms of
gasoline head (ii) rate of flow. Assume frictional and other losses are negligible.
[AU, May / June - 2007]
1.235) Water enters a reducing pipe horizontally and comes out vertically in the
downward direction. If the inlet velocity is 5 m/s and pressure is 80 kPa (gauge) and
the diameters at the entrance and exit sections are 30 cm and 20 cm respectively,
calculate the components of the reaction acting on the pipe.
[AU, May / June - 2007]
1.236) A horizontal pipe has an abrupt expansion from 10 cm to 16 cm. The water
velocity in the smaller section is 12 m/s, and the flow is turbulent. The pressure in
the smaller section is 300 kPa. Determine the downstream pressure, and estimate the
error that would have occurred if Bernoulli’s equation had been used.
[AU, Nov / Dec - 2011]

19
1.237) Air flows through a pipe at a rate of 20 L/s. The pipe consists of two sections of
diameters20 cm and 10 cm with a smooth reducing section that connects them. The
pressure difference between the two pipe sections is measured by a water
manometer. Neglecting frictional effects, determine the differential height of water
between the two pipe sections. Take the air density to be 1.20 kg/m3
.
1.238) A horizontal venturimeter with inlet diameter 200 mm and throat diameter 100
mm is employed to measure the flow of water. The reading of the differential
manometer connected to the inlet is 180 mm of mercury. If Cd = 0.98, determine
the rate of flow. [AU, April / May - 2010]
1.239) A horizontal venturimeter of specification 200mm * 100mm is used to measure
the discharge of an oil of specific gravity 0.8. A mercury manometer is used for the
purpose. If the discharge is 100 litres per second and the coefficient of discharge of
meter is 0.98, find the manometer deflection. [AU, May / June - 2007]
1.240) Determine the pressure difference between inlet and throat of a vertical
venturimeter of size 150 mm x 75 mm carrying oil of S = 0.8 at flow rate of 40 lps.
The throat is 150 mm above the inlet.
1.241) A pipe of 300 mm diameter inclined at 30° to the horizontal is carrying gasoline
(specific gravity = 0.82). A venturimeter is fitted in the pipe to find out the flow rate
whose throat diameter is 150 mm. The throat is 1.2 m from the entrance along its
20 cm
air
200 L/s
h

20
length. The pressure gauges fitted to the venturimeter read 140 kN/m2
and
80kN/m2
respectively. Find out the co-efficient of discharge of venturimeter if the
flow is 0.20 m3
/s. [AU, April / May - 2010]
1.242) A venturimeter of throat diameter 0.085m is fitted in a 0.17m diameter vertical
pipe in which liquid a relative density 0.85 flows downwards. Pressure gauges ate
fitted at the inlet and to the throat sections. The throat being 0.9m below the inlet.
Taking the coefficient of the meter as 0.95 find the discharge when the pressure
gauges read the same and also when the inlet gauge reads 15000N/m2
higher than
the throat gauge. [AU, April / May - 2011]
1.243) A Venturimeter having inlet and throat diameters 30 cm and 15 cmis fitted in a
horizontal diesel pipe line (Sp. Gr. = 0.92) to measurethe discharge through the pipe.
The venturimeter is connected to amercury manometer. It was found that the
discharge is 8 litres /sec. Find the reading of mercury manometer head in cm. Take
Cd =0.96. [AU, Nov / Dec - 2011]
1.244) A venturimeter is inclined at 60° to the vertical and its 150 mm diameter throat
is 1.2 m from the entrance along its length. It is fitted to a pipe of diameter 300 mm.
The pipe conveys gasoline of S = 0.82 and flowing at 0.215 m3
/s upwards. Pressure
gauges inserted at entrance and throat show the pressures of 0.141 N/mm2
and 0.077
N/mm2
respectively. Determine the co-efficient of discharge of the venturimeter.
Also determine the reading in mm of differential mercury column, if instead of
pressure gauges the entrance and the throat of the venturimeter are connected to the
limbs of a U tube mercury manometer.
1.245) A horizontal venturimeter with inlet and throat diameter 300mm and 100mm
respectively is used to measure the flow of water. The pressure intensity at inlet is
130 kN/m2
while the vacuum pressure head at throat is 350 mm of mercury.
Assuming 3% head lost between the inlet and throat. Find the value of coefficient of
discharge for venturimeter and also determine the rate of flow.
1.246) A vertical venturimeter carries a liquid of relative density 0.8 and has inlet throat
diameters of 150mm and 75mm. The pressure connection at the throat is 150mm

21
above the inlet. If the actual rate of flow is 40litres/sec and Cd = 0.96, find the
pressure difference between inlet and throat in N/m2
. [AU, May / June - 2006]
1.247) A 300 mm x 150 mmventurimeter is provided in a vertical pipeline carrying oil
of relative density 0.9, the flow being upwards. The differential U tube mercury
manometer shows a gauge deflection of 250 mm. Calculate the discharge of oil, if
the co-efficient of meter is 0.98. [AU, Nov / Dec - 2007]
1.248) In a vertical pipe conveying oil of specific gravity 0.8, two pressure gauges have
been installed at A and B, where the diameters are 160mm a 80mm respectively. A
is 2m above B. The pressure gauge readings have shown that the pressure at B is
greater than at A by 0.981 N/cm2
. Neglecting all losses, calculate the flow rate. If the
gauges at A and B are replaced by tubes filled with the same liquid and connected to
a U – tube containing mercury, calculate the difference in the level of mercury in the
two limbs of the U – tube. [AU, May / June - 2012]
1.249) Determine the flow rate of oil of S = 0.9 through an orificemeter of size 15 cm
diameter fitted in a pipe of 30 cm diameter. The mercury deflection of U tube
differential manometer connected on the two sides of the orifice is 50 cm. Assume
Cd of orificemeter as 0.64.
1.250) A submarine moves horizontally in sea and has its axis 15 m below the surface
of water. A pitot static tube properly placed just in front of the submarine along its
axis and is connected to the two limbs of a U - tube containing mercury. The
difference of mercury level is found to be170 mm. Find the speed of submarine
knowing that the sp. gr of sea water is 1.026.
1.251) A submarine fitted with a Pitot tube move horizontally in sea. Its axis is 20m
below surface of water. The Pitot tube placed in front of the submarine along its axis
is connected to a differential mercury manometer showing the deflection of 20cm.
Determine the speed of the submarine. [AU, April / May - 2005]
1.252) A pitot-static probe is used to measure the velocity of an aircraft flying at 3000
m. If the differential pressure reading is 3 kPa, determine the velocity of the aircraft.
1.253) A 15 cm diameter vertical pipe is connected to 10 cm diameter vertical pipe
with a reducing socket. The pipe carries a flow of 1001/s. At point 1 in 15 cm pipe

22
gauge pressure is 250 kPa. At point 2 in the 10 cm pipe located 1.0 m below point 1
the gauge pressure is 175 kPa.
 Find whether the flow is upwards / downwards.
 Head loss between the two points.
1.254) Water enters a reducing pipe horizontally and comes out vertically in the
downward direction. If the inlet velocity is 5 m/sec and pressure is 80 kPa (gauge)
and the diameters at the entrance and exit sections are 300 mm and 200 mm
respectively. Calculate the components of the reaction acting on the pipe.
UNIT - II - FLOW THROUGH CIRCULAR CONDUCTS
PART - A
2.1) How are fluid flows classified? [AU, May / June - 2012]
2.2) Distinguish between Laminar and Turbulent flow. [AU, Nov / Dec - 2006]
2.3) Write down Hagen Poiseuille’s equation for viscous flow through a pipe.

23
2.4) Write down Hagen Poiseuille’s equation for laminar flow.
2.5) Write the Hagen – Poiseuille’s Equation and enumerate its importance.
2.6) State Hagen – Poiseuille’s formula for flow through circular tubes.
[AU, May / June - 2012]
2.7) Write down the Darcy - Weisbach’s equation for friction loss through a pipe
2.8) What is the relationship between Darcy Friction factor, Fanning Friction Factor
and Friction coefficient? [AU, May / June - 2012]
2.9) Mention the types of minor losses. [AU, April / May - 2010]
2.10) List the minor losses in flow through pipe.
[AU, April / May - 2005, May / June - 2007]
2.11) What are minor losses? Under what circumstances will they be negligible?
[AU, May / June - 2012]
2.12) Distinguish between the major loss and minor losses with reference to flow
through pipes. [AU, May / June - 2009]
2.13) List the causes of minor energy losses in flow through pipes.
[AU, Nov / Dec - 2009]
2.14) What are the losses experienced by a fluid when it is passing through a pipe?
2.15) What is a minor loss in pipe flows? Under what conditions does a minor loss
become a major loss?
2.16) What do you understand by minor energy losses in pipes?
[AU, Nov / Dec - 2008]
2.17) List out the various minor losses in a pipeline
2.18) What are ‘major’ and ‘minor losses’ of flow through pipes?
[AU, May / June, Nov / Dec - 2007, April / May - 2010]
2.19) List the minor and major losses during the flow of liquid through a pipe.
2.20) Enlist the various minor losses involved in a pipe flow system.
[AU, Nov / Dec - 2008]

24
2.21) What factors account in energy loss in laminar flow. [AU, May / June - 2012]
2.22) Differentiate between pipes in series and pipes in parallel.
[AU, Nov / Dec - 2006]
2.23) What is Darcy's equation? Identify various terms in the equation.
2.24) What is the relation between Dracy friction factor, Fanning friction factor and
friction coefficient? [AU, Nov / Dec - 2010]
2.25) When is the pipe termed to be hydraulically rough? [AU, Nov / Dec - 2009]
2.26) What is the physical significance of Reynold's number?
2.27) Write the Navier's Stoke equations for unsteady 3 - dimensional, viscous,
incompressible and irrotational flow. [AU, April / May - 2008]
2.28) Define Moody’s diagram
2.29) What are the uses of Moody’s diagram? [AU, Nov / Dec - 2008]
2.30) Write down the formulae for loss of head due to
(i) sudden enlargement in pipe diameter
(ii) sudden contraction in pipe diameter and
(iii) Pipe fittings.
2.31) Define (i) relative roughness and (ii) absolute roughness of a pipe inner surface.
2.32) What do you mean by flow through parallel pipes?
2.33) What is equivalent pipe?
2.34) What is the use of Dupuit’s equations?
2.35) What is the condition for maximum power transmission through a pipe line?
2.36) Give the expression for power transmission through pipes?
[AU, Nov / Dec - 2008]
2.37) Write down the formula for friction factor of pipe having viscous flow.
2.38) Define boundary layer and boundary layer thickness. [AU, Nov / Dec - 2007]
2.39) Define boundary layer thickness. [AU, May / June - 2006, Nov / Dec - 2009]
2.40) What is boundary layer? Give its sketch of a boundary layer region over a flat
plate. [AU, April / May - 2003]
2.41) What is boundary layer? Why is it significant? [AU, Nov / Dec - 2009]

25
2.42) Define boundary layer and give its significance. [AU, April / May - 2010]
2.43) What is boundary layer and write its types of thickness?
[AU, Nov / Dec – 2005, 2006]
2.44) What do you understand by the term boundary layer? [AU, Nov / Dec - 2008]
2.45) Define the following (i) laminar boundary layer (ii) turbulent boundary layer
(iii) laminar sub layer.
2.46) What is a laminar sub layer? [AU, Nov / Dec - 2010]
2.47) Define the following:
(i) Displacement thickness (ii) Momentum thickness
(iii)Energy thickness.
2.48) What do you mean by displacement thickness and momentum thickness?
[AU, Nov / Dec - 2008]
2.49) What do you understand by hydraulic diameter? [AU, Nov / Dec - 2011]
2.50) What is hydraulic gradient line? [AU, May / June - 2009]
2.51) Define hydraulic gradient line and energy gradient line.
2.52) Brief on HGL. [AU, April / May - 2011]
2.53) Differentiate between Hydraulic gradient line and total energy line.
[AU, Nov / Dec - 2003, April / May - 2005, 2010, May / June–2007, 2009]
2.54) What is T.E.L? [AU, Nov / Dec - 2009]
2.55) Distinguish between hydraulic and energy gradients. [AU, Nov / Dec - 2011]
2.56) What are stream lines, streak lines and path lines in fluid flow?
[AU, Nov / Dec –2006, 2009]
2.57) What do you mean by Prandtl’s mixing length?
2.58) Draw the typical boundary layer profile over a flat plate.
2.59) Define flow net. [AU, Nov / Dec - 2008]
2.60) What is flow net and state its use? [AU, April / May - 2011]
2.61) Define lift. [AU, Nov / Dec - 2005]
2.62) Define the terms: drag and lift. [AU, Nov / Dec – 2007, May / June - 2009]
2.63) Define drag and lift co-efficient.
2.64) Give the expression for Drag coefficient and Lift coefficient.

26
2.65) Considering laminar flow through a circular pipe, draw the shear stress and
velocity distribution across the pipe section. [AU, Nov / Dec - 2010]
2.66) A circular and a square pipe are of equal sectional area. For the same flow rate,
determine which section will lead to a higher value of Reynolds number.
[AU, Nov / Dec - 2011]
2.67) A 20cm diameter pipe 30km long transport oil from a tanker to the shore at
0.01m3
/s. Find the Reynolds number to classify the flow. Take the viscosity μ = 0.1
Nm/s2
and density ρ = 900 kg/m3
for oil. [AU, April / May - 2003]
2.68) Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a
diameter 0f 400 mm. Rate of flow of water through the pipe is 250 litres/s.
PART - B
2.69) What are the various types of fluid flows? Discuss [AU, Nov / Dec - 2010]
2.70) Define minor losses. How they are different from major losses?
[AU, May / June - 2009]
2.71) Which has a greater minor loss co-efficient during pipe flow: gradual expansion
or gradual contraction? Why? [AU, April / May - 2008]
2.72) What is the hydraulic gradient line? How does it differ from the total energy line?
Under what conditions do both lines coincide with the free surface of a liquid?
2.73) Write notes on the following:
 Concept of boundary layer.
 Hydraulic gradient
 Moody diagram.
2.74) For a flow of viscous fluid flowing through a circular pipe under laminar flow
conditions, show that the velocity distribution is a parabola.
2.75) For flow of viscous fluids through an annulus derive the following expressions:
 Discharge through the annulus.
 Shear stress distribution. [AU, May / June – 2007, 2012]
2.76) For a laminar flow through a pipe line, show that the average velocity is half of
the maximum velocity.

27
2.77) Prove that the Hagen-Poiseuille’s equation for the pressure difference between
two sections 1 and 2 in a pipe is given by with usual notations.
2.78) Derive Hagen – Poiseuille’s equation and state its assumptions made.
[AU, Nov / Dec - 2005]
2.79) Derive Hagen – Poiseuille’s equation [AU, Nov / Dec - 2008]
2.80) Obtain the expression for Hagen – Poiseuille’s flow. Deduce the condition of
maximum velocity. [AU, Nov / Dec - 2007]
2.81) Give a proof a Hagen – Poiseuille’s equation for a fully – developed laminar flow
in a pipe and hence show that Darcy friction coefficient is equal to 16/Re, where Re
is Reynold’s number. [AU, May / June - 2012]
2.82) Derive an expression for head loss through pipes due to friction.
2.83) Explain Reynold’s experiment to demonstrate the difference between laminar
flow and turbulent flow through a pipe line.
2.84) Derive Darcy - Weisbach formula for calculating loss of head due to friction in a
pipe. [AU, Nov / Dec - 2011]
2.85) Derive Darcy - Weisbach formula for head loss due to friction in flow through
pipes. [AU, Nov / Dec - 2005]
2.86) Obtain expression for Darcy – Weisbach friction factor f for flow in pipe.
[AU, May / June - 2012]
2.87) Explain the losses of energy in flow through pipes. [AU, Nov / Dec - 2009]
2.88) Derive an expression for Darcy – Weisbach formula to determine the head loss
due to friction. Give an expression for relation between friction factor ‘f’ and
Reynolds’s number ‘Re’ for laminar and turbulent flow. [AU, April / May - 2003]
2.89) Prove that the head lost due to friction is equal to one third of the total head at
inlet for maximum power transmission through pipes. [AU, Nov / Dec - 2008]
2.90) Show that for laminar flow, the frictional loss of head is given by
hf= 8 fLQ2
/gπ2
D5
[AU, Nov / Dec - 2009]
2.91) Derive Euler’s equation of motion for flow along a stream line. What are the
assumptions involved. [AU, Nov / Dec - 2009]

28
2.92) A uniform circular tube of bore radius R1 has a fixed co axial cylindrical solid
core of radius R2. An incompressible viscous fluid flows through the annular passage
under a pressure gradient (-∂p/∂x). Determine the radius at which shear stress in the
stream is zero, given that the flow is laminar and under steady state condition.
[AU, May / June - 2009]
2.93) If the diameter of the pipe is doubled, what effect does this have on the flow rate
for a given head loss for laminar flow and turbulent flow.
2.94) Derive an expression for the variation of jet radius r with distance y downwards
for a jet directed downwards. The initial radius is R and the head of fluid is H.
[AU, Nov / Dec - 2011]
2.95) Distinguish between pipes connected in series and parallel.
[AU, Nov / Dec - 2005]
2.96) Determine the equivalent pipe corresponding to 3 pipes in series with lengths and
diameters l1,l2,l3,d1,d2,d3 respectively. [AU, Nov / Dec - 2009]
2.97) For sudden expansion in a pipe flow, work out the optimum ratio between the
diameter of before expansion and the diameter of the pipe after expansion so that the
pressure rise is maximum. [AU, May / June - 2012]
2.98) Obtain the condition for maximum power transmission through a pipe line.
2.99) What are the uses and limitations of flow net? [AU, May / June - 2009]
2.100) Define momentum thickness and energy thickness.
[AU, May / June – 2007, 2012]
2.101) Define the term boundary layer. [AU, May / June - 2009]
2.102) Define the terms boundary layer, boundary thickness. [AU, Nov / Dec - 2008]
2.103) Briefly explain about boundary layer separation. [AU, Nov / Dec - 2008]
2.104) Explain on boundary layer separation and its control.
2.105) Considering a flow over a flat plate, explain briefly the development of
hydrodynamic boundary layer. [AU, Nov / Dec - 2010]
2.106) Discuss in detail about boundary layer thickness and separation of boundary
layer. [AU, April / May - 2011]

29
2.107) What is boundary layer and write its types of thickness?
2.108) Explain in detail
 Drag and lift coefficients
 Boundary layer thickness
 Boundary layer separation
 Navier’s – strokes equation. [AU, May / June - 2012]
2.109) In a water reservoir flow is through a circular hole of diameter D at the side wall
at a vertical distance H from the free surface. The flow rate through an actual hole
with a sharp-edged entrance (kL
= 0.5) will be considerably less than the flow rate
calculated assuming frictionless flow. Obtain a relation for the equivalent diameter
of the sharp-edged hole for use in frictionless flow relations.
[AU, Nov / Dec - 2011]
2.110) Define : Boundary layer thickness(δ); Displacement thickness(δ*
); Momentum
thickness(θ) and energy thickness(δ**
). [AU, April / May - 2010]
2.111) Find the displacement thickness momentum thickness and energy thickness for
the velocity distribution in the boundary layer given by (u/v) = (y/δ), where ‘u’is the
velocity at a distance ‘y’ from the plate and u=U at y=δ, where δ = boundary layer
thickness. Also calculate (δ*
/θ). [AU, Nov / Dec - 2007, April / May - 2010]
2.112) What is hydraulic gradient line? How does it differ from the total energy line?
Under what conditions do both lines coincide with surface of the liquid?
2.113) Derive an expression for the velocity distribution for viscous flow through a
circular pipe. [AU, May / June - 2007]
2.114) Write a brief note on velocity potential function and stream function.
[AU, May / June - 2009]
2.115) Derive an expression for the velocity distribution for viscous flow through a
circular pipe. Also sketch the distribution of velocity cross a section of the pipe.
[AU, Nov / Dec - 2011]

30
PROBLEMS
2.116) A 20 cm diameter pipe 30 km long transports oil from a tanker to the shore at
0.01m3
/s. Find the Reynold’s number to classify the flow. Take viscosity and
density for oil.
2.117) A pipe line 20cm in diameter, 70m long, conveys oil of specific gravity 0.95 and
viscosity 0.23 N.s/m2
. If the velocity of oil is 1.38m/s, find the difference in pressure
between the two ends of the pipe. [AU, May / June - 2012]
2.118) Oil of absolute viscosity 1.5 poise and density 848.3kg/m3
flows through a
300mm pipe. If the head loss in 3000 m, the length of pipe is 200m, assuming
laminar flow, find
(i) the average velocity,
(ii) Reynolds’s number and
(iii) Friction factor. [AU, May / June - 2012]
2.119) An oil of specific gravity 0.7 is flowing through the pipe diameter 30cm at the
rate of 500litres/sec. Find the head lost due to friction and power required to maintain
the flow for a length of 1000m. Take γ = 0.29 stokes.
2.120) A pipe line 10km, long delivers a power of 50kW at its outlet ends. The pressure
at inlet is 5000kN/m2
and pressure drop per km of pipeline is 50kN/m2
. Find the size
of the pipe and efficiency of transmission. Take 4f = 0.02.
[AU, Nov / Dec - 2005]
2.121) A lubricating oil flows in a 10 cm diameter pipe at 1 m/s. Determine whether the
flow is laminar or turbulent.
2.122) For the lubricating oil 2 μ = 0.1Ns /m and ρ = 930 kg/m3
. Calculate also
transition and turbulent velocities. [AU, April / May - 2011]
2.123) Oil of ,mass density 800kg/m3
and dynamic viscosity 0.02 poise flows through
50mm diameter pipe of length 500m at the rate of 0.19 liters/ sec. Determine
 Reynolds number of flow
 Center line of velocity
 Pressure gradient
 Loss of pressure in 500m length

31
 Wall shear stress
 Power required to maintain the flow. [AU, May / June - 2012]
2.124) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway
between the wall surface and the center line) is measured to be 6m/s. Determine the
velocity at the center of the pipe. [AU, April / May - 2008]
2.125) A pipe 85m long conveys a discharge of 25litres per second. If the loss of head
is 10.5m. Find the diameter of the pipe take friction factor as 0.0075.
[AU, Nov / Dec - 2009]
2.126) A smooth pipe carries 0.30m3
/s of water discharge with a head loss of 3m per
100m length of pipe. If the water temperature is 20°C, determine diameter of the
pipe. [AU, May / June - 2012]
2.127) Water is flowing through a pipe of 250 mm diameter and 60 m long at a rate of
0.3 m3
/sec. Find the head loss due to friction. Assume kinematic viscosity of water
0.012 stokes.
2.128) A pipe of 12cm diameter is carrying an oil (μ = 2.2 Pa.s and ρ = 1250 kg/m3
)
with a velocity of 4.5 m/s. Determine the shear stress at the wall surface of the pipe,
head loss if the length of the pipe is 25 m and the power lost.
[AU, Nov / Dec - 2011]
2.129) Find the head loss due to friction in a pipe of diameter 30cm and length 50cm,
through which water is flowing at a velocity of 3m/s using Darcy’s formula.
[AU, Nov / Dec - 2008]
2.130) For a turbulent flow in a pipe of diameter 300 mm, find the discharge when the
center-line velocity is 2.0 m/s and the velocity at a point 100 mm from the center as
measured by pitot-tube is 1.6 m/s. [AU, April / May - 2010]
2.131) A laminar flow is taking place in a pipe of diameter 20cm. The maximum
velocity is 1.5m/s. Find the mean velocity and radius at which this occurs. Also
calculate the velocity at 4cm from the wall pipe. [AU, May / June - 2009]
2.132) Water is flowing through a rough pipe of diameter 60 cm at the rate of
600litres/second. The wall roughness is 3 mm. Find the power loss for 1 km length
of pipe.

32
2.133) Water flows in a 150 mm diameter pipe and at a sudden enlargement, the loss of
head is found to be one-half of the velocity head in 150 mm diameter pipe. Determine
the diameter of the enlarged portion.
2.134) A pipe line carrying oil of specific gravity 0.85, changes in diameter from
350mm at position 1 to 550mm diameter to a position 2, which is at 6m at a higher
level. If the pressure at position 1 and 2 are taken as 20N/cm2
and 15N/cm2
respectively and discharge through the pipe is 0.2m3
/s. Determine the loss of head.
[AU, May / June - 2007]
2.135) A pipe line carrying oil of specific gravity 0.87, changes in diameter from
200mm at position A to 500mm diameter to a position B, which is at 4m at a higher
level. If the pressure at position A and B are taken as 9.81N/cm2
and 5.886N/cm2
respectively and discharge through the pipe is 200 litres/s. Determine the loss of head
and direction of flow. [AU, Nov / Dec - 2008]
2.136) A 30cm diameter pipe of length 30cm is connected in series to a 20 cm diameter
pipe of length 20cm to convey discharge. Determine the equivalent length of pipe
diameter 25cm, assuming that the friction factor remains the same and the minor
losses are negligible. [AU, April / May - 2003]
2.137) A pipe of 0.6m diameter is 1.5 km long. In order of augment the discharge,
another line of the same diameter is introduced parallel to the first in the second half
of the length. Neglecting minor losses. Find the increase in discharge, if friction
factor f= 0.04. The head at inlet is 40m. [AU, Nov / Dec – 2004, 2005]
2.138) A pipe of 10 cm in diameter and 1000 m long is used to pump oil of viscosity
8.5 poise and specific gravity 0.92 at the rate of1200 lit./min. The first 30 m of the
pipe is laid along the ground sloping upwards at 10° to the horizontal and remaining
pipe is laid on the ground sloping upwards 15° to the horizontal. State whether the
flow is laminar or turbulent? Determine the pressure required to be developed by the
pump and the power required for the driving motor if the pump efficiency is 60%.
Assume suitable data for friction factor, if required.
[AU, Nov / Dec - 2010]
2.139) Oil with a density of 900 kg/m3
and kinematic viscosity of 6.2 × 10-4
m2
is being
discharged by a 6 mm diameter, 40 m long horizontal pipe from a storage tank open

33
to the atmosphere. The height of the liquid level above the center of the pipe is 3 m.
Neglecting the minor losses, determine the flow rate of oil through the pipe.
[AU, Nov / Dec - 2011]
2.140) The velocity of water in a pipe 200mm diameter is 5m/s. The length of the pipe
is 500m. Find the loss of head due to friction, if f = 0.008. [AU, Nov / Dec - 2005]
2.141) A 200mm diameter (f = 0.032) 175m long discharges a 65mm diameter water jet
into the atmosphere at a point which is 75m below the water surface at intake. The
entrance to the pipe is reentrant with ke = 0.92 and the nozzle loss coefficient is 0.06.
Find the flow rate and the pressure head at the base of the nozzle.
2.142) A pipe line 2000m long is used for power transmission 110kW is to be
transmitted through a pipe in which water is having a pressure of 5000kN/m2
at inlet
is flowing. If the pressure drop over a length of a pipe is 1000kN/m2
and coefficient
of friction is 0.0065, find the diameter of the pipe and efficiency of transmission.
[AU, May / June - 2012]
2.143) A horizontal pipe of 400 mm diameter is suddenly contracted to a diameter of
200 mm. The pressure intensities in the large and small pipe are given as 15 N/cm2
and 10 N/cm2
respectively. Find the loss of head due to contraction, if Cc = 0.62,
determine also the rate of flow of water.
2.144) A 15cm diameter vertical pipe is connected to 10cm diameter vertical pipe with
a reducing socket. The pipe carries a flow of 100 l/s. At a point 1 in 15cm pipe gauge
pressure is 250kPa. At point 2 in the 10cm pipe located 1m below point 1 the gauge
pressure is 175kPa.
 Find weather the flow is upwards /downwards
 Head loss between the two points [AU, Nov / Dec - 2008]
2.145) The rate of flow of water through a horizontal pipe is 0.25 m3
/sec. The diameter
of the pipe, which is 20 cm, is suddenly enlarged to 40 cm. The pressure intensity
in the smaller pipe is 11.7 N/cm2
. Determine the loss of head due to sudden
enlargement and pressure intensity in the larger pipe, power loss due to enlargement.
[AU, May / June - 2009]

34
2.146) A 45° reducing bend is connected to a pipe line. The inlet and outlet diameters
of the bend being 600mm and 300mm respectively. Find the force exerted by water
on the bend, if the intensity of pressure at inlet to bend is 8.829N/cm2
and the rate of
flow of water is 600 liters/s. [AU, Nov / Dec - 2007]
2.147) Horizontal pipe carrying water is gradually tapering. At one section the diameter
is 150mm and the flow velocity is 1.5m/s. If the drop pressure is 1.104bar is reduced
section, determine the diameter of that section. If the drop is 5kN/m2
, what will be
the diameter – Neglect the losses? [AU, Nov / Dec - 2009]
2.148) The rate of flow of water through a horizontal pipe is 0.3m3
/sec. The diameter
of the pipe, which is 25cm, is suddenly enlarged to 50 cm. The pressure intensity in
the smaller pipe is 14N/cm2
. Determine the loss of head due to sudden enlargement,
pressure intensity in the larger pipe power lost due to enlargement.
[AU, Nov / Dec - 2003]
2.149) Water at 15°C ( ρ =999.1 kg/m3
andμ = 1.138 x 10-3
kg/m. s) is flowing steadily
in a30-m-long and 4 cm diameter horizontal pipe made of stainless steel at a rate of
8 L/s. Determine (i) the pressure drop, (ii) the head loss, and (iii) the pumping power
requirement to overcome this pressure drop. Assume friction factor for the pipe as
0.015. [AU, April / May - 2008]
2.150) The discharge of water through a horizontal pipe is 0.25m3/s. The diameter of
above pipe which is 200mm suddenly enlarges to 400mm at a point. If the pressure
of water in the smaller diameter of pipe is 120kN/m2
, determine loss of head due to
sudden enlargement; pressure of water in the larger pipe and the power lost due to
sudden enlargement. [AU, May / June - 2009]
2.151) A pipe of varying sections has a sectional area of 3000, 6000 and 1250 mm2
at
point A, B and C situated 16 m, 10 m and 2 m above the datum. If the beginning of
the pipe is connected to a tank which is filled with water to a height of 26 m above
the datum, find the discharge, velocity and pressure head at A, B and C. Neglect all
losses. Take atmospheric pressure as 10 m of water.
2.152) An existing 300mm diameter pipeline of 3200m length connects two reservoirs
having 13m difference in their water levels. Calculate the discharge Q1. If a parallel
pipe 300mm in diameter is attached to the last 1600m length of the above existing

35
pipe line, find the new discharge Q2. What is the change in discharge? Express it as
a % of Q1. Assume friction factor f = 0.14 in Darcy – Weisbach formula.
[AU, May / June - 2009]
2.153) Two reservoirs with a difference in water surface elevation of 15 m are
connected by a pipe line ABCD that consists of three pipes AB, BC and CD joined
in series. Pipe AB is 10 cm in diameter, 20 m long and has f = 0.02. Pipe BC is of
16 cm diameter, 25 m long and has f = 0.018. Pipe CD is of 12 cm diameter, 15 m
long and has f = 0.02. The junctions with the reservoirs and between the pipes are
abrupt. (a) Calculate the discharge (b) What difference in reservoir elevation is
necessary to have a discharge of 20 litres/sec? Include all minor losses.
2.154) Three pipes of 400mm, 350mm and 300mm diameter connected in series
between two reservoirs. With difference in level of 12m. Friction factor is 0.024,
0.021 and 0.019 respectively. The lengths are 200m, 300m and 250m. Determine
flow rate neglecting the minor losses. [AU, Nov / Dec - 2009]
2.155) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths450 m, 255
m and 315 m respectively are connected in series. The difference in water surface
levels in two tanks is 18 m. Determine the rate of flow of water if coefficients of
friction are 0.0075, 0.0078and 0.0072 respectively considering: the minor losses and
by neglecting minor losses. [AU, Nov / Dec - 2011]
2.156) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 300 m, 170
m and 210 m respectively are connected in series. The difference in water surface
levels in two tanks is 12 m. Determine the rate of flow of water if coefficients of
friction are 0.005, 0.0052 and 0.0048 respectively considering: the minor losses and
by neglecting minor losses [AU, May / June– 2012]
2.157) Three pipes connected in series to make a compound pipe. The diameters and
lengths of pipes are respectively, 0.4m, 0.2m, 0.3m and 400m, 200m, 300m. The
ends of the compound pipe are connected to 2 reservoirs whose difference in water
levels is 16m. The friction factor for all the pipes is same and equal to 0.02. The
coefficient of contraction is 0.6. Find the discharge through the compound pipe if,
minor losses are negligible. Also find the discharge if minor losses are included.
[AU, Nov / Dec - 2010]

36
2.158) A compound piping system consists of 1800 m of 0.5 m, 1200 m of 0.4 m and
600 m of 0.3 m new cast-iron pipes connected in series. Convert the system to (i) an
equivalent length of0.4 m diameter pipe and (ii) an equivalent size of pipe of 3600
m length. [AU, April / May - 2003]
2.159) A pipe line of 600 mm diameter is 1.5 km long. To increase the discharge,
another line of the same diameter is introduced parallel to the first in the second half
of the length. If f = 0.01 and head at inlet is 30 m, calculate the increase in discharge.
2.160) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another
line of same diameter is introduced in parallel to the first in second half of the length.
Neglecting the minor losses, find the increase in discharge if 4f = 0.04. The head at
inlet is 30cm. [AU, April / May - 2011]
2.161) Two pipes of 15cm and 30cm diameters are laid in parallel to pass a total
discharge of 100 litres per second. Each pipe is 250m long. Determine discharge
through each pipe. Now these pipes are connected in series to connect two tanks
500m apart, to carry same total discharge. Determine water level difference between
the tanks. Neglect the minor losses in both cases, f=0.02 fn both pipes.
[AU, May / June - 2007]
2.162) Two pipes of diameter 40 cm and 20 cm are each 300 m long. When the pipes
are connected in series and discharge through the pipe line is0.10 m3
/sec, find the
loss of head incurred. What would be the loss of head in the system to pass the same
total discharge when the pipes are connected in parallel? Take f = 0.0075 for each
pipe. [AU, May / June – 2007, 2012, Nov / Dec - 2010]
2.163) A main pipe divides into two parallel pipes, which again forms one pipe. The
length and diameter for the first parallel pipe are 2000m and 1m respectively, while
the length and diameter of second parallel pipe are 200m and 0.8m respectively. Find
the rate of flow in each parallel pipe, if total flow in the main is 3m3
/s. The coefficient
of friction for each parallel pipe is same and equal to 0.005.
[AU, May / June - 2007]
2.164) For a town water supply, a main pipe line of diameter 0.4 m is required. As pipes
more than 0.35m diameter are not readily available, two parallel pipes of same
diameter are used for water supply. If the total discharge in the parallel pipes is same

37
as in the single main pipe, find the diameter of parallel pipe. Assume co-efficient of
discharge to be the same for all the pipes. [AU, April / May - 2010]
2.165) Two pipes of identical length and material are connected in parallel. The
diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to
be the same in both cases and disregarding minor losses, determine the ratio of the
flow rates in the two pipes. [AU, April / May - 2008]
2.166) A pipe line 30cm in diameter and 3.2m long is used to pump up 50Kg per second
of oil whose density is 950 Kg/m3
and whose kinematic viscosity is 2.1 strokes, the
center of the pipe line at the upper end is 40m above than the lower end. The
discharge at the upper end is atmospheric. Find the pressure at the lower end and
draw the hydraulic gradient and total energy line. [AU, April / May - 2011]
2.167) Two water reservoirs A and B are connected to each other through a 50 m long,
2.5 cm diameter cast iron pipe with a sharp-edged entrance. The pipe also involves
a swing check valve and a fully open gate valve. The water level in both reservoirs
is the same, but reservoir A is pressurized by compressed air while reservoir B is
open to the atmosphere. If the initial flow rate through the pipe is 1.5 l/s, determine
the absolute air pressure on top of reservoir A. Take the water temperature to be
25°C. [AU, Nov / Dec - 2011]
2.168) When water is being pumped is a pumping plant through a 600mm diameter
main, the friction head was observed as 27m. In order to reduce the power
consumption, it is proposed to lay another main of appropriate diameter along the
side of existing one, so that the two pipes will work in parallel for the entire length
and reduce the friction head to 9.6m only. Find the diameter of the new main if with
the exception of diameter; it is similar to the existing one in all aspects.
[AU, Nov / Dec - 2007]
2.169) Determine the
 Pressure gradient
 The shear stress at the two horizontal parallel plates and
 Discharge per meter width for the laminar flow of oil with maximum
velocity 2m/s between two horizontal parallel fixed plates which are
10cm apart. Given μ = 2.4525 Ns/m2

38
2.170) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway
between the wall surface and the centerline) is measured to be 6 m/s. Determine the
velocity at the center of the pipe. [AU, April / May - 2008]
2.171) A smooth two –dimensional flat plate is exposed to a wind velocity of 100 km/h.
If laminar boundary layer exists up to a value of Rexequal to 3 x 105
, find the
maximum distance up to which laminar boundary layer exists and find its maximum
thickness. Assume kinematic viscosity of air as 1.49 x 10-5
m2
/sec.
2.172) Air is flowing over a flat plate with a velocity of 5 m/s. The length of the plate
is 2.5 m and width 1 m. The kinematic viscosity of air is given as 0.15 x 10-4
m2
/s.
Find the
(i) boundary layer thickness at the end of plate
(ii) shear stress at 20 cm from the leading edge
(iii) shear stress at 175 cm from the leading edge
(iv) drag force on one side of the plate.
(v) Take the velocity profile over a plate as and the density of air1.24 kg/m3
.
2.173) Water at 20° C enters a pipe with a uniform velocity (U) of 3m/s. What is the
distance at which the transition (x) occurs from a laminar to a turbulent boundary
layer? If the thickness of this initial laminar boundary layer is given by 4.91√(vx/U)
what is its thickness at the point of transition?(v – kinematic viscosity).
2.174) A flat plate 1.5 m x 1.5 m moves at 50 km/h in stationary air of density 1.15
kg/m3
. If the co-efficient of drag and lift are 0.15 and 0.75 respectively, determine
the
(i) Lift force
(ii) Drag force
(iii) The resultant force and
(iv) The power required to set the plate in motion. [AU, Nov / Dec - 2007]
2.175) A jet plane which weighs 29430 N and has the wing area of 20m2
flies at the
velocity of 250km/hr. When the engine delivers 7357.5kW. 65% of power is used to

39
overcome the drag resistance of the wing. Calculate the coefficient of lift and
coefficient of drag for the wing. Take density of air = 1.21 kg/m3
[AU, May / June - 2009]
2.176) For the velocity profile in laminar boundary layer as u/U = 3/2 (y/δ)-1/2(y/δ)3
.
Find the thickness of the boundary layer and shear stress, 1.8m from the leading edge
of a plate. The plate is 2.5 m long and 1.5 m wide is placed in water, which is moving
with a velocity of 15 cm/sec. Find the drag on one side of the plate if the viscosity
of water is 0.01 poise. [AU, Nov / Dec - 2003]
2.177) The velocity distribution for flow over a plate is given by u = 2y – y2
where u is
the velocity in m/sec at a distance y meters above the plate. Determine the velocity
gradient and shear stress at the boundary and 0.15m from it. Dynamic viscosity of
the fluid is 0.9Ns/m2
2.178) The velocity distribution in the boundary layer is given by u/U = y/δ, where u is
the velocity at the distance y from the plate u = U at y = δ, δ being boundary layer
thickness. Find the displacement thickness, momentum thickness and energy
thickness. [AU, April / May - 2010]
2.179) The flow rate in a 260mm diameter pipe is 220 litres/sec. The flow is turbulent,
and the centerline velocity is 4.85m/s. Plot the velocity profile, and determine the
head loss per meter of pipe. [AU, April / May - 2011]
2.180) The velocity distribution over a plate is given by u = (3/4) * y – y2
where u is
velocity in m/s and at depth y in m above the plate. Determine the shear stress at a
distance of 0.3m from the top of plate. Assume dynamic viscosity of the fluid is taken
as 0.95 Ns/m2
2.181) An oil of viscosity 0.9Pa.s and density 900kg/m3 flows through a pipe of 100mm
diameter. The rate of pressure drop for every meter length of pipe is 25kPa. Find the
oil flow arte, drag force per meter length, pumping power required to maintain the
flow over a distance of 1km, velocity and shear stress at 15, from the pipe wall.
[AU, Nov / Dec - 2010]
2.182) Consider the flow of a fluid with viscosity m through a circular pipe. The
velocity profile in the pipe is given as where is the maximum flow velocity, which
occurs at the centerline; r is the radial distance from the centerline; is the flow

40
velocity at any position r; and R is the Reynold's number. Develop a relation for the
drag force exerted on the pipe wall by the fluid in the flow direction per unit length
of the pipe. [AU, April / May - 2008]
2.183) Velocity components in flow are given by U = 4x, V = -4y. Determine the stream
and potential functions. Plot these functions for φ 60, 120, 180, and 240 and Ф 0, 60,
120, 180, +60, +120, +180. Check for continuity. [AU, Nov / Dec - 2009]
2.184) A fluid of specific gravity 0.9 flows along a surface with a velocity profile given
by v = 4y - 8y3m/s, where y is in m. What is the velocity gradient at the boundary?
If the kinematic viscosity is 0.36S, what is the shear stress at the boundary?
[A.U. Nov / Dec - 2008]
2.185) In a two dimensional incompressible flow the fluid velocities are given by u = x
– ay and v = - y – 4x. Show that the velocity potential exists and determine its form.
Find also the stream function. [AU, May / June - 2009]
2.186) A smooth flat plate with a sharp leading edge is placed along a free stream of
water flowing at 3m/s. Calculate the distance from the leading edge and the boundary
thickness where the transition from laminar to turbulent- flow may commence.
Assume the density of water as 1000 kg/m3
and viscosity as 1centipoise.
2.187) A smooth two dimensional flat plate is exposed to a wind velocity of 100 km/hr.
If laminar boundary layer exists up to a value of RN
= 3 x105
, find the maximum
distance up to which laminar boundary layer persists and find its maximum
thickness. Assume kinematic viscosity of air as 1.49x10-5
m2
/s.
[AU, Nov / Dec - 2008]
2.188) A power transmission pipe 10 cm diameter and 500 m long is fitted with a nozzle
at the exit, the inlet is from a river with water level 60 m above the discharge nozzle.
umax
u(r) = umax(1-r / R )n n
R
r
o

41
Assume f = 0.02, calculate the maximum power which can be transmitted and the
diameter of nozzle required. [AU, Nov / Dec - 2008]
UNIT - III - DIMENSIONAL ANALYSIS
PART - A
3.1) What do you understand by fundamental units and derived units?

42
3.2) Differentiate between fundamental units and derived units. Give examples.
[AU, Nov / Dec - 2011]
3.3) Define dimensional analysis.
3.4) What do you mean by dimensional analysis? [AU, Nov / Dec - 2009]
3.5) Define dimensional homogeneity.
3.6) What is dimensional homogeneity and write any one sample equation?
[AU, Nov / Dec - 2006]
3.7) Explain the term dimensional homogeneity. [AU, Nov / Dec - 2011]
3.8) Give the methods of dimensional analysis.
3.9) State a few applications, usefulness of ‘dimensional analysis’.
[AU, May / June - 2007]
3.10) What is a dimensionally homogenous equation? Give example.
[AU, Nov / Dec - 2003]
3.11) Cite examples for dimensionally homogeneous and non-homogeneous equations.
[AU, Nov / Dec - 2010]
3.12) Check whether the following equation is dimensionally homogeneous.
Q =Cd .a √(2 gh) . [AU, April / May - 2011]
3.13) Define Rayleigh's method.
3.14) Give the Rayleigh method to determine dimensionless groups.
[AU, Nov / Dec - 2011]
3.15) State any two choices of selecting repeating variables in Buckingham π theorem.
3.16) State Buckingham’s π theorem. [AU, Nov / Dec - 2008]
3.17) What is Buckingham's π theorem?
3.18) Distinguish between Rayleigh's method and Buckingham's π- theorem.
3.19) Under what circumstances, will Buckingham’s π theorem yield incorrect number
of dimensionless group?
3.20) State a few applications / usefulness of dimensional analysis.
3.21) Define Euler's number. [AU, May / June - 2009]
3.22) List out any four rules to select repeating variable.

43
3.23) Define similitude.
3.24) Give the three types of similarities.
3.25) Define geometric similarity.
3.26) Define kinematic similarity.
3.27) Define dynamic similarity.
3.28) What is meant by dynamic similarity? [AU, Nov / Dec - 2008]
3.29) What is dynamic similarity? [AU, Nov / Dec - 2009]
3.30) What is similarity in model study? [AU, April / May - 2005]
3.31) What is scale effect in physical model study?
[AU, Nov / Dec – 2005, 2006, May / June– 2012]
3.32) If two systems (model and prototype) are dynamically similar, is it implied that
they are also kinematically and geometrically similar? [AU, May / June - 2012]
3.33) Distinguish between a control and differential control volume.
3.34) Mention the circumstances which necessitate the use of distorted models.
[AU, Nov / Dec - 2010]
3.35) Give the types of forces in a moving fluid.
3.36) Give the dimensions of power and specific weight. [AU, Nov / Dec - 2009]
3.37) Define inertia force.
3.38) Define viscous force.
3.39) Define gravity and pressure force.
3.40) Define surface tension force.
3.41) Define dimensionless numbers.
3.42) Give the types of dimensionless numbers.
3.43) Define Reynold’s number. What its significance? [AU, Nov / Dec - 2010]
3.44) Define Reynold’s number and Froude’s numbers. [AU, Nov / Dec – 2007,2011]
3.45) Define Froude's number.
[AU, Nov / Dec – 2005, 2009, 2008, April / May – 2010, May / June - 2012]
3.46) Define Euler number and Mach number. [AU, May / June - 2007]
3.47) Define Mach number. [AU, May / June - 2009]
3.48) What is Mach number? Mention its field of use. [AU, April / May - 2003]

44
3.49) Define Mach's number and mention its field of use.
3.50) Write down the dimensionless number for pressure. [AU, Nov / Dec - 2011]
PART - B
3.51) What is repeating variables? How are these selected? [AU, May / June - 2007]
3.52) State the similarity laws used in model analysis. [AU, April / May - 2010]
3.53) State and explain the various laws of similarities between model and its prototype.
3.54) What is meant by geometric, kinematic and dynamic similarities?
[AU, May / June - 2007]
3.55) What is meant by geometric, kinematic and dynamic similarities? Are these
similarities truly attainable? If not, why? [AU, May / June - 2009]
3.56) Explain the different types of similarities exist between a proto type and its model.
[AU, Nov / Dec - 2003]
3.57) What is distorted model and also give suitable example?
3.58) Define dimensional homogeneity and also give example for homogenous
equation. [AU, April / May - 2005]
3.59) Classify Models with scale ratios. [AU, Nov / Dec - 2009]
3.60) Derive on the basis of dimensional analysis suitable parameters to present the
thrust developed by a propeller. Assume that the thrust P depends upon the angular
velocity ω , speed of advance V, diameter D, dynamic viscosity μ, mass density ρ ,
elasticity of the fluid medium which can be denoted by the speed of sound in the
medium C. [AU, Nov / Dec - 2011]
3.61) Check the following equations are dimensionally homogenous
 Drag force = ½ ( Cd ρU2
A) where Cd is coefficient of drag which is
constant
 F = γQ ( U1 – U2) / g – ( P1A1 – P2A2)
 Total energy per unit mass = v2
/2 + gz + P/ρ
 Q = δ / 15Cd tan(θ/2) √(2g) * (H)5/2
where Cd is coefficient of discharge
constant [AU, April / May - 2004, 2010, Nov / Dec - 2005]
3.62) Define and explain Reynold’s number, Froude’s number, Euler’s number and
Mach’s number. [AU, Nov / Dec - 2003]

45
3.63) What are the significance and the role of the following parameters?
 Reynolds number
 Froude number
 Mach number
 Weber number. [AU, April / May - 2011]
3.64) Explain the Reynolds model law and state its applications.
3.65) Use dimensionless analysis to arrange the following groups into dimensionless
parameters; ∆p, V, γ, g and f, ρ, L, V use MLT system. [AU, April / May - 2011]
3.66) Consider force F acting on the propeller of an aircraft, which depends upon the
variable U, ρ, μ, D and N. Derive the non – dimensional functional form F/(ρU2
D2
)
= f ((UDρ/μ),(ND/U)) [AU, Nov / Dec - 2003]
3.67) The frictional torque T of a disc diameter D rotating at a speed N in a fluid of
viscosity μ and density ρ in a turbulent flow is given by
T = D5
N2
ρФ[μ/D2
Nρ]. Prove this by Buckingham’s π theorem.
[AU, Nov / Dec - 2003]
3.68) Resistance R, to the motion of a completely submerged body is given by R =
ρv2
l2
φ(VL/γ), where ρ and γ are the mass density and kinematic viscosity of the fluid;
v– velocity of flow; l – length of the body. If the resistance of a one – eighth scale
air - ship model when tested in water at 12m/s is 22N, what will be the resistance of
the air –ship at the corresponding aped, in air? Assume kinematic viscosity of air is
13times that of water and density of water is 810 times of air.
3.69) The resisting force R to a supersonic plane during flight can be considered as
dependent upon the length of the aircraft l, velocity V, air viscosity m, air density
and bulk modulus of air K. Express the functional relationship between these
variables and the resisting force.
3.70) The resisting force F of a plane during flight can be considered as dependent upon
the length of aircraft (l), velocity (v), air viscosity(μ ), air density (ρ ) and bulk
modulus of air (K). Express the functional relationship between these variables using
dimensional analysis. Explain the physical significance of the dimensionless groups
arrived. [AU, Nov / Dec - 2010]

46
3.71) The resistance R, to the motion of a completely submerged body depends upon
the length of the body (L), velocity of flow (V), mass density of fluid (ρ), kinematic
viscosity (γ). Prove by dimensional analysis that
R = ρV2
L2
φ(VL/γ) [AU, May / June - 2009]
3.72) The power developed by hydraulic machines is found to depend on the head h,
flow rate Q, density ρ, speed N, runner diameter D, and acceleration due to gravity
g. Obtain suitable dimensionless parameters to correlate experimental results.
[AU, Nov / Dec - 2011]
3.73) Show that the power P developed in a water turbine can be expressed as:
Where, r = Mass density of the liquid,
N = Speed in rpm,
D = Diameter of the runner,
B = Width of the runner and
m = Dynamic viscosity [AU, Nov / Dec - 2011]
3.74) The capillary rise h is found to be influenced by the tube diameter D, density ρ,
gravitational acceleration g and surface tension σ. Determine the dimensionless
parameters for the correlation of experimental results. [AU, Nov / Dec - 2011]
3.75) Using dimensional analysis, obtain a correlation for the frictional torque due to
rotation of a disc in a viscous fluid. The parameters influencing the torque can be
identified as the diameter, rotational speed, viscosity and density of the fluid.
[AU, Nov / Dec - 2011]
3.76) The drag force on a smooth sphere is found to be affected by the velocity of flow,
u, the diameter D of the sphere and the fluid properties density ρ and viscosity μ.
Find the dimensionless groups to correlate the parameters.
[AU, Nov / Dec - 2011]
3.77) State Buckingham's π - theorem. What do you mean by repeating variables? How
are the repeating variables selected in dimensional analysis?

47
3.78) State Buckingham's π - theorem. What are the considerations in the choice of
repeating variables? [AU, April / May - 2010]
3.79) Express efficiency in terms of dimensionless parameters using density, viscosity,
angular velocity, diameter of rotor and discharge using Buckingham π theorem.
[AU, Nov / Dec - 2009]
3.80) State the Buckingham π theorem. What are the criteria for selecting repeating
variable in this dimensional analysis? [AU, Nov / Dec - 2009]
3.81) State Buckingham – π theorem. Mention the important principle for selecting the
repeating variables. [AU, May / June - 2009]
3.82) State and prove Buckingham π theorem.
[AU, Nov / Dec – 2009, April / May - 2010]
3.83) Using Buckingham’s π- theorem show that the velocity through a circular orifice
is given by V = √(2gH) φ [(D/H), (μ/ρVH)
Where H is the head causing the flow
D is the diameter of the orifice
μ is the coefficient of velocity
ρ is the mass density
g is the acceleration due to gravity [AU, Nov / Dec - 2008, April / May - 2010]
3.84) Using Buckingham's π- theorem, show that the pressure difference DP in a pipe
of diameter D and length l due to turbulent flow depends on the velocity V, viscosity
m, density and roughness k.
3.85) The efficiency (η) of a fan depends on ρ (density), μ (viscosity) of the fluid, ω
(angular velocity), d(diameter of rotor) and Q(discharge). Express η in terms of non-
dimensional parameters. Use Buckingham's theorem.
[AU, April / May - 2010, 2011]
3.86) The power required by the pump is a function of discharge Q, head H, acceleration
due to gravity g, viscosity μ, mass density of the fluid ρ, speed of rotation N and
impeller diameter D. Obtain the relevant dimensionless parameters. [AU, May / June
- 2012]
PROBLEMS

48
3.87) Find the discharge through a weir model by knowing the discharge over the actual
(proto type) weir is measured as 1.5m3/s. The horizontal dimension of the model =
1/50 of the horizontal dimensions of the proto type and the vertical dimension of the
model = 1/10 of the vertical dimension of the proto type. (Hint: Apply Froude model
law) [AU, April / May - 2004]
3.88) Model of an air duct operating with water produces a pressure drop of 10 kN/m2
over 10 m length. If the scale ratio is 1/50. Density of water is 1000 kg/m3
and density
of air is 1.2 kg/m3
. Viscosity of water is 01.001 Ns/m2
and viscosity of air 0.00002
Ns/m2
. Estimate corresponding drop in a 20m long air duct.
[AU, Nov / Dec - 2004, 2005, April / May - 2010]
3.89) A model of a hydroelectric power station tail race is proposed to build by selecting
vertical scale 1 in 50 and horizontal scale 1 in 100. If the design pipe has flow rate
of 600m3
/s and allow the discharge of 800m3
/s. Calculate the corresponding flow
rates for the model testing. [AU, April / May - 2005]
3.90) In order to predict the pressure in a large air duct model is constructed with linear
dimensions (1/10)th
that of the prototype and the water was used as the testing fluid.
If water is 1000 times denser than that of air and has 100 times the viscosity of air,
determine the pressure drop in the prototype, for the conditions corresponding to a
pressure drop of 70kPa, in the model. [AU, May / June - 2009]
3.91) In an aero plane model of size 1/10 of its prototype, the pressure drop is 7.5kN/m2
.
The model is tested in water; find the corresponding drop in prototype. Assume
density of air = 1.24kg/m3
; density of water = 1000kg/m3
; viscosity of air = 0.00018
poise; viscosity of water = 0.01 poise. [AU, May / June - 2007]
3.92) A geometrically similar model of an air duct is built to 1/25 scale and tested with
water which is 50 times more viscous and 800 times denser than air. When tested
under dynamically similar conditions, the pressure drop is 200 kN/m2
in the model.
Find the corresponding pressure drop in the full scale prototype and express in cm
of water. [AU, Nov / Dec - 2010]
3.93) Model tests have conducted to study the energy losses in a pipe line of 1m
diameter required to transport kerosene of specific gravity 0.80 and dynamic
viscosity 0.02 poise at the rate of 2000 litre/sec. Tests were conducted on a 10cm

49
diameter pipe using water at 20°C. What is the flow rate in the model? If the energy
head loss in 30m length of the model is measured as 44cm of water, what will be the
corresponding head loss in the prototype? What will be the friction factor for the
prototype pipe. [AU, May / June - 2012]
3.94) An agitator of diameter D rotates at a speed N in a liquid of density ρ and
viscosity μ. Show that the power required to mix the liquid is expressed by a
functional form [AU, April / May - 2011]
UNIT –IV- ROTO DYNAMIC MACHINES
PART - A

50
4.1) Define turbo machines.
4.2) Define turbine.
4.3) Classify fluid machines. [AU, April / May - 2010]
4.4) Give the classification of turbines.
4.5) How are hydraulic turbines classified
[AU, May / June - 2009,Nov / Dec - 2009 April / May - 2011]
4.6) What are high head turbines? Give example. [AU, Nov / Dec - 2009]
4.7) State the principles on which turbo-machines are based. [AU, Nov / Dec - 2010]
4.8) Explain specific speed. [AU, Nov / Dec - 2005]
4.9) Define specific speed. [AU, Nov / Dec - 2009]
4.10) Define specific speed of a turbine. [AU, Nov
/ Dec – 2003, 2008, 2009, May / June–2007, 2009, April / May –2010, 2011]
4.11) Define specific speed of a turbine. What is its usefulness?
[AU, Nov / Dec - 2007]
4.12) How is specific speed of a turbine defined? [AU, May / June - 2006]
4.13) What is meant by specific speed of a turbine? [AU, April / May - 2010]
4.14) What is hydraulic turbine? [AU, May / June - 2006]
4.15) Classify turbines according to flow. [AU, Nov / Dec - 2005]
4.16) Define impulse turbine and give examples.
4.17) Explain the working of impulse turbine. [AU, April / May - 2011]
4.18) Define reaction turbine and give examples.
4.19) What is reaction turbine? Give examples [AU, April / May - 2003]
4.20) Differentiate between reaction turbine and impulse turbine.
[AU, Nov / Dec - 2003, April / May - 2008, May / June - 2012]
4.21) What is a ‘breaking jet’ in Pelton wheel/turbine?
4.22) Draw velocity triangle diagram for Pelton wheel turbine.
[AU, Nov / Dec - 2008]
4.23) Define tangential flow turbine.
4.24) Define radial flow - turbine.
4.25) Define axial flow turbine.

51
4.26) Define mixed flow turbine.
4.27) Draw a sketch of a Francis turbine and name its components.
4.28) What is a draft tube? Explain why it is necessary in reaction turbine.
4.29) What is draft tube? In which type of turbine is mostly used?
[AU, Nov / Dec - 2003]
4.30) Write the function of draft tube in turbine outlet?
[AU, April / May - 2005, 2008, Nov / Dec - 2011]
4.31) What is the function of draft tube?
[AU ,May / June– 2007, Nov / Dec - 2009]
4.32) What are the different types of draft tubes? [AU, Nov / Dec - 2009]
4.33) Why does a Pelton wheel not possess any draft tube? [AU, May / June - 2012]
4.34) Mention the importance of Euler turbine equation. [AU, Nov / Dec - 2011]
4.35) What are the different efficiencies of turbine to determine the characteristics of
turbine? [AU, May / June– 2012]
4.36) Define hydraulic efficiency of turbine
4.37) Define hydraulic efficiency and jet ratio of a Pelton wheel.
[AU, Nov / Dec - 2010]
4.38) What are the different efficiencies of turbine to determine the characteristics of
turbine? [AU, Nov / Dec - 2006]
4.39) Define overall efficiency and plant efficiency of turbines.
[AU, May / June– 2007, 2012]
4.40) Draw the characteristics curves of a turbine with head variation.
4.41) What is the difference between a turbine and a pump?
4.42) Differentiate between pumps and turbines.
[AU, May / June, Nov / Dec – 2007, 2008]
4.43) Define centrifugal pump.
4.44) How centrifugal pumps are classified based on casing? [AU, May / June - 2006]
4.45) Define impeller.

52
4.46) Define casing.
4.47) List the commonly used casings in centrifugal pumps. [AU, Nov / Dec - 2010]
4.48) What is the role of a volute chamber of a centrifugal pump?
[AU, Nov / Dec - 2005]
4.49) What precautions are to be taken while starting and closing the centrifugal pump?
[AU, May / June - 2012]
4.50) Define priming of centrifugal pump.
4.51) What is priming? [AU, Nov / Dec - 2010]
4.52) Why priming is necessary in a centrifugal pump?
[AU, May / June - 2007, April / May - 2010]
4.53) What is meant by priming of pumps? [AU, April / May - 2008]
4.54) What is priming? Why is it necessary? [AU, Nov / Dec - 2011]
4.55) Define cavitation. [AU, Nov / Dec - 2008]
4.56) Define cavitation in a pump. [AU, May / June - 2007]
4.57) What is the effect of cavitation in pump? [AU, April / May - 2011]
4.58) What are the effects of cavitation? Give necessary precautions against
cavitations? [AU, May / June - 2012]
4.59) Define the characteristic curves of centrifugal pump.
4.60) List out the types of characteristic curves.
4.61) Define multistage centrifugal pump and give its function.
4.62) What are the advantages of centrifugal pump over reciprocating pumps?
[AU, May / June - 2009]
4.63) What is a delivery pipe?
4.64) Define manometric efficiency and mechanical efficiency of a centrifugal pump.
4.65) What is the maximum theoretical suction head possible for a centrifugal pump?
4.66) How does the specific speed of a centrifugal pump differ from that of a turbine?
4.67) Write the equation for specific speed for pumps and also for turbine.
[AU, Nov / Dec - 2005]
4.68) Define specific speed as applied to pumps. [AU, May / June - 2009]
4.69) Define specific speed. [AU, Nov / Dec - 2007]

53
4.70) What is specific speed of a pump? How are pumps classified based on this
number? [AU, Nov / Dec - 2009]
4.71) What is a type number?
4.72) Give examples of machines handling gases with high pressure rise.
4.73) What do you mean by manometric efficiency and mechanical efficiency of a
centrifugal pump? [AU, Nov / Dec - 2007]
4.74) A shaft transmits 150 Kw at 600 rpm. What is the torque in Newton –meters?
4.75) The mean velocity of the buckets of the Pelton wheel is 10 m/s. The jet supplies
water at 0.7 m3
/s at a head of 30 m. The jet is deflected through an angle of 160° by
the bucket. Find the hydraulic efficiency. Take CV = 0.98.
4.76) A water turbine has a velocity of 8.5m/s at the entrance of draft tube and velocity
of 2.2m/s at exit. The frictional loss is 0.15m and the tail race water is 4m below the
entrance of draft tube. Calculate the pressure head at entrance.
4.77) A centrifugal pump delivers 20 litres/s of water against a head of 850 mm at 900
rpm. Find the specific speed of pump. [AU, April / May - 2010]
4.78) The following data refer to a centrifugal pump which is designed to run at 1500
rpm. D1
= 100 mm, D2
= 300 mm, B1
= 50 mm, B2
= 20 mm, Vf1
= 3 m/s.Find the
velocity of flow at outlet. [AU, April / May - 2010]
4.79) A pump is to discharge 0.82 m3/s at a head of 42 m when running at 300 rpm.
What type of pump will be required? [AU, Nov / Dec - 2011]
PART - B
4.80) Derive the general equation of turbo machines and draw the inlet and outlet
triangles. [AU, April / May - 2011]
4.81) How will you classify the turbines? [AU, Nov / Dec - 2008]

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