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39. ----~--~---------------------=~---~-----~---
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pumps
A pump f.s o dev~ce.

40. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 48
UNIT - III - DIMENSIONAL ANALYSIS
PART - A
3.1) What do you understand by fundamental units and derived units?
[AU, April / May - 2010]
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) Brief on dimensional variables with examples. [AU, Nov / Dec - 2014]
3.6) Brief on Intuitive method. Give some examples. [AU, Nov / Dec - 2014]
3.7) Define dimensional homogeneity.
3.8) What is dimensional homogeneity and write any one sample equation?
[AU, Nov / Dec - 2006]
3.9) Explain the term dimensional homogeneity. [AU, Nov / Dec - 2011]
3.10) Give the methods of dimensional analysis.
3.11) State a few applications, usefulness of ‘dimensional analysis’.
[AU, May / June - 2007]
3.12) What is a dimensionally homogenous equation? Give example.
[AU, Nov / Dec - 2003]
3.13) Cite examples for dimensionally homogeneous and non-homogeneous equations.
[AU, Nov / Dec - 2010]
3.14) Check whether the following equation is dimensionally homogeneous.
Q =Cd .a √(2 gh) . [AU, April / May - 2011]
3.15) Define Rayleigh's method.
3.16) Give the Rayleigh method to determine dimensionless groups.
[AU, Nov / Dec - 2011]
3.17) State any two choices of selecting repeating variables in Buckingham π theorem.
[AU, April / May - 2011]
3.18) State Buckingham’s π theorem. [AU, Nov / Dec – 2008, 2012, April / May - 2015]
3.19) What is Buckingham's π theorem?

41. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 49
3.20) The excess pressure Δp inside a bubble is known to be a function of the surface
tension and the radius. By dimensional reasoning determine how the excess pressure.
Will vary if we double the surface tension and the radius.
[AU, Nov / Dec - 2013]
3.21) Distinguish between Rayleigh's method and Buckingham's π- theorem.
[AU, April / May - 2011]
3.22) Under what circumstances, will Buckingham’s π theorem yield incorrect number
of dimensionless group?
3.23) State a few applications / usefulness of dimensional analysis.
3.24) Define Euler's number. [AU, May / June - 2009]
3.25) List out any four rules to select repeating variable.
3.26) Define similitude.
3.27) Give the three types of similarities.
3.28) What are the types of similarities? [AU, Nov / Dec - 2012]
3.29) Define geometric similarity.
3.30) Define kinematic similarity.
3.31) What is meant by kinematic similarity? [AU, Nov / Dec - 2014]
3.32) Define dynamic similarity.
3.33) What is meant by dynamic similarity? [AU, Nov / Dec - 2008]
3.34) What is dynamic similarity? [AU, Nov / Dec - 2009]
3.35) What is similarity in model study? [AU, April / May - 2005]
3.36) What is scale effect in physical model study?
[AU, Nov / Dec – 2005, 2006, May / June– 2012]
3.37) If two systems (model and prototype) are dynamically similar, is it implied that
they are also kinematically and geometrically similar? [AU, May / June - 2012]
3.38) Distinguish between a control and differential control volume.
[AU, April / May - 2011]
3.39) Mention the circumstances which necessitate the use of distorted models.
[AU, Nov / Dec - 2010]
3.40) Give the types of forces in a moving fluid.
3.41) Give the dimensions of power and specific weight. [AU, Nov / Dec - 2009]
3.42) Define inertia force.

42. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 50
3.43) Define viscous force.
3.44) Define gravity and pressure force.
3.45) Define surface tension force.
3.46) Define dimensionless numbers.
3.47) Give the types of dimensionless numbers.
3.48) Give the dimensions of the following physical quantities: surface tension and
dynamic viscosity. [AU, May / June - 2013]
3.49) Write the dimensions of surface tension and vapour pressure in MLT system.
[AU, April / May - 2015]
3.50) Define Reynold’s number. What its significance? [AU, Nov / Dec - 2010]
3.51) Define Reynold’s number and state its significance? [AU, April / May - 2015]
3.52) Define Reynold’s number and Froude’s numbers. [AU, Nov / Dec – 2007, 2011]
3.53) Define the Froude's dimensionless number. [AU, May / June - 2014]
3.54) Define Froude's number.
[AU, Nov / Dec – 2005, 2009, 2008, April / May – 2010, May / June - 2012]
3.55) State Froude's model law. [AU, May / June - 2013]
3.56) Define Euler number and Mach number. [AU, May / June - 2007]
3.57) Define Reynold’s number and Mach number. [AU, Nov / Dec - 2012]
3.58) Define Mach number. [AU, May / June - 2009]
3.59) What is Mach number? Mention its field of use. [AU, April / May - 2003]
3.60) Define Mach's number and mention its field of use.
3.61) Define -Mach number and state its application. [AU, Nov / Dec - 2014]
3.62) Write down the dimensionless number for pressure. [AU, Nov / Dec - 2011]
3.63) What are the similitudes that should exist between the model and its prototype?
[AU, April / May - 2015]
PART - B
3.64) Discuss on Buckingham's π theorem. [AU, Nov / Dec - 2014]
3.65) What is repeating variables? How are these selected? [AU, May / June - 2007]
3.66) Discuss on the applications of dimensionless parameters. [AU, Nov / Dec - 2014]
3.67) State the similarity laws used in model analysis. [AU, April / May - 2010]
3.68) State and explain the various laws of similarities between model and its prototype.

43. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 51
3.69) What is meant by geometric, kinematic and dynamic similarities?
[AU, May / June – 2007, 2014]
3.70) What is meant by geometric, kinematic and dynamic similarities? Are these
similarities truly attainable? If not, why? [AU, May / June - 2009]
3.71) Explain the different types of similarities exist between a proto type and its model.
[AU, Nov / Dec - 2003]
3.72) What is distorted model and also give suitable example?
[AU, April / May - 2004]
3.73) What are distorted models? State merits and demerits. [AU, May / June - 2014]
3.74) Define dimensional homogeneity and also give example for homogenous
equation. [AU, April / May - 2005]
3.75) Classify Models with scale ratios. [AU, Nov / Dec - 2009]
3.76) 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, 2012]
3.77) 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]
3.78) Define and explain Reynold’s number, Froude’s number, Euler’s number and
Mach’s number. [AU, Nov / Dec - 2003]
3.79) What are the significance and the role of the following parameters?
 Reynolds number
 Froude number
 Mach number
 Weber number. [AU, April / May - 2011]

44. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 52
3.80) Define the following dimensionless numbers and state their significance for fluid
flow problems. [AU, May / June - 2014]
 Reynolds number
 Mach number
3.81) Explain the Reynolds model law and state its applications.
3.82) 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]
3.83) Use dimensional analysis and the MLT system to arrange the following into a
dimensionless number: L, ρ , µ and a. [AU, Nov / Dec - 2013]
3.84) 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]
3.85) 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
ρ Ф[μ/D2
Nρ]. Prove this by Buckingham’s π theorem.
[AU, Nov / Dec - 2003]
3.86) 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.
[AU, Nov / Dec - 2007, April / May - 2010]
3.87) 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.
3.88) 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]

45. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 53
3.89) Derive an expression for the shear stress at the pipe wall when an incompressible
fluid flows through a pipe under pressure. Use dimensional analysis with the
following significant parameters: pipe diameter D, flow velocity V, and viscosity µ
and density ρ of the fluid. [AU, Nov / Dec - 2013]
3.90) 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]
3.91) Obtain a relation using dimensional analysis, for the resistance to uniform motion
of a partially submerged body in a viscous compressible fluid.
[AU, Nov / Dec - 2014]
3.92) Using Buckingham π method of dimensional analysis obtain an expression for the
drag force R on a partially submerged body moving with a relative velocity V in a
fluid; the other variables being the linear dimension L, height of surface roughness
K, Fluid density ρ and the gravitational acceleration g. [AU, April / May - 2015]
3.93) 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, 2014]
3.94) Show that the power P developed in a water turbine can be expressed as:
Where, ρ = Mass density of the liquid,
N = Speed in rpm,
D = Diameter of the runner,
B = Width of the runner and
µ = Dynamic viscosity [AU, Nov / Dec - 2011]
3.95) 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]

46. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 54
3.96) 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]
3.97) 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]
3.98) State Buckingham's π - theorem. What do you mean by repeating variables? How
are the repeating variables selected in dimensional analysis?
3.99) State Buckingham's π - theorem. What are the considerations in the choice of
repeating variables? [AU, April / May - 2010]
3.100) 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]
3.101) State the Buckingham π theorem. What are the criteria for selecting repeating
variable in this dimensional analysis? [AU, Nov / Dec - 2009]
3.102) State Buckingham – π theorem. Mention the important principle for selecting
the repeating variables. [AU, May / June - 2009]
3.103) State and prove Buckingham π theorem.
[AU, Nov / Dec – 2009, April / May - 2010]
3.104) 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 viscosity
ρ is the mass density
g is the acceleration due to gravity [AU, Nov / Dec - 2008, April / May - 2010]
3.105) Using Buckingham's π- theorem, show that the pressure difference ∆P in a pipe
of diameter D and length l due to turbulent flow depends on the velocity V, viscosity
µ, density ρ and roughness k.
3.106) 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-

47. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 55
dimensional parameters. Use Buckingham's theorem.
[AU, April / May - 2010, 2011]
3.107) 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 Rayleigh’s method. [AU, April / May - 2015]
3.108) The pressure difference Δp in a pipe of diameter D and length L due to viscos
flow depends on the velocity V, viscosity µ and density ρ. Using Buckingham's π
theorem, obtain an expression for Δp. [AU, May / June – 2014, April / May - 2015]
3.109) 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]
3.110) State Buckingham's π -theorem. The discharge of a centrifugal pump (Q) is
dependent on N (speed of pump), d (diameter of impeller), g (acceleration due to
gravity), H (manometric head developed by pump) and ρ and µ (density and dynamic
viscosity of the fluid). Using the dimensional analysis and Buckingham's π -theorem,
prove that it is given by [AU, May / June - 2013]
𝑄 = 𝑁𝑑3
𝑓 (
𝑔𝐻
𝑁2 𝑑2
,
𝜇
𝑁𝑑2 𝜌
)
3.111) Consider viscous flow over a very small object. Analysis of the equations of
motion shows that the inertial terms are much smaller than viscous and pressure
terms. Fluid density drops out, and these are called creeping flows. The only
important parameters are velocity U, viscosity µ, and body length scale d. For three-
dimensional bodies,. Like spheres, creeping flow analysis yields very good results.
It is uncertain, however, if creeping flow applies to two-dimensional bodies, such as
cylinders, since even though the diameter may be very small, the length of the
cylinder is infinite. Let us see if dimensional analysis can help. (1) Apply the Pi
theorem to two-dimensional drag force F2-D, as a function of the other parameters.
Be careful: two-dimensional drag has dimensions of fake per unit length, not simply
force. (2) Is your analysis in part (1) physically plausible? If not, explain why not.
(3) It turns out that fluid density ρ cannot be neglected in analysis of creeping flow
over two dimensional bodies. Repeat the dimensional analysis, this time including ρ

48. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 56
as a variable, and find the resulting non dimensional relation between the parameters
in this problem. [AU, Nov / Dec - 2013]
3.112) Oil is moved up in a lubricating system by a rope dipping in the sump containing
oil and moving up. The quantity of oil pumped Q, depends on the speed u of the
rope, the layer thickness 6, the density and viscosity of the oil and acceleration due
to gravity. Obtain the dimensionless parameters to correlate the flow.
[AU, Nov / Dec - 2014]
3.113) When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow
and then undergoes transition to turbulence at a time t, which depends upon the pipe
diameter D, fluid acceleration a, density ρ and viscosity µ. Arrange this into a
dimensionless relation between t and D. [AU, Nov / Dec - 2013]
3.114) What are the similarities between model and prototype? Mention the
applications of model testing. [AU, May / June - 2013]
PROBLEMS
3.115) 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]
3.116) 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]
3.117) 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]
3.118) A pipe of diameter 1.5 m is required to transport an oil of specific gravity 0.90
and viscosity 3 * 10-2
poise at the rate 3000 litre / sec. Test where conducted on a

49. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 57
15cm diameter pipe using water at 20º C. Find the velocity and the rate of flow in
model. Viscosity of water at 20ºC = 0.01poise. [AU, Nov / Dec - 2012]
3.119) 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]
3.120) 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]
3.121) 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, May / June - 2014]
3.122) 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
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]
3.123) In a geometrically similar model of spillway the discharge per meter length is
0.2m3
/sec. if the scale of the model is 1/36, find the discharge per meter run of the
prototype. [AU, May / June - 2014]
3.124) A spillway model is to be built to a geometrically similar scale of
1
50
- across a
flume of 600 mm width. The prototype is 15 m high and maximum head on it is
expected to be 1.5 m.
 What height of model and what head on the model should be used?

50. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 58
 If the flow over the model at a particular head is 12 litres per second, what
flow per metre length of the prototype is expected?
 If the negative pressure in the model is 200 mm, what is the negative
pressure in prototype? Is it practicable? [AU, May / June - 2013]
3.125) The characteristics of the spillway are to be studied by means of a geometrically
similar modal constructed to the scale ratio of 1:10.
 If the maximum rate of flow in the prototype is 28.3m3
, what will be the
corresponding flow in model?
 If the measured velocity in the model at a point on the spillway is 2.4m/s,
what will be the corresponding velocity in prototype?
 If the hydraulic jump at the foot of the model is 50mm high, what will be
the height of jump in prototype?
 If the energy dissipated per second in the model is 3.5Nm, what energy is
dissipated per second in the prototype? [AU, April / May - 2015]
3.126) Vortex shedding at the rear of a structure of a given section can create harmful
periodic vibration. To predict the shedding frequency, a smaller model is to be tested
in a water tunnel. The air speed is expected to be about 75 kmph. If the geometric
scale is 1 : 6.5 and the water temperature is 25°C determine the speed to be used in
the tunnel. Consider air temperature as 38°C. If the shedding frequency of the model
was 60 Hz, determine the shedding frequency of the prototype. The dimensions of
the structure are diameter 0.12 m and height 0.36 m. [AU, Nov / Dec - 2014]
3.127) 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]