Flow through Pipes
•Characteristics of flow through pipes
•Energy (head) losses in flow through pipes
•Major losses such as loss of head due to friction Darcy Wisbach
•Minor losses such as loss of head at entry, change in diameter,
•Problems on head losses
•Hydraulic Gradient Line (H.G.L.) & Total Energy Line (T.E.L.)
•Effect of entry at pipe, change in diameter, bend etc. on H.G.L. &
•Plotting of H.G.L. & T.E.L.
•Design of pipeline for given flow --using formulae ---using
•Computation of height of reservoir
•Compound pipe and equivalent sizes
Where the fluid moves slowly in layers in a pipe, without much mixing
among the layers.
• Typically occurs when the velocity is low or the fluid is very viscous.
•Opposite of laminar, where considerable mixing occurs, velocities
•Laminar and Turbulent flows can be characterized and quantified
using Reynolds Number
•established by Osborne Reynold and is given as –
Laminar and Turbulent Flow Summary
• Laminar Flow
Layers of water flow over one another at different speeds with virt
ually no mixing between layers. The flow velocity profile for laminar
flow in circular pipes is parabolic in shape, with a maximum flow in the
center of the pipe and a minimum flow at the pipe walls. The average
flow velocity is approximately one half of the maximum velocity.
• Turbulent Flow
The flow is characterized by the irregular movement of particles of the
fluid. The flow velocity profile for turbulent flow is fairly flat across the
center section of a pipe and drops rapidly extremely close to the walls.
The average flow velocity is approximately equal to the velocity at the
center of the pipe.
• Viscosity is the fluid property that measures the resistance of
the fluid to deforming due to a shear force.
For most fluids, temperature and viscosity are inversely
• An ideal fluid is one that is incompressible and has no viscosity.
• In the analysis of piping systems, pressure losses are
commonly expressed in terms of the equivalent fluid column
height called head loss hL.
• It also represents the additional height that the fluid needs to
be raised by a pump inorder to overcome the frictional losses
in the pipe
Laminar Flow Friction Factor
l D gh
Slope of __-1 on log-log plot
f independent of roughness!
Smooth, Rough, Transition
• Hydraulically smooth
pipe law (von Karman, 1930)
• Rough pipe law
(von Karman, 1930)
• Transition function
for both smooth and
rough pipe laws (Colebrook)
1 Re f
f 3.7 Re f
u V (used to draw the Moody diagram)
Friction losses in Pipes
• Vary with laminar or turbulent flow
• Energy equation can be given as –
p1/γ + z1 + v12/2g + hA – hR – hL = p2/γ + z2 + v22/2g
• where hA, hR, hL are the heads associated with addition,
removal and friction loss in pipes, respectively.
• The head loss in pipes = hL can be expressed as
• Darcy’s equation for energy loss (GENERAL FORM)
• f – friction factor
• L – length of pipe
• D – diameter of pipe
• v – velocity of flow
• Another equation was developed to compute hL under
Laminar flow conditions only
called the Hagen-Poiseuille equation
• If you equate Darcy’s equation and Hagen-Poiseuille equation
• Then we can find the friction factor f
Thus the friction factor is a
function of Reynold’s number!
Moody Diagram that can be used to estimate friction coefficients
• The Moody friction factor - λ (or f) - is used in the Darcy-
Weisbach major loss equation
• If the flow is transient - 2300 < Re < 4000 - the flow varies
between laminar and turbulent flow and the friction coefficient
is not possible to determine.
• The friction factor can usually be interpolated between the
laminar value at Re = 2300 and the turbulent value at Re =
DARCY WEISBACH EQUATION
• Weisbach first proposed the equation we now know as the
Darcy-Weisbach formula or Darcy-Weisbach equation:
• hf = f (L/D) x (v2/2g)
where: hf = head loss (m)
• f = friction factor L = length of pipe work (m) d = inner
diameter of pipe work (m) v = velocity of fluid (m/s) g =
acceleration due to gravity (m/s²)
• Piping systems include fittings, valves, bends, elbows, tees,
inlets, exits, enlargements, and contractions.
• These components interrupt the smooth flow of fluid and
cause additional losses because of flow separation and mixing.
• The minor losses associated with these components:
KL is the loss coefficient.
• Is different for different components.
• Typically provided by manufacturers.
• Total head loss in a system is comprised of major losses (in
the pipe sections) and the minor losses (in the components)
i pipe sections j components
• If the entire piping system has a constant diameter, then
Laminar Boundary Layer Flow
• The laminar boundary layer is a very smooth flow, while the
turbulent boundary layer contains swirls or “eddies.”
• The laminar flow creates less skin friction drag than the
turbulent flow, but is less stable.
• Boundary layer flow over a wing surface begins as a smooth
laminar flow. As the flow continues back from the leading
edge, the laminar boundary layer increases in thickness.
Turbulent Boundary Layer Flow
• At some distance back from the leading edge, the smooth
laminar flow breaks down and transitions to a turbulent flow.
• From a drag standpoint, it is advisable to have the transition
from laminar to turbulent flow as far aft on the wing as
possible, or have a large amount of the wing surface within the
laminar portion of the boundary layer.
• The low energy laminar flow, however, tends to break down
more suddenly than the turbulent layer.
Flow through the pipes in series
– Pipes in series is defined as the pipes of different lengths
and different diameters connected end to end to form a
L1,L2,L3 = length of pipes 1,2 and 3
d1,d2,d3 = diameter of pipes 1,2,3
v1,v2,v3 = velocity of flow through pipes 1,2,3
f1,f2,f3 = coefficient of frictions for pipes 1,2,3
H = difference of water level in the two tanks
The discharge passing through the pipe is same.
– The difference in liquid surface levels is equal to the sum
of the total head loss in the pipes
Parallel pipe system
• Consider a main pipe which divide into two or more branches as
shown in figure
Again join together downstream to form a single pipe then the branch
pipes are said to be connected in parallel. The discharge through the
main is increased by connecting pipes in parallelthe rate of flow in the
main pipe is equal to the sum of rate of flow through branch pipes.
hence Q =Q1+Q2
• In this arrangement loss of head for each pipe is same
Loss of head for branch pipe1=loss of head for branch pipe 2
• Total energy gradient line is equal to sum of
pressure head ,velocity head and datum head
EL = H = p / W + v2 / 2 g + h = constant along a
(EL ) Energy Line
• For a fluid flow without any losses due to friction (major losses)
or components (minor losses) - the energy line would be at a
constant level. In a practical world the energy line decreases
along the flow due to losses.
• A turbine in the flow reduces the energy line and a pump or fan
in the line increases the energy line
Hydraulic Grade Line (HGL )
• Hydraulic gradient line is the sum of pressure head and datum
HGL = p / W + h
The hydraulic grade line lies one velocity head below the