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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 
formula 
•Minor losses such as loss of head at entry, change in diameter, 
bend etc. 
•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. & 
•T.E.L. 
•Plotting of H.G.L. & T.E.L. 
•Design of pipeline for given flow --using formulae ---using 
nomograms 
•Computation of height of reservoir 
•Compound pipe and equivalent sizes
Laminar flow: 
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. 
Turbulent flow 
•Opposite of laminar, where considerable mixing occurs, velocities 
are high. 
•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 
proportional.
• An ideal fluid is one that is incompressible and has no viscosity. 
http://www.ceb.cam.ac.uk/pages/mass-transport.html
6 
Head Loss 
• 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 
fLV 
2gd 
 
P 
g 
h 
2 
L avg 
L  
 

7
8
9 
Hagen – Poiseuille’s Law
4 December 2014 10
4 December 2014 11
Friction Factor : Major losses 
• Laminar flow 
• Turbulent (Smooth, Transition, Rough) 
• Colebrook Formula 
• Moody diagram 
• Swamee-Jain
Laminar Flow Friction Factor 
Hagen-Poiseuille 
Darcy-Weisbach 
2 
gD hl 
32 
V 
L 
 
 
 
32 LV 
h 
 
 
f 2 
gD 
 
2 
f f 
L V 
2 
h 
D g 
 
32 2 
g 
L 
V 
D 
LV 
 
gD 
2 
f 
2  
 
64 64 
f 
 
l D gh 
  
128 
Q 
  Slope of __-1 on log-log plot 
VD Re 
 
f hV 
4 
f independent of roughness! 
l 
 

Turbulent Flow: 
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) 
2 
f f 
LV 
2 
h 
Dg 
 
  
1 Re f 
 2log 
  
f 2.51 
  
1 3.7 
2log 
f 
D 
 
  
   
  
 D  
1 2.51 
  2log 
   
f 3.7 Re f 
  
* 
f 
8 
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) 
Where 
• 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 
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 = 
4000
• Moody diagram
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)
21 
Minor Losses 
• 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.
22
• Total head loss in a system is comprised of major losses (in 
23 
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
24
25
26
27
Laminar flow
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 
pipe line. 
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. 
Q=A1V1=A2V2=A3V3 
– 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
• 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 
streamline 
where 
(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 
head 
HGL = p / W + h 
where 
The hydraulic grade line lies one velocity head below the 
energy line.

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Flow through pipes

  • 1. 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 formula •Minor losses such as loss of head at entry, change in diameter, bend etc. •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. & •T.E.L. •Plotting of H.G.L. & T.E.L. •Design of pipeline for given flow --using formulae ---using nomograms •Computation of height of reservoir •Compound pipe and equivalent sizes
  • 2. Laminar flow: 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. Turbulent flow •Opposite of laminar, where considerable mixing occurs, velocities are high. •Laminar and Turbulent flows can be characterized and quantified using Reynolds Number •established by Osborne Reynold and is given as –
  • 3.
  • 4. 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 proportional.
  • 5. • An ideal fluid is one that is incompressible and has no viscosity. http://www.ceb.cam.ac.uk/pages/mass-transport.html
  • 6. 6 Head Loss • 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 fLV 2gd  P g h 2 L avg L   
  • 7. 7
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  • 9. 9 Hagen – Poiseuille’s Law
  • 12. Friction Factor : Major losses • Laminar flow • Turbulent (Smooth, Transition, Rough) • Colebrook Formula • Moody diagram • Swamee-Jain
  • 13. Laminar Flow Friction Factor Hagen-Poiseuille Darcy-Weisbach 2 gD hl 32 V L    32 LV h   f 2 gD  2 f f L V 2 h D g  32 2 g L V D LV  gD 2 f 2   64 64 f  l D gh   128 Q   Slope of __-1 on log-log plot VD Re  f hV 4 f independent of roughness! l  
  • 14. Turbulent Flow: 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) 2 f f LV 2 h Dg    1 Re f  2log   f 2.51   1 3.7 2log f D          D  1 2.51   2log    f 3.7 Re f   * f 8 u V (used to draw the Moody diagram)
  • 15. 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) Where • f – friction factor • L – length of pipe • D – diameter of pipe • v – velocity of flow
  • 16. • Another equation was developed to compute hL under Laminar flow conditions only called the Hagen-Poiseuille equation
  • 17. • 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!
  • 18. Moody diagram 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 = 4000
  • 20. 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)
  • 21. 21 Minor Losses • 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.
  • 22. 22
  • 23. • Total head loss in a system is comprised of major losses (in 23 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
  • 24. 24
  • 25. 25
  • 26. 26
  • 27. 27
  • 29. 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.
  • 30. 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.
  • 31.
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  • 34. 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 pipe line. 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. Q=A1V1=A2V2=A3V3 – The difference in liquid surface levels is equal to the sum of the total head loss in the pipes
  • 35. 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
  • 37. • 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 streamline where (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
  • 38. Hydraulic Grade Line (HGL ) • Hydraulic gradient line is the sum of pressure head and datum head HGL = p / W + h where The hydraulic grade line lies one velocity head below the energy line.