This document provides information on calculating head losses in piping systems. It discusses the use of Bernoulli's equation to relate total head between two points in a piping system. It also covers friction losses using the Darcy-Weisbach equation and the Moody diagram, as well as "minor losses" from fittings, valves, etc. The document presents methods to calculate head loss or flow rate given the other, including iterative techniques. It concludes with an example problem calculating maximum flow between reservoirs considering major and minor losses.

1. 
Major & Minor Losses
Under Supervision of:
Prof. Dr. Mahmoud Fouad
By students:
Mahmoud Bakr 533
Mohammed Abdullah 511
Moaz Emad
619 Mohammed Nabil Abbas 525

2. Applications

3. How big does the
pipe have to be to carry
3
a flow of x m /s?

4. Bernoulli's Equation
The basic approach to all piping systems is to write 
the Bernoulli equation between two points, connected
by a streamline, where the conditions are known. For
example, between the surface of a reservoir and a pipe
. outlet
The total head at point 0 must match with the total
head at point 1, adjusted for any increase in head due
to pumps, losses due to pipe friction and so-called
"minor losses" due to entries, exits, fittings, etc. Pump
head developed is generally a function of the flow
through the system

5. Bernoulli's Equation

6. Friction Losses in Pipes
Friction losses are a complex function of the system
geometry, the fluid properties and the flow rate in the
system. By observation, the head loss is roughly
proportional to the square of the flow rate in most
engineering flows (fully developed, turbulent pipe
flow). This observation leads to the Darcy-Weisbach
equation for head loss due to friction

9. For laminar flow, the head loss is proportional to
velocity rather than velocity squared, thus the friction
factor is inversely proportional to velocity

10. Turbulent flow
For turbulent flow, Colebrook (1939) found an
implicit correlation for the friction factor in round
pipes. This correlation converges well in few
iterations. Convergence can be optimized by slight
under-relaxation.

11. The familiar Moody Diagram is a log-log plot of the Colebrook
correlation on axes of friction factor and Reynolds number,
combined with the f=64/Re result from laminar flow. The plot
below was produced in an Excel spreadsheet

12. An explicit approximation

13. Pipe roughness
pipe material
glass, drawn brass, copper
commercial steel or wrought iron
asphalted cast iron
galvanized iron
cast iron
concrete
rivet steel
corrugated metal
PVC
pipe roughness ε (mm)
0.0015
0.045
ε
0.12
d Must be
0.15 dimensionless!
0.26
0.18-0.6
0.9-9.0
45
0.12

14. Calculating Head Loss for a Known Flow
From Q and piping determine Reynolds Number,
relative roughness and thus the friction factor.
Substitute into the Darcy-Weisbach equation to
obtain head loss for the given flow. Substitute into the
Bernoulli equation to find the necessary elevation or
pump head

15. Calculating Flow for a Known Head
Obtain the allowable head loss from the Bernoulli
equation, then start by guessing a friction factor. (0.02
is a good guess if you have nothing better.) Calculate
the velocity from the Darcy-Weisbach equation. From
this velocity and the piping characteristics, calculate
Reynolds Number, relative roughness and thus
. friction factor
Repeat the calculation with the new friction factor until
sufficient convergence is obtained. Q = VA

16. "Minor Losses"
Although they often account for a major portion of the head loss,
especially in process piping, the additional losses due to entries
and exits, fittings and valves are traditionally referred to as
minor losses. These losses represent additional energy
dissipation in the flow, usually caused by secondary flows
induced by curvature or recirculation. The minor losses are any
head loss present in addition to the head loss for the same
. length of straight pipe
Like pipe friction, these losses are roughly proportional to the
square of the flow rate. Defining K, the loss coefficient, by

17. . K is the sum of all of the loss coefficients in the
length of pipe, each contributing to the overall head
loss
Although K appears to be a constant coefficient, it
varies with different flow conditions
: Factors affecting the value of K include
.,the exact geometry of the component
.the flow Reynolds number , etc

18. Some types of minor losses
Head Loss due to Gradual Expansion (Diffuser)
(V1 −V2 ) 2
hE = K E
2g
2
2

V A
hE = K E 2  2 −1
2 g  A1

KE
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
diffusor angle ()


19. Sudden Contraction
2
1
 V2
hc = 
−1 2
C
 2g
 c

V2
V1
flow separation
losses are reduced with a gradual contraction = Ac
C
c
A2

20. Sudden Contraction
Cc
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0
0.2
0.4
0.6
A2/A1
Qorifice = CAorifice 2 gh
0.8
1

21. Entrance Losses
Losses can be
reduced by
accelerating the
flow gradually and
eliminating the
he = K e
K e ≈1.0
K e ≈ 0 .5
vena contracta
K e ≈ 0.04
V2
2g

22. Head Loss in Bendspressure
High
Head loss is a function of
the ratio of the bend radius
to the pipe diameter (R/D)
Velocity distribution
returns to normal several
pipe diameters
downstream
Possible
separation
from wall
R
D
Low pressure
hb = K b
Kb varies from 0.6 - 0.9
V2
2g

23. Head Loss in Valves
Function of valve type and valve
position
The complex flow path through
valves can result in high head loss
(of course, one of the purposes of
a valve is to create head loss when
it is not fully open)
hv = K v
V2
2g

24. To calculate losses in piping systems with both pipe
friction and minor losses use

25. Solution Techniques
Neglect minor losses
Equivalent pipe lengths
Iterative Techniques
Simultaneous Equations
Pipe Network Software

26. Iterative Techniques for D and Q
(given total head loss)
Assume all head loss is major head loss.
Calculate D or Q using Swamee-Jain equations
Calculate minor losses
Find new major losses by subtracting minor losses
from total head loss

27. Solution Technique: Head Loss
Can be solved directly
hminor = K
Re =
V
2
hminor = K
2g
4Q
π ν
D
f =
8Q 2
gπ 2 D 4
0.25
2

 ε
5.74 


+
log

3.7 D Re 0.9 

hl = ∑ f +∑ minor
h
h
hf = f
8
LQ 2
gπ 2 D 5

28. Solution Technique:
Discharge or Pipe Diameter
Iterative technique
Set up simultaneous equations in Excel
Re =
4Q
π ν
D
hminor = K
f =
0.25
2

 ε
5.74 

log
+


0 .9 
3.7 D Re 

8Q 2
gπ 2 D 4
hl = ∑ f +∑ minor
h
h
hf = f
8
LQ 2
gπ 2 D 5
Use goal seek or Solver to
find discharge that makes the
calculated head loss equal
the given head loss.

29. Example: Minor and Major Losses
Find the maximum dependable flow between the
reservoirs for a water temperature range of 4ºC to 20ºC.
Water
25 m elevation difference in reservoir water levels
Reentrant pipes at reservoirs
Standard elbows
2500 m of 8” PVC pipe
1500 m of 6” PVC pipe
Sudden contraction
Gate valve wide open

30. Directions
Assume fully turbulent (rough pipe law)
find f from Moody (or from von Karman)
Find total head loss
Solve for Q using symbols (must include minor
losses) (no iteration required)
Obtain values for minor losses from notes or text

31. Example (Continued)
What are the Reynolds number in the two pipes?
Where are we on the Moody Diagram?
What value of K would the valve have to produce to
reduce the discharge by 50%?
What is the effect of temperature?
Why is the effect of temperature so small?

32. Example (Continued)
Were the minor losses negligible?
Accuracy of head loss calculations?
What happens if the roughness increases by a factor
of 10?
If you needed to increase the flow by 30% what could
you do?
Suppose I changed 6” pipe, what is minimum
diameter needed?