1. CHAPTER 1: Water Flow in Pipes
University of Palestine
Engineering Hydraulics
2nd semester
CHAPTER 1: Water Flow in Pipes

2. Description of A Pipe Flow
Water pipes in our homes and the distribution system
Pipes carry hydraulic fluid to various components of vehicles and machines
Natural systems of “pipes” that carry blood throughout our body and air into and out of our lungs.

3. Description of A Pipe Flow
Pipe Flow: refers to a full water flow in a closed conduits or circular cross section under a certain pressure gradient.
The pipe flow at any cross section can be described by:
cross section (A),
elevation (h), measured with respect to a horizontal reference datum.
pressure (P), varies from one point to another, for a given cross section variation is neglected
The flow velocity (v), v = Q/A.

4. Difference between open-channel flow and the pipe flow
The pipe is completely filled with the fluid being transported.
The main driving force is likely to be a pressure gradient along the pipe.
Open-channel flow
Water flows without completely filling the pipe.
Gravity alone is the driving force, the water flows down a hill.

5. Types of Flow Steady and Unsteady flow For a steady flow
The flow parameters such as velocity (v), pressure (P) and density (r) of a fluid flow are independent of time in a steady flow. In unsteady flow they are independent.
For a steady flow
For an unsteady flow
If the variations in any fluid’s parameters are small, the average is constant, then the fluid is considered to be steady

6. Types of Flow Uniform and non-uniform flow
A flow is uniform if the flow characteristics at any given instant remain the same at different points in the direction of flow, otherwise it is termed as non-uniform flow.
For a uniform flow
For a non-uniform flow

7. Types of Flow Examples:
The flow through a long uniform pipe diameter at a constant rate is steady uniform flow.
The flow through a long uniform pipe diameter at a varying rate is unsteady uniform flow.
The flow through a diverging pipe diameter at a constant rate is a steady non-uniform flow.
The flow through a diverging pipe diameter at a varying rate is an unsteady non-uniform flow.

8. Types of Flow Laminar and turbulent flow Laminar flow:
The fluid particles move along smooth well defined path or streamlines that are parallel, thus particles move in laminas or layers, smoothly gliding over each other.
Turbulent flow:
The fluid particles do not move in orderly manner and they occupy different relative positions in successive cross-sections.
There is a small fluctuation in magnitude and direction of the velocity of the fluid particles
Transitional flow
The flow occurs between laminar and turbulent flow

9. Types of Flow Reynolds Experiment
Reynolds performed a very carefully prepared pipe flow experiment.

10. Increasing flow velocity

11. Types of Flow Reynolds Experiment
Reynold found that transition from laminar to turbulent flow in a pipe depends not only on the velocity, but only on the pipe diameter and the viscosity of the fluid.
This relationship between these variables is commonly known as Reynolds number (NR)
It can be shown that the Reynolds number is a measure of the ratio of the inertial forces to the viscous forces in the flow

12. Types of Flow Reynolds number where V: mean velocity in the pipe [L/T]
D: pipe diameter [L]
: density of flowing fluid [M/L3]
: dynamic viscosity [M/LT]
: kinematic viscosity [L2/T]

13. Types of Flow

14. Types of Flow
It has been found by many experiments that for flows in circular pipes, the critical Reynolds number is about 2000
Flow laminar when NR < Critical NR
Flow turbulent when NR > Critical NR
The transition from laminar to turbulent flow does not always happened at NR = 2000 but varies due to experiments conditions….….this known as transitional range

15. Types of Flow Laminar Vs. Turbulent flows low velocities
Laminar flows characterized by:
low velocities
small length scales
high kinematic viscosities
NR < Critical NR
Viscous forces are dominant.
Turbulent flows characterized by
high velocities
large length scales
low kinematic viscosities
NR > Critical NR
Inertial forces are dominant

16. Types of Flow
Example 1
40 mm diameter circular pipe carries water at 20oC. Calculate the largest flow rate (Q) which laminar flow can be expected.

17. Energy Head in Pipe Flow
Water flow in pipes may contain energy in three basic forms:
1- Kinetic energy.
2- potential energy.
3- pressure energy.
Bernoulli Equation
Energy per unit weight of water
OR: Energy Head

18. Energy Head in Pipe Flow
Energy head and Head loss in pipe flow

19. Energy Head in Pipe Flow
Kinetic head
Pressure head
Elevation head = + +
Notice that:
In reality, certain amount of energy loss (hL) occurs when the water mass flow from one section to another.
The energy relationship between two sections can be written as:

20. Energy Head in Pipe Flow
Example

21. Energy Head in Pipe Flow
Example In the figure shown: Where the discharge through the system is 0.05 m3/s, the total losses through the pipe is 10 v2/2g where v is the velocity of water in 0.15 m diameter pipe, the water in the final outlet exposed to atmosphere.

22. Energy Head in Pipe Flow
Calculate the required height (h =?)
below the tank

23. Energy Head in Pipe Flow
Without calculation sketch the (E.G.L) and (H.G.L)

24. Basic components of a typical pipe system

25. Calculation of Head (Energy) Losses
In General:
When a fluid is flowing through a pipe, the fluid experiences some resistance due to which some of energy (head) of fluid is lost.
Energy Losses
(Head losses)
Major Losses
Minor losses
Loss due to the change of the velocity of the flowing fluid in the magnitude or in direction as it moves through fitting like Valves, Tees, Bends and Reducers.
loss of head due to pipe friction and to viscous dissipation in flowing water

26. Head Losses in Pipelines
Calculation of Head (Energy) Losses
Head Losses in Pipelines
Part A:Major Losses

27. Losses of Head due to Friction
Energy loss through friction in the length of pipeline is commonly termed the major loss hf
This is the loss of head due to pipe friction and to the viscous dissipation in flowing water.
Several studies have been found the resistance to flow in a pipe is:
- Independent of pressure under which the water flows
- Linearly proportional to the pipe length, L
- Inversely proportional to some water power of the pipe diameter D
- Proportional to some power of the mean velocity, V
- Related to the roughness of the pipe, if the flow is turbulent

28. Energy Head & Head loss in pipe flow
Losses of Head due to Friction
Energy Head & Head loss in pipe flow

29. Major losses formulas
Several formulas have been developed in the past. Some of these formulas have faithfully been used in various hydraulic engineering practices.
Darcy-Weisbach ( f )
Hazen-William (CHW)
Manning (n)
The Chezy Formula
The Strickler Formula

30. The resistance to flow in a pipe is a function of:
Major losses formulas
The resistance to flow in a pipe is a function of:
The pipe length, L
The pipe diameter, D
The mean velocity, V
The properties of the fluid .
The roughness of the pipe, (the flow is turbulent).

31. Darcy-Weisbach Equation
Major losses formulas
Darcy-Weisbach Equation
Where:
f is the friction factor
L is pipe length
D is pipe diameter
Q is the flow rate
hL is the loss due to friction
It is conveniently expressed in terms of velocity (kinetic) head in the pipe
The friction factor is function of different terms:
Renold number
Relative roughness

32. Major losses formulas
Friction Factor: (f )
For Laminar flow: (NR < 2000) [depends only on Reynolds’ number and not on the surface roughness]
For turbulent flow in smooth pipes (e/D = 0) with < NR < 105 is

33. Major losses formulas Colebrook-White Equation for f
For turbulent flow ( NR > 4000 ) with e/D > 0.0, the friction factor can be founded from:
Th.von Karman formulas:
Colebrook-White Equation for f

34. Major losses formulas
There is some difficulty in solving this equation
So, Miller improve an initial value for f , (fo)
The value of fo can be use directly as f if:
Pandtle - Colebrook Equation
There are other Equation such as Karman Equation see Text book 2

35. Friction Factor f
The thickness of the laminar sublayer d decrease with an increase in NR
laminar flow
NR < 2000
pipe wall e
f independent of relative roughness e/D
Smooth
f varies with NR and e/D e
pipe wall
transitionally
rough
Colebrook formula
turbulent flow e
pipe wall
f independent of NR
NR > 4000
rough

36. Moody diagram
A convenient chart was prepared by Lewis F. Moody and commonly called the Moody diagram of friction factors for pipe flow, There are 4 zones of pipe flow in the chart:
A laminar flow zone where f is simple linear function of Re
A critical zone (shaded) where values are uncertain because the flow might be neither laminar nor truly turbulent
A transition zone where f is a function of both Re and relative roughness
A zone of fully developed turbulence where the value of f depends solely on the relative roughness and independent of the Reynolds Number

37. Moody diagram

38. Moody diagram Laminar Marks Reynolds Number independence Transition
critical

39. Moody diagram
Notes:
Colebrook formula
is valid for the entire nonlaminar range (4000 < Re < 108) of the Moody chart
In fact , the Moody chart is a graphical representation of this equation

40. Moody diagram
Bonus:
Find the theoretical formulation for friction factor for laminar flow.

41. Typical values of the absolute roughness (e) are given

42. Absolute roughness
Materials Roughness

43. Problems (head loss)
Three types of problems for uniform flow in a single pipe:
Type 1:
Given the kind and size of pipe and the flow rate
head loss ?
Type 2:
Given the kind and size of pipe and the head loss
flow rate ?
Type 3:
Given the kind of pipe, the head loss and flow rate
size of pipe ?

44. Problems type I (head loss)

45. Example 2
The water flow in Asphalted cast Iron pipe (e = 0.12mm) has a diameter 20cm at 20oC. Is 0.05 m3/s. determine the losses due to friction per 1 km
Type 1:
Given the kind and size of pipe and the flow rate
head loss ?
Moody
f = 0.018

46. Example 3
The water flow in commercial steel pipe (e = 0.045mm) has a diameter 0.5m at 20oC. Q=0.4 m3/s. determine the losses due to friction per 1 km
Type 1:
Given the kind and size of pipe and the flow rate
head loss ?

47. Example 3-cont.
Use other methods to solve f
1- Cole brook

48. Example 3-cont.
2- Pandtle - Colebrook Equation

49. Problems type II (head loss)

50. Method for solution of Type 2 problems

51. Relative roughness e/D

52. Example 4:

54. Example 4:

61. Example 5:
Cast iron pipe (e = 0.26), length = 2 km, diameter = 0.3m. Determine the max. flow rate Q , If the allowable maximum head loss = 4.6m. T=10oC
Type 2:
Given the kind and size of pipe and the head loss
flow rate ?

62. Example 5:cont. V= 0.82 m/s , Q = V*A = 0.058 m3/s Another solution?
Trial 1
Trial 2
Another solution?
V= 0.82 m/s , Q = V*A = m3/s

63. Example 6:
Compute the discharge capacity of a 3-m diameter, wood stave pipe in its best condition carrying water at 10oC. It is allowed to have a head loss of 2m/km of pipe length.
Type 2:
Given the kind and size of pipe and the head loss
flow rate ?
Solution 1:
Table 3.1 : wood stave pipe: e = 0.18 – 0.9 mm, take e = 0.3 mm
At T= 10oC, n = 1.31x10-6 m2/sec

64. Solve by trial and error: Iteration 1:
Assume f = 0.02
From moody Diagram:
Iteration 2:
update f =
From moody Diagram:
Iteration f V NR
106
Solution:
106
Convergence
Another solution?

65. Example 6:Another solution?
Compute the discharge capacity of a 3-m diameter, wood stave pipe in its best condition carrying water at 10oC. It is allowed to have a head loss of 2m/km of pipe length.
Type 2: Given the kind and size of pipe and the head loss
flow rate ?
Solution 2:
At T= 10oC, n = 1.31x10-6 m2/sec
Table 3.1 : wood pipe: e = 0.18 – 0.9 mm, take e = 0.3 mm
From moody Diagram:

66. f =

67. Problems type III (head loss)

68. Example 7:

70. Example 7:cont.

71. Example 8:
Estimate the size of a uniform, horizontal welded-steel pipe installed to carry 14 ft3/sec of water of 70oF (20oC). The allowable pressure loss is 17 ft/mi of pipe length.
Solution 2:
From Table : Steel pipe: ks = mm
Darcy-Weisbach:
Let D = 2.5 ft, then
V = Q/A = 2.85 ft/sec
Now by knowing the relative roughness and the Reynolds number:
We get f =0.021

72. Example 8:cont.
A better estimate of D can be obtained by substituting the latter values into equation a, which gives
A new iteration provide V = 4.46 ft/sec NR = 8.3 x 105 e/D = f = 0.022, and D = 2.0 ft. More iterations will produce the same results.

74. Example 9:

75. Empirical Formulas 1
Hazen-Williams
Simplified

76. Empirical Formulas 1

77. Empirical Formulas 1

78. Empirical Formulas 1

79. Empirical Formulas 1
Where: CH = corrected value CHo = value from table Vo = velocity at CHo V = actual velocity

80. Empirical Formulas 2 Manning
This formula has extensively been used for open channel designs. It is also quite commonly used for pipe flows
Manning
Simplified

81. Empirical Formulas 2 n = Manning coefficient of roughness (See Table)
Rh and S are as defined for Hazen-William formula.

82. Empirical Formulas 2

83. Empirical Formulas 2

84. Empirical Formulas 3
The Chezy Formula
where C = Chezy coefficient

85. Empirical Formulas 3
It can be shown that this formula, for circular pipes, is equivalent to Darcy’s formula with the value for
[f is Darcy Weisbeich coefficient]
The following formula has been proposed for the value of C:
[n is the Manning coefficient]

86. The Strickler Formula:
Empirical Formulas 4
The Strickler Formula:
where kstr is known as the Strickler coefficient.
Comparing Manning formula and Strickler formula, we can see that

87. Empirical Formulas
Relations between the coefficients in Chezy, Manning , Darcy , and Strickler formulas.

88. Example 10
New Cast Iron (CHW = 130, n = 0.011) has length = 6 km and diameter = 30cm. Q= 0.32 m3/s, T=30o. Calculate the head loss due to friction using:
Hazen-William Method
b) Manning Method

89. Head Losses in Pipelines
Calculation of Head (Energy) Losses
Head Losses in Pipelines
Part B:Minor Losses

90. Minor Losses
Additional losses due to entries and exits, fittings and valves are traditionally referred to as minor losses

91. Flow pattern through a valve
Minor Losses
It is due to the change of the velocity of the flowing fluid in the magnitude or in direction [turbulence within bulk flow as it moves through and fitting]
Flow pattern through a valve

92. Minor Losses The minor losses occurs du to : It has the common form
Valves
Tees
Bends
Reducers
And other appurtenances
It has the common form
“minor” compared to friction losses in long pipelines but,
can be the dominant cause of head loss in shorter pipelines

94. Losses due to contraction
Minor Losses
Losses due to contraction
A sudden contraction in a pipe usually causes a marked drop in pressure in the pipe due to both the increase in velocity and the loss of energy to turbulence.
Along centerline
Along wall

95. Minor Losses
Value of the coefficient Kc for sudden contraction V2

96. Head Loss Due to a Sudden Contraction
Minor Losses
Head Loss Due to a Sudden Contraction 96

97. Minor Losses
Head losses due to pipe contraction may be greatly reduced by introducing a gradual pipe transition known as a confusor

98. Head Loss Due to Gradual Contraction (reducer or nozzle)
Minor Losses
Head Loss Due to Gradual Contraction (reducer or nozzle) a
100
200
300
400 KL
0.2
0.28
0.32
0.35
A different set of data is : 98

99. Losses due to Enlargement
Minor Losses
Losses due to Enlargement
A sudden Enlargement in a pipe

100. Minor Losses
Head losses due to pipe enlargement may be greatly reduced by introducing a gradual pipe transition known as a diffusor

101. smaller head loss than in the case of an abrupt expansion
Minor Losses
Note that the drop in the energy line is much larger than in the case of a contraction
abrupt expansion
gradual expansion
smaller head loss than in the case of an abrupt expansion

102. Head Loss Due to a Sudden Enlargement
Minor Losses
Head Loss Due to a Sudden Enlargement
or :

103. Head Loss Due to Gradual Enlargement (conical diffuser)
Minor Losses
Head Loss Due to Gradual Enlargement (conical diffuser) a
100
200
300
400 KL
0.39
0.80
1.00
1.06

104. Minor Losses
Gibson tests

105. Loss due to pipe entrance
Minor Losses
Loss due to pipe entrance
General formula for head loss at the entrance of a pipe is also expressed in term of velocity head of the pipe

106. increasing loss coefficient
Minor Losses
Different pipe inlets
increasing loss coefficient

107. Head Loss at the Entrance of a Pipe (flow leaving a tank)
Minor Losses
Head Loss at the Entrance of a Pipe (flow leaving a tank)
Reentrant
(embeded)
KL = 0.8
Sharp
edge
KL = 0.5
Slightly
rounded
KL = 0.2
Well
rounded
KL = 0.04

108. Another Typical values for various amount of rounding of the lip
Minor Losses
Another Typical values for various amount of rounding of the lip

109. Loss at pipe exit (discharge head loss)
Minor Losses
Loss at pipe exit (discharge head loss)
In this case the entire velocity head of the pipe flow is dissipated and that the discharge loss is

110. Head Loss at the Exit of a Pipe (flow entering a tank)
Minor Losses
Head Loss at the Exit of a Pipe (flow entering a tank)
KL = 1.0
the entire kinetic energy of the exiting fluid (velocity V1) is dissipated through viscous effects as the stream of fluid mixes with the fluid in the tank and eventually comes to rest (V2 = 0).

111. Loss of head in pipe bends
Minor Losses
Loss of head in pipe bends

112. Minor Losses
Miter bends
For situations in which space is limited,

113. Loss of head through valves
Minor Losses
Loss of head through valves

114. Minor Losses

115. The loss coefficient for elbows, bends, and tees
Minor Losses
The loss coefficient for elbows, bends, and tees

116. Loss coefficients for pipe components (Table)
Minor Losses
Loss coefficients for pipe components (Table)

117. Minor loss coefficients (Table)

118. Minor loss calculation using equivalent pipe length
Minor Losses
Minor loss calculation using equivalent pipe length

119. Minor Losses
Note that the above values are average typical values, actual values will depend on the make (manufacturer) of the components.
See:
Catalogs
Hydraulic handbooks !!

120. Energy and hydraulic grade lines
Minor Losses
Energy and hydraulic grade lines
Unless local effects are of particular interests the changes in the EGL and HGL are often shown as abrupt changes (even though the loss occurs over some distance)

121. Minor Losses
Example 11
In the figure shown two new cast iron pipes in series, D1 =0.6m , D2 =0.4m length of the two pipes is 300m, level at A =80m , Q = 0.5m3/s (T=10oC).there are a sudden contraction between Pipe 1 and 2, and Sharp entrance at pipe 1.
Fine the water level at B
e = 0.26mm
v = 1.31×10-6
Q = 0.5 m3/s

122. Minor Losses
Solution

123. Minor Losses
ZB = 80 – = m

124. Minor Losses
Example 12
A pipe enlarge suddenly from D1=240mm to D2=480mm. the H.G.L rises by 10 cm calculate the flow in the pipe

125. Solution

126. Minor Losses
Solution