HEAD LOSSES IN PIPE FITTINGS
OBJECTIVES
 To demonstrate and estimate energy losses (major and minor) in the flow of a
Newtonian fluid through pipes.
 To determine the coefficient of energy loss in bends and pipe fittings.
 To compare of head losses in various pipe configurations.
 To obtain the loss of head in sudden expansion and sudden contraction of pipes.
EQUIPMENT REQUIRED
1. Head Losses in pipe fittings apparatus
2. Stopwatch
3. Measuring cylinder
INTRODUCTION
Two types of energy loss predominate in fluid flow through a pipe network: major
losses, and minor losses. Major losses are associated with frictional energy loss that is
caused by the viscous effects of the medium and roughness of the pipe wall. Minor
losses, on the other hand, are due to pipe fittings, changes in the flow direction, and
changes in the flow area. Due to the complexity of the piping system and the number
of fittings that are used, the head loss coefficient (K) is empirically derived as a quick
means of calculating the minor head losses.
THEORY
An energy balance in any flow system is given by the Bernoulli's equation.
𝑣12
2𝑔
+
𝑝1
𝛾
+ 𝑧1 =
𝑣22
2𝑔
+
𝑝2
𝛾
+ 𝑧2 + ℎ𝐿 ..............(1)
where,
p1, p2 are pressure at points 1 and 2 respectively (N/m2)
v1, v2 are average flow velocity at points 1 and 2 respectively (m/s)
𝜌 is density of the fluid in pipe (kg/m3)
hL is energy requirement (major and minor losses) (J/kg)
1
When a fluid under pressure flows through a pipe, the pipe offers resistance to the flow
due to which total head (or energy) of flowing fluid gets reduced by certain amount
which is called head loss (hL) in pipe flow. There are two types of head losses in pipe
flow system i.e. Major head loss and Minor head loss. Head loss in pipe flow system
due to viscous effect i.e. due to friction is referred as major head loss and will be
indicated by hL-Major. Head loss in pipe flow system due to various piping components
such as valves, fittings, elbows, contractions, enlargement, tees, bends, and exits is
referred as minor head loss and will be indicated by hL-Minor.
Therefore, complete head loss or pressure loss in pipe flow will be summation of major
head loss and minor head loss and will be indicated by h L.
h L = h L-Major + h L-Minor
Major Head loss
Major Head losses in pipe flow problem will be calculated with the help of DarcyWeisbach formula as mentioned below and this Darcy-Weisbach formula will be used
to calculate the major loss in pipe flow, it does not matter that pipe is horizontal, vertical
or on inclined plane.
𝑓(𝑙)(𝑣)2
h L-Major =
2𝑔𝐷
where,
h L-Major =Head losses (m)
f = Darcy-Weisbach friction factor
D=Diameter of pipe (m)
L=Length of pipe (m)
v=flow velocity (m/s)
g=acceleration due to gravity = 9.81 m/s
2
Friction factor as mentioned above will be determined based on type of flow i.e.
Laminar flow, Transition flow and turbulent flow.
Minor Head loss
Minor head losses are pressure losses in pipe flow system due to various piping
components such as valves, fittings, elbows, contractions, enlargement, tees,
bends and exits.
𝑘𝑣 2
h L-Minor= 2𝑔
where, k is minor loss coefficient.
Minor head losses occur due to geometry of construction and can also be given by,

Sudden enlargement (he ) =

Sudden contraction(hc ) =

𝑣2
Entrance (hi ) = 0.5 2𝑔
𝑣2
Exit (ho ) = k ∗ 2𝑔
𝑣2
Bend (hb ) = k ∗ 2𝑔



(𝑣1 −𝑣2 )2
2𝑔
(𝑣2 −𝑣1 )2
2𝑔
𝑣2
Pipe fittings (hp ) = k ∗ 2𝑔
PROCEDURE
 Carefully fill the manometer tubes with water to eliminate any air pockets from the
system.
 Ensure all connecting pipes are free from air bubbles to maintain accurate
measurements.
 Measure the volume of water at the output and record the time taken. This
information is crucial for determining the flow rate.
 Record the readings from the piezometer and table manometer for all pipes.
 Repeat the measurements of volume and time to demonstrate that the flow rate
remains constant during the experiment.
 Perform steps 1 to 5 for at least two different flow rates. This allows for a
comprehensive analysis of energy losses under varying conditions.
 When the experiment is complete, drain the apparatus to ensure it is ready for
subsequent use.
3
OBSERVATION
 Diameter at point A (dA) = 12.5mm = 12.5*10-3 m
 Diameter at point G (dG) = 25.0mm = 25*10-3 m
Manometer Reading (cm)
Tank Reading (ml)
SN
1
1
26.5
2
37
3
53.5
4
63.5
2
3
4
5
6
7
8
9
Time
(s)
Initial
(L1)
Final
(L2)
Difference
(L2-L1)
t
Discharge
(ml/s)
𝑄=
𝐿2 − 𝐿1
𝑡
8.8
17
32.5
30.5
20.5
17
15.5
7
0
250
250
1.89
132.28
15.8
23
39
35.5
24
20.5
19
8.5
0
406.7
406.7
2.68
151.75
26.8
33
48.5
43
30
25
24
11
0
466.7
466.7
2.92
159.85
33.5
39.5
54
48.5
33
28.5
27
12.5
0
473.3
473.3
2.83
167.24
LINE DIAGRAM OF PIPE FITTINGS:
4
CALCULATION
FOR OBSERVATION 1
Flow rate (Q1) =
L2 −L1
t
=
250
=132.28 cm3/s=132.28*10-6 m3/s
1.89
At point A,
Area AA =
2
𝜋𝑑𝐴
4
=
𝜋∗(0.0125)2
4
Q
= 0.00012272 m2 = 122.72*10-6 m2
132.28 ∗10−6
velocity (vA1) = A 1 = 122.72∗10−6 = 1.08 m/s
A
At point G,
Area AG =
πd2G
4
=
𝜋∗(0.025)2
4
𝑄
=4.908* 10-4 m2
132.28 ∗10−6
velocity (vG1) = 𝐴 1 = 4.908∗10−4 = 0.27 m/s
𝐴
Head losses between 1 and 2 = 17.7 cm = 0.177 m
Head losses between 2 and 3 = 4.3 cm = 0.043 m
Head losses between 3 and 4 = 3.0 cm = 0.03 m
Head losses between 4 and 5 = 5 cm = 0.05 m
Head losses between 5 and 6 = 10 cm = 0.1 m
Head losses between 6 and 7 = 3.5 cm = 0.035 m
Head losses between 7 and 8 = 1.5 cm = 0.015 m
Head losses between 8 and 9 = 8.5 cm = 0.085
We have,
1. For pipe 1 - 2, only friction loss occurs and is given by,
Head loss=hf = 17.7 cm = 0.177 m
Also,
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×2×1.082
= 2×9.81×0.0125= 0.177
Hence, f= 0.00465.
2.
For pipe 2-3, there is friction loss as well as bend loss.
bend loss= hb =4.3 cm = 0.043 m
5
ℎ𝑏 = 𝑘 ×
𝑣2
=𝑘×
2𝑔
1.082
=0.043
2×9.81
Hence, k=0.72
3. For pipe 3-4, there is friction loss only.
Head loss= hf = 3 cm = 0.03 m
Also,
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×0.18×1.082
= 2×9.81×0.0125=0.03
Hence, f = 0.00876
4. For pipe 4-5, there is bend loss only. As the distance between two pipes is
negligible, we neglect friction loss.
Head loss= hb =8 cm = 0.05 m
𝑣2
1.082
ℎ𝑏 = 𝑘 × 2𝑔 = 𝑘 × 2×9.81 =0.05
Hence, k= 0.841
5. for pipe 5-6, there is friction loss only.
Head loss= hf =10 cm = 0.1 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×0.627×1.082
=
2×9.81×0.0125
=0.1
Hence, f= 0.00838
6. For pipe 6-7, there are two losses: expansion and friction loss.
Head losses between 6 and 7 = 3.5 cm = 0.035 m
7. For pipe 7-8, there is frictional loss only.
hf = 1.5 cm = 0.015 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×0.84×0.272
=
2×9.81×0.025
= 0.015
Hence, f= 0.0300
8. For pipe 8-9, there is friction loss and contraction loss.
Head losses between 8 and 9 =8.5 cm = 0.085 m
FOR OBSERVATION 2
Flow rate (Q2) =
L2 −L1
t
=
406.7
2.68
=151.75 cm3/s=1.5175 *10-4 m3/s
At point A,
Area AA =
2
𝜋𝑑𝐴
4
=
𝜋∗(0.0125)2
4
Q
= 0.00012272 m2 = 122.72*10-6 m2
1.5175 ∗10−4
velocity (vA2) = A 2 = 122.72∗10−6 = 1.24 m/s
A
At point G,
6
Area AG =
πd2G
4
=
𝜋∗(0.025)2
4
=4.908* 10-4 m2
1.5175 ∗10−4
𝑄
velocity (vG2) = 𝐴 2 = 4.908∗10−4 = 0.31 m/s
𝐴
Head losses between 1 and 2 = 21.2 cm = 0.212 m
Head losses between 2 and 3 = 5.3 cm = 0.053 m
Head losses between 3 and 4 = 2.0 cm = 0.02 m
Head losses between 4 and 5 = 6 cm = 0.06 m
Head losses between 5 and 6 = 11.5 cm = 0.115 m
Head losses between 6 and 7 = 3.5 cm = 0.035 m
Head losses between 7 and 8 = 1.5 cm = 0.015 m
Head losses between 8 and 9 =10.5 cm = 0.105 m
We have,
9. For pipe 1 - 2, only friction loss occurs and is given by,
Head loss=hf = 21.2 cm= 0.212 m
Also,
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
=
4𝑓×2×1.242
= 0.212
2×9.81×0.0125
Hence, f= 0.00423.
10. For pipe 2-3, there is friction loss as well as bend loss.
bend loss= hb =5.3 cm = 0.053 m
𝑣2
1.242
ℎ𝑏 = 𝑘 × 2𝑔 = 𝑘 × 2×9.81=0.053
Hence, k=0.68
11. For pipe 3-4, there is friction loss only.
Head loss= hf = 2 cm = 0.02 m
Also,
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×0.18×1.242
= 2×9.81×0.0125=0.02
Hence, f = 0.00443
12. For pipe 4-5, there is bend loss only. As the distance between two pipes is
negligible, we neglect friction loss.
Head loss= hb =6 cm = 0.06 m
7
ℎ𝑏 = 𝑘 ×
𝑣2
=𝑘×
2𝑔
1.242
2×9.81
=0.06
Hence, k= 0.766
13. for pipe 5-6, there is friction loss only.
Head loss= hf =11.5cm = 0.115 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
4𝑓×0.627×1.242
=
2𝑔𝐷
2×9.81×0.0125
=0.115
Hence, f= 0.0073.
14. For pipe 6-7, there is two losses: expansion and friction loss.
Head losses between 6 and 7 = 3.5 cm = 0.035 m
15. For pipe 7-8, there is frictional loss only.
hf = 1.5 cm = 0.015 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
4𝑓×0.84×0.312
=
2𝑔𝐷
2×9.81×0.025
= 0.015
Hence, f= 0.0228
16. For pipe 8-9, there is friction loss and contraction loss.
Head losses between 8 and 9 =10.5 cm = 0.105 m
FOR OBSERVATION 3
Flow rate (Q3) =
L2 −L1
t
=
406.7
2.68
=159.85 cm3/s=1.5985 *10-4 m3/s
At point A,
Area AA =
2
𝜋𝑑𝐴
4
=
𝜋∗(0.0125)2
4
Q
= 0.00012272 m2 = 122.72*10-6 m2
1.5985 ∗10−4
velocity (vA3) = A 3 = 122.72∗10−6 = 1.30 m/s
A
At point G,
Area AG =
πd2G
4
=
𝜋∗(0.025)2
4
𝑄
=4.908* 10-4 m2
1.5985 ∗10−4
velocity (vG3) = 𝐴 3 = 4.908∗10−4 = 0.33 m/s
𝐴
Head losses between 1 and 2 = 26.7 cm 0.267 m
Head losses between 2 and 3 = 6.3 cm = 0.063 m
Head losses between 3 and 4 = 2.5 cm = 0.025 m
Head losses between 4 and 5 = 8 cm = 0.08 m
Head losses between 5 and 6 = 13 cm = 0.13 m
Head losses between 6 and 7 = 5 cm = 0.05 m
Head losses between 7 and 8 = 1 cm = 0.01 m
8
Head losses between 8 and 9 = 13 cm = 0.13 m
We have,
17. For pipe 1 - 2, only friction loss occurs and is given by,
Head loss=hf = 26.7 cm= 0.267 m
Also,
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×2×1.302
= 2×9.81×0.0125= 0.267
Hence, f= 0.00484
18. For pipe 2-3, there is friction loss as well as bend loss.
bend loss= hb =6.3 cm = 0.063 m
𝑣2
1.302
ℎ𝑏 = 𝑘 × 2𝑔 = 𝑘 × 2×9.81=0.063
Hence, k=0.731
19. For pipe 3-4, there is friction loss only.
Head loss= hf = 2.5 cm = 0.025 m
Also,
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×0.18×1.302
= 2×9.81×0.0125=0.025
Hence, f = 0.00504
20. For pipe 4-5, there is bend loss only. As the distance between two pipes is
negligible, we neglect friction loss.
Head loss= hb =8 cm = 0.08 m
𝑣2
1.302
ℎ𝑏 = 𝑘 × 2𝑔 = 𝑘 × 2×9.81 =0.08
Hence, k= 0.929
21. for pipe 5-6, there is friction loss only.
Head loss= hf =13 cm = 0.13 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
=
4𝑓×0.627×1.302
2×9.81×0.0125
=0.13
Hence, f= 0.0075
22. For pipe 6-7, there is two losses: expansion and friction loss.
Head losses between 6 and 7 = 5 cm = 0.05 m
23. For pipe 7-8, there is frictional loss only.
hf = 1 cm = 0.01 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
=
4𝑓×0.84×0.332
2×9.81×0.025
= 0.01
9
Hence, f= 0.0134
24. For pipe 8-9, there is friction loss and contraction loss.
Head losses between 8 and 9 =13 cm = 0.13 m
FOR OBSERVATION 4
Flow rate (Q4) =
L2 −L1
t
=
473.33
2.83
=167.24 cm3/s=1.6724 *10-4 m3/s
At point A,
Area AA =
2
𝜋𝑑𝐴
4
=
𝜋∗(0.0125)2
4
= 0.00012272 m2 = 122.72*10-6 m2
1.6724 ∗10−4
Q
velocity (vA4) = A 4 = 122.72∗10−6 = 1.36 m/s
A
At point G,
Area AG =
πd2G
4
=
𝜋∗(0.025)2
4
=4.908* 10-4 m2
1.6724 ∗10−4
𝑄
velocity (vG4) = 𝐴 4 = 4.908∗10−4 = 0.34 m/s
𝐴
Head losses between 1 and 2 = 30 cm = 0.300 m
Head losses between 2 and 3 = 6.5 cm = 0.065 m
Head losses between 3 and 4 = 3.5 cm = 0.035 m
Head losses between 4 and 5 = 8 cm = 0.080 m
Head losses between 5 and 6 = 15.5 cm = 0.155 m
Head losses between 6 and 7 = 4.5 cm = 0.045 m
Head losses between 7 and 8 = 1.5 cm = 0.015 m
Head losses between 8 and 9 = 14.5 cm = 0.145
1. For pipe 1 - 2, only friction loss occurs and is given by,
Head loss=hf = 30 cm= 0.3 m
Also,
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
4𝑓×2×1.362
= 2×9.81×0.0125=0.30
Hence, f= 0.00497
2. For pipe 2-3, there is friction loss as well as bend loss.
bend loss= hb =6.5 cm = 0.065 m
𝑣2
1.362
ℎ𝑏 = 𝑘 × 2𝑔 = 𝑘 × 2×9.81=0.065
Hence, k= 0.690
10
3. For pipe 3-4, there is friction loss only.
Head loss= hf = 3.5cm = 0.035 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
=
4×𝑓×0.18×1.362
2×9.81×0.0125
= 0.035
Hence, f= 0.00645
4. For pipe 4-5, there is bend loss only. As the distance between two pipes is
negligible, we neglect friction loss.
Head loss= hb =8 cm = 0.08 m
𝑣2
1.362
ℎ𝑏 = 𝑘 × 2𝑔 = 𝑘 × 2×9.81=0.08
Hence, k=0.85
5. For pipe 5-6, there is friction loss only.
Head loss= hf =15.5 cm = 0.155 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
=
4×𝑓×0.627×1.362
2×9.81×0.0125
=0.155
Hence, f= 0.0082
6. For pipe 6-7, there are two losses: expansion and friction loss.
Head losses between 6 and 7 = 4.5 cm = 0.045 m
7. For pipe 7-8, there is frictional loss only.
hf = 1.5 cm = 0.015 m
ℎ𝑓 =
4𝑓𝐿𝑣 2
2𝑔𝐷
=
4×𝑓×0.84×0.342
2×9.81×0.025
=0.015
Hence, f = 0.0189
8. For pipe 8-9, there is friction loss and contraction loss.
Head losses between 8 and 9 = 14.5 cm = 0.145
MAJOR LOSSES
Value
Observation 1 Observation 2 Observation 3 Observation 4
Frictional Losses, hf (1-2)
0.177
0.212
0.212
0.3
Coefficient of friction (f)
0.00465
0.00423
0.267
0.00497
Frictional Losses, hf (3-4)
0.03
0.02
0.00484
0.035
Coefficient of friction (f)
0.00876
0.00443
0.025
0.00645
Frictional Losses, hf (5-6)
0.1
0.115
0.00504
0.155
Coefficient of friction (f)
0.00838
0.0073
0.13
0.0082
Frictional Losses, hf (7-8)
0.015
0.015
0.0075
0.015
Coefficient of friction (f)
0.0300
0.0228
0.01
0.0189
11
MINOR LOSSES
Type of losses
Observation 1
Observation 2
Observation 3
Observation 4
Bend (2-3)
0.043
0.053
0.063
0.065
Loss Coefficient (K)
0.72
0.68
0.731
0.690
Bend (4-5)
0.05
0.06
0.08
0.08
Loss Coefficient (K)
0.841
0.766
0.929
0.85
Sudden Enlargement
0.035
0.035
0.050
0.045
0.085
0.105
0.130
0.145
(6-7)
Sudden Contraction
(8-9)
GRAPH
1. Graph between major head losses and discharge.
MAJOR HEAD LOSSES, ∆h
∆h Vs Q
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
120
130
140
150
160
170
DISCHARGE, Q
(1-2)
(3-4)
(5-6)
(7-8)
12
2. Graph between minor head losses and discharge.
∆h Vs Q
MINOR HEAD LOSSES, ∆h
0,16
0,14
0,12
0,1
0,08
0,06
0,04
0,02
0
120
125
130
135
140
145
150
155
160
165
170
DISCHARGE, Q
(2-3)
(4-5)
(6-7)
(8-9)
RESULT AND DISCUSSION
From the experiment conducted, it is evident that there are significant head losses in
the flow of fluid through pipes due to both major and minor factors. Major losses,
primarily attributed to friction, were calculated using the Darcy-Weisbach formula,
while minor losses, caused by pipe fittings and changes in flow direction, were
estimated using appropriate coefficients.
The observed values for major losses (frictional losses) varied depending on the pipe
section, and minor losses such as those associated with bends, sudden enlargements,
and contractions were determined through calculations. Comparing the results between
the two observations, it's evident that the magnitude of head losses varies with different
flow rates and configurations of pipe fittings. The coefficients of friction and loss
coefficients for bends and fittings also show variation based on the flow conditions.
CONCLUSION
In conclusion, through this experiment, it can be concluded that both major and minor
losses contribute significantly to the total head loss in pipe flow systems. The energy
losses in pipe flow are influenced by various factors including pipe geometry, flow
velocity, and the presence of fittings. The obtained coefficients can be used for further
13
calculations and design optimizations in piping systems.
PRECAUTION
 Be careful while filling the water to prevent air bubbles.
 Avoid water leakage.
 Handle the apparatus with care.
14