PRACTICAL
5: HEAD LOSSES IN SMALL BOR
HEAD LOSSES IN SMALL BORE PIPE SYSTEMS
INTRODUCTION
The minor losses are those which are caused by change in
pipe cross section, presence of bends,valves and fittings.Although in long
pipelines the losses due to the local disturbances caused by these fittings are
of minor importance and often can be neglected,they may however outweigh the
friction losses in short pipe.
The source of losses is usually confined to every short
length of the pipe.A theoretical determination of the minor losses is seldom
possible except for the loss due to sudden enlargement.Since the losses have
been experimentally found to vary approximately as the square of the mean
velocity, they are normally expressed in the form
H_{L }=K_{L }V^{2}
2g
In which K_{L}is known as the loss
coefficient. For a geometry,the value ifK_{L} is practically
constant at high Reynolds number, the magnitude of the loss coefficient is
experimentally determined and is governed primarily by the shape of the
obstruction or pipe fitting.
OBJECTIVES
 To examine the minor energy head losses ( i.e shock losses ) for :
 90^{0} elbow bend
 90^{0}mitre bend
 90^{0} large radius bendTo verify that h_{shock}= DhDh = k v^{2}2g
 To show that the shock losses due to a sudden contraction are also proportional to the velocity head and to calculate the coefficient of contraction
H_{L }=kv^{2}= (1/C_{c} 1)^{2 }v^{2}
2g 2g
whereC_{c }= coefficient
of contraction.
 To confirm the BordaCarnot equation for hea6+d loss in a sudden expansion from experimental results.
H_{L }= (v_{1} v_{2})^{2}
2g
PROCEDURES
 The pump was started and both the bench supply valve and apparatus control valve were opened. The water was allowed to flow for two to three minutes.
 Then the apparatus control valve was partially closed.
 The manometer was purged using the vent valve.
 Then the apparatus control valve was closed.
 The air was pumped into the manometer to obtain zero pressure difference in the piezometer tubes at the convenient level.
 At least seven readings for Q (discharge) and H_{diff}(pressure head difference) were required, (H_{diff}), being reduced in equal decrements.
DATA COLLECTION
Pipe system:Piezometric Head Losses at various Rates of flow
Pipe diameter D_{1} =
22.5mm Pipe diameter D_{2}
= 29.6mm
Volume
(L)

Time
(sec)

Mitre bend
H_{diff}
12
(m)

Elbow Bend H_{diff}
34
(m)

Sudden enlargement
H_{diff}
56
(m)

Sudden contraction
H_{diff}
78
(m)

Large radius bend H_{diff}910
(m)

5

9.12

0.160

0.110

0.040

0.110

0.060

5

13.25

0.130

0.090

0.030

0.090

0.050

5

14.33

0.110

0.080

0.030

0.070

0.040

5

15.46

0.090

0.070

0.020

0.060

0.030

5

17.16

0.005

0.040

0.010

0.035

0.020

5

23.09

0.004

0.030

0.010

0.025

0.015

Pipe system:Piezometric Head Losses at various Rates of flow
Pipe diameter D_{1} =
22.5mm Pipe diameter D_{2}
= 29.6mm
A_{1} = 3.98×10^{4}m^{2} A_{2} =
6.88×10^{4}m^{2}
Discharge
Q
×10^{4}
(m^{3}/sec)

Velocity in D_{1
}pipe
V (m/sec)

Velocity Head
V^{2}
2g
(m)

Pressure Change
0.034V^{2}
(m)

Sudden Enlargement
H_{shock}=
0.034V^{2}
 H_{diff}
(m)

Sudden Contraction
H_{shock}=
H_{diff}  0.034V^{2}
(m)

5.482

1.379

0.097

0.065

0.025

0.045

3.774

0.949

0.046

0.031

0.001

0.059

3.489

0.877

0.039

0.026

0.004

0.044

3.234

0.813

0.034

0.022

0.002

0.038

2.914

0.733

0.027

0.018

0.008

0.017

2.165

0.544

0.015

0.001

0.009

0.024

GRAPHS
AND ANALYSIS FROM THE GRAPHS
For
90^{0}mitre bend
The value of k for mitrebend is 2.0661
For
90^{0 }elbow bend;
The value ofk
for elbow bend is 1.5024
For90^{0} large radius
bend
The value of k
for large radius bend is 0.7967
The value of k
for large sudden enlargement is 0.1035
The value of k
for large sudden contraction is 0.7793
The graph which shows the shock losses due sudden
contraction are also proportional to the velocity head and to calculate the
coefficient of contraction.
From the graph
H_{L }= K
v^{2} = (1/C_{c} 1)^{2}v^{2}
2g 2g
(1/C_{c} 1)^{2 }= 0.7793
1 – 1 =0.8828
C_{c}
C_{c} = 0.531
The coefficient of contraction,C_{c }is 0.531
ANALYSIS AND CALCULATIONS
Given;
D_{1} = 22.5mm
D_{2}
= 29.6mm
A_{1}
= 3.98×10^{4}m^{2}
A_{2} = 6.88×10^{4}m^{2}
Q =volume(m^{3})
time(s)
Q = 5×10^{3}m^{3}
= 5.482×10^{4}m^{3}/s
9.12(sec)
The same for rest of volume and time and results were
recorded as shown in the table.
Velocity
Q =A_{1}×V_{1}
V = Q /A_{1}
V = 5.482×10^{4}m^{3}/s = 1.377m/s
3.98×10^{4}m^{2}
The same procedure were repeated and tabulated
Velocity head =V^{2} Given
g =9.81m/s^{2}
2g
= (1.377m/s)^{2}
2×9.81m/s^{2}
Velocity head = 0.0702m
For each value of velocity,velocity head was determined.
H_{shock} in
sudden enlargement
H_{shock} = 0.034V^{2}  H_{diff}
H_{shock} = 0.034×1.377^{2} – 0.04 = 0.024m
The same was repeated for each value of velocity and H_{diff}
and the results were recorded.
H_{shock} in
sudden contraction
H_{shock}= H_{diff }0.034V^{2}
= 0.045m
For each value of velocity and H_{diff},shock value
was determined and tabulated.
To confirm the Borda –Carnot equation for head loss in sudden
expansion from experimental results
H_{L }= (V_{1} – V_{2})^{2}
2g
From continuity
equation
V_{2} =A_{1}V_{1}
A_{2}
h_{L }= (V_{1}{
A_{1}V_{1}/A_{2}})^{2}
2g
h_{L}= (1  A_{1}/A_{2})^{2}V_{1}^{2}
2g
h_{L}=kV^{2}
2g
But A_{2 }= 688.1mm^{2}, A_{1 }=
398.mm^{2}
k= (1 – (398mm^{2}/688.1mm^{2}))^{ 2}
The theoretical value of k is 0.178
From the graph the value of k is 0.1035
The value of k obtained from Borda – Carnot
equation and that obtained from graph varies greatly due to error which was
previously made by neglecting of frictional losses in the pipe. Since Head
losses the pipe is caused by friction which is the major loss and suddenly
enlargement and contraction which are the minor loss.
SOURCES OF ERRORS
 Parallax
 Fluctuation of liquid level in manometer
 Timing error while recording the quantity of discharge
 Approximately of value in calculationCONCLUSIONGenerally change in direction of fluid flow have always brought loss, but the loss brought about by the bends varies from high head loss in sharply bend to minimum losses in slightly bent pipes.The loss is highly brought about by the reaction which is exerted by water flowing at the bend.Also verification of BordaCarnot equation has proved some failure since the value are neither close nor the same. This was caused by assuming that losses due to friction were not present in the pipes.