UNIVERSITY OF DAR ES SALAAM
DEPARTMENT OF WATER RESOURCES ENGINEERING
FLUID MECHANICS FOR CIVIL ENGINEERS
WR 211 PRACTICAL No: 1
HEAD LOSSES IN SMALL BORE PIPE SYSTEMS
NAME: BILALI AHMAD
REGISTRATION NO: 2020-04-00746
DEGREE PROGRAMME: BSc. IN MINING ENGINEERING
DEPARTMENT: WATER RESOURCES ENGINEERING
DATE OF SUBMISSION: 23 DECEMBER 2022
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
HL =KL V2/ 2g
In which KLis known as the loss coefficient. For geometry, the value if KL 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
Part 1: To examine the minor energy head losses(i.e shock losses) for;
1. 900 elbow bend (small radius)
2. 900 mitre bend
3. 900 large radius bend
Verify that; hshock
∆h
=∆h
=K
Part 2: To show that shock losses due to sudden contraction are also proportional to the velocity
head and to calculate the coefficient of contraction.
hL=K.V2/2g= (1/CC-1)2.V2/2g
where CC is the coefficient of contraction.
The graph of hfvs v2/2g would be drawn to verify the value of K.
Part 3: To confirm the Borda –Carnot equation for head loss in a sudden expansion from the
experimental results.
Note:Borda-Carnot equations is obtained by using 3-equations.These equations are:
 Continuity equation
 Momentum equation
 Energy equation.
The Borda-Carnot equations for Head losses is given by:
HL =
(
)
APPARATUS
 Hydraulic circuit: It consists of Piezometer tappings and thus pressure changes across
each of the components are measured by a pair of pressurized piezometer tubes.
 Hydraulic bench: Used to circulate and measure volume of water in litres.
 Stop watch:Was used to record the time taken to measure a particular volume
Piezometric apparatus and its block diagram
PROCEDURE
The pump was started and the bench supply and apparatus valves were opened. Water
was allowed to flow for some 2 minutes.
The apparatus control valve was then partially closed and the manometer was purged in
using the vent valve. The apparatus control valve was then closed.
Air was then pumped into the manometer to obtain zero pressure differences in the
piezometer tubes at the convenient level. And six readings for Q (discharge) and H diff
(pressure head difference) was recorded,Hdiff being reduced in equal decrements.
DATA COLLECTION
Given the following;
Pipe Diameter D1 = 22.5mm
Pipe Diameter D 2 = 29.6mm
A1 = 3.98 X 10-4m2
A 2= 6.88 X 10-4m2
PIPE SYSTEM: PIEZOMETRIC HEAD LOSSES AT VARIOUS RATES OF FLOW
Pipe diameter D1= 22.5mm
Pipe diameter D2= 29.6mm
Data Sheet
VOLUME
TIME
MITRE
ELBOW
SUDDEN
SUDDEN
V
(T)
BEND
BEND
(L)
(sec)
Hdiff
Hdiff
Hdiff
Hdiff
BEND
1-2
3-4
5-6
7-8
Hdiff
(m)
(m)
(m)
(m)
9-10
ENLARGEMENT CONTRACTION
LARGE
RADIUS
(m)
5
10.59
0.14
0.095
-0.04
0.095
0.06
5
12.80
0.115
0.08
-0.035
0.08
0.05
5
15.21
0.095
0.066
-0.025
0.069
0.042
5
15.70
0.075
0.055
-0.020
0.060
0.032
5
20.81
0.055
0.045
-0.015
0.045
0.025
5
22.21
0.045
0.035
-0.010
0.030
0.020
5
31.63
0.03
0.025
-0.003
0.025
0.015
5
41.98
0.02
0.02
-0.001
0.015
0.010
Note
The negative sign indicate that there is sudden enlargement
Table of results
Where;
Velocity (Velocity in D1 pipe) V = Q/A1
Discharge
Q X 10
-4
Velocity in
D1 pipe
3
(m /s)
Velocity Head
2
V /2g
V
(m)
(m/s)
Pressure
Sudden
Sudden
Change
Enlargement
Contraction
Hshock=
Hshock=
0.034V2-Hdiff
Hdiff-0.034V2
(m)
(m)
0.034V
(m)
2
4.72
1.19
0.072
0.048
0.008
0.047
3.91
0.99
0.050
0.033
-0.002
0.047
3.29
0.83
0.035
0.022
-0.003
0.047
3.19
0.80
0.033
0.022
0.002
0.038
2.40
0.60
0.018
0.012
-0.003
0.033
2.25
0.57
0.017
0.011
-0.001
0.02
1.58
0.40
0.008
0.005
0.002
0.02
1.19
0.30
0.004
0.003
0.002
0.012
GRAPHS AND ANALYSIS FROM THE GRAPHS
THE GRAPH OF HSHOCK(M) AGAINST V2/2g(M) FOR
THE METRE BEND, ELBOW AND LARGE RADIUS
0.16
y = 1.817x + 0.018
0.14
Hshock(m)
0.12
y = 1.138x + 0.018
0.1
0.08
METRE BEND
y = 0.755x + 0.009
0.06
ELBOW
LARGE RADIUS
0.04
0.02
0
0
0.01
0.02
V2/2g
0.03
The value of k for mitre bend is 1.817
The value ofk for elbow bend is 1.138
The value of k for large radius bend is 0.755
0.04
0.05
0.06
0.07
0.08
THE GRAPH OF HSHOCK(M) AGAINST V2/2g(M)
FOR THE SUDDEN CONTRACTION
0.06
0.05
y = 0.532x + 0.017
Hshock(m)
0.04
0.03
Series1
Linear (Series1)
0.02
0.01
0
0
0.02
0.04
0.06
Axis Title
From the graph the value of k=0.532
ANALYSIS AND CALCULATIONS
From the graph above; K = 0.532
But K =
Thus
−1
=0.6984 where Cc = coefficient of contraction
= √0.532 + 1
∴ 𝐂𝐜 = 𝟎. 𝟓𝟕𝟖2
The coefficient of contraction,Cc is 0.531
0.08
THE GRAPH OF HSHOCK(M) AGAINST V2/2g (M)
FOR THE SUDDEN ENLARGEMENT.
0.01
0.008
Hshock(m)
0.006
0.004
0.002
y = 0.065x - 0.001
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-0.002
-0.004
V2/2g(m)
From the graph the value of k=0.065
ANALYSIS AND CALCULATIONS
To confirm the Borda –Carnot equation for head loss in sudden expansion from experimental
results
HL = (V1 – V2)2
2g
From continuity equation
V2 =A1V1/ A2
hL = (V1-{ A1V1/A2})2
2g
hL= (1 - A1/A2)2V12
2g
hL=kV2
2g
But A2 = 688.1mm2, A1 = 398.mm2
k= (1 – (398mm2/688.1mm2)) 2
The theoretical value of k is 0.178
From the graph the value of k is 0.065
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 calculation
CONCLUSION
Generally 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 Borda-Carnot 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.