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RESULTS
Table 1: Data measured for the 28 x 1mm Cu pipe (Pipe 1, d=26mm)
Flow rate /m
3
h
-1
Upstreampressure /m
Downstreampressure /m
Pressuredifference (=Head
loss due to
friction, Hf)/m
4.0 0.452 0.205 0.247
3.0 0.378 0.230 0.148
2.0 0.322 0.249 0.073
Flow rate /L h-1 Upstreampressure /m
Downstreampressure /m
Pressuredifference (=Head
loss due to
friction, Hf)/m
500 0.270 0.264 0.006
250 0.267 0.265 0.002
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Table 2: Data measured for the 18 x 1mm Cu pipe (Pipe 2, d=16mm)
Flow rate /m3h
-1 Upstream pressure /m Downstream pressure
/m
Pressure difference
(=Head loss due to
friction, Hf)/m
2 0.570 0.350 0.220
1 0.418 0.143 0.275
Flow rate /L h-1
Upstream pressure /m Downstream pressure
/m
Pressure difference
(=Head loss due to
friction, Hf)/m
500 0.329 0.240 0.089
400 0.300 0.248 0.052
300 0.331 0.271 0.060
100 0.329 0.279 0.050
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Table 3: Data measured for the St galvanized pipe (Pipe 3, d=16mm)
Flow rate /L h-1
Upstream pressure /m Downstream pressure
/m
Pressure difference
(=Head loss due to
friction, Hf)/m
500 0.469 0.224 0.245
400 0.423 0.270 0.153
300 0.396 0.308 0.088
200 0.374 0.335 0.039
Flow rate /m3h
-1 Upstream pressure /m Downstream pressure
/m
Pressure difference
(=Head loss due to
friction, Hf)/m
0.4 0.504 0.190 0.314
d
Table 4: Results calculated for mean velocity (u) and Reynolds number (Re)
Pipe Area of pipe/m2 Volumetric Flow
(Q)/m3s-1
Uniform velocity of
flow (u)/ms-1
Reynolds Number
1 5.31 x 10-4 11.20 x 10-4 2.11 61364.65
8.34 x 10-4 1.57 45659.96
5.56 x 10-4
1.05 30536.91
1.39x 10-4
0.26 7561.52
0.70 x 10 -4 0.13 3780.76
2 2.01 x 10 -4 5.56 x 10-4 2.77 49574.94
2.78 x 10-4
1.38 24697.99
1.39 x 10-4
0.69 12348.99
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1.11 x 10-4 0.55 9843.40
8.34 x 10-5 0.41 7337.81
2.78 x 10-5
0.14 2505.59
3 2.01 x 10-4
1.11 x 10-4
0.55 9843.40
1.39 x 10-4 0.69 12348.99
1.11 x 10-4 0.55 9843.40
8.34 x 10-5
0.41 7337.81
5.56 x 10-5 0.28 5011.19
Table 5: Results calculated for experimental friction factor, theoretical friction factor and Reynolds
number for each pipe
Pipe Head loss due
to friction, Hf
/m
Reynolds
Number
Typical
Roughness
Height (k)/m
Theoretical
Friction Factor
Experimental
Friction Factor
(Darcys Friction
Factor)
1 0.247 61364.65 0.001 x 10-3
0.019904 0.02177
0.148 45659.96 0.021236 0.023561
0.073 30536.91 0.02329 0.025982
0.006 7561.52 0.033433 0.034828
0.002 3780.76 0.04117 0.046438
2 0.220 49574.94 0.020921 0.006924
0.275 24697.99 0.024545 0.03487
0.089 12348.99 0.029241 0.045141
0.052 9843.40 0.031082 0.04151
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0.060 7337.81 0.033743 0.08619
0.050 2505.59 0.047122 0.616013
3 0.245 9843.40 0.1 x 10-3
0.031082 0.195576
0.153 12348.99 0.029241 0.077601
0.088 9843.40 0.031082 0.070248
0.039 7337.81 0.033743 0.056024
0.314 5011.19 0.037746 0.96714
Table 6: Results calculated to plot a graph of log against log Re for each pipe
Pipe Reynolds number,
Re
Log (Re) Theoretical
friction factor
Log( )
1 61364.65 4.787918 0.019904 -1.70106
45659.96 4.659536 0.021236 -1.67293
30536.91 4.484825 0.02329 -1.63283
7561.52 3.878609 0.033433 -1.47582
3780.76 3.577579 0.04117 -1.38542
2 49574.94 4.695262 0.020921 -1.67942
24697.99 4.392662 0.024545 -1.61004
12348.99 4.091631 0.029241 -1.53401
9843.40 3.993145 0.031082 -1.50749
7337.81 3.865566 0.033743 -1.47182
2505.59 3.39891 0.047122 -1.32678
3 9843.40 3.993145 0.031082 -1.50749
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12348.99 4.091631 0.029241 -1.53401
9843.40 3.993145 0.031082 -1.50749
7337.81 3.865566 0.033743 -1.47182
5011.19 3.699941 0.037746 -1.42313
SAMPLE CALCULATIONS
Converting Lh-1to m3h-1
1m3= 1000000 cm
3
But 1L = 1000cm3
1m3= 1000L
1L= 10-3m3 If Q= 600 Lh
-1,
then Q= (600 x 10-3) =0.6m3h-1
Converting m3h
-1to m
3s
-1
1 h= 3600s
1h-1=(1/3600)= 2.78 x 10-4
If Q= 0.6m3h
-1,
Then Q= 0.6 x (2.78 x 10-4
) = 1.67 x 10-4
m3s
-1
Calculating uniform velocity of flow (u) in ms-1
Re: Q= u A
u= Q/A
A= r2= (0.013)
2= 5.31 x 10
-4m
2(For pipe 1)
For Q= 1.67 x 10-4
and A= 5.31 x 10-4
m2,
u= (1.67 x 10-4)/ (5.31 x 10-4)
u= 0.315 ms-1
Calculating Reynolds Number
v
udRe , where v=0.894 x 10-6for water at 25oC
For u=0.315, d=0.026m and v= 0.894 x 10-6
,
07.916110894.0
)026.0)(315.0(Re
6
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Calculating the Theoretical Friction Factor ( )
Recall Haalands Relationship:
11.1
71.3Re
9.6
log8.1
1
d
k
where is the friction factor for the pipe
k is the typical roughness height (m)
Re is Reynolds number
d is the diameter of the pipe
For Cu pipe of diameter 0.026 m, k=0.001 x 10-3
, Re=9161.07
1 = -1.8 log {[6.9/9161.07]+[0.001 x 10-3/3.71(0.026)]1.11}
= -1.8 log {(0.000753) + (0.000010366)1.11}
= -1.8 log (0.000753 + 0.000002933)
=-1.8(-3.12)
=5.616
= 1/(5.616) = 0.178
= (0.178)2= 0.0317
Calculating the Experimental Friction Factor( )Recall Equation to calculate Darcy Friction Factor:
2
2
Lu
gdhf
where L is the length of the pipes under study= 1.3m
hfis head loss due to friction
g is acceleration due to gravity = 9.81 m2s
-1
d is diameter of the pipe
u is the uniform velocity of flow
For hf= 0.025, d= 0.026m, u=0.315 ms-1
= [(0.025)x2(9.81)(0.026)] /[(1.35)(0.315)2]
= (0.012753)/(0.13396)
=0.0952
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Calculating for the Cu (28x1mm) pipe
Average Re= (7619.69 + 9161.07 + 15239.37 + 30536.91 + 45659.96)/ 5
= 21643.4
Using the Haaland Equation,
1
= -1.8 log {(6.9/21643.4) + [(0.001x10-3)/ (3.71)(0.026)]1.11}
= -1.8 log [(3.19x10-4)+ (2.933x10-6)
=-1.8 log (3.22x10-4
)
=-1.8(-3.492)
=6.286
= [1/ (6.286)]2
= (0.159)2
= 0.0253
Average hf=(0.005+ 0.025+ 0.043 + 0.10+ 0.175)/5
=0.0786
Average U= (0.262+ 0.315+ 0.524+ 1.05 +1.57)/5
= 0.744 ms-1
Using equation for the Darcy Friction Factor,
= {(0.0786)(2)(9.81)(0.026)/[(1.35)(0.744)2
]}
= (0.0401)/(0.747)
=0.0537
Calculating for the Cu (18 x 1mm) pipe
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Average Re= (4957.49 + 7409.40 + 9879.19 + 14872.48 + 49574.94)/ 5
= 17338.7
Using the Haaland Equation,
1
= -1.8 log{(6.9/17338.7) + [(0.001X10-3
)/(3.71x 0.016)]1.11
}
= -1.8 log[(3.98x10-4
) + (5.028x10-6
)]
= -1.8 log(4.03x10-4)
= -1.8(-3.395)
=6.111
= [(1/6.111)2]
= (0.164)2
= 0.0269
Average hf= (0.008+ 0.002 +0.031 +0.085 +0.233)/5
= 0.0718
Average U= (0.277 +0.414 +0.552 +0.831 +2.77)/5
= 0.969 ms-1
Using the equation for Darcy Friction Factor,
= {[(0.0718)(2)(9.81)(0.016)]/[(1.35)(0.969)2]}
= (0.0225)/(1.27)
= 0.0177
Calculating for the St galvanized pipe
Average Re= (2469.80 + 4957.49+ 7409.40+ 9879.19 +14872.48)/5
= 7917.7
Using the Haaland Equation,
1
= -1.8 log{(6.9/7917.7) + [(0.1x10-3
)/(3.71 x 0.016)]1.11
}
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= -1.8 log[(8.71x10-4) + (8.344x10-4)]
= -1.8 log(1.71x10-3)
=-1.8(-2.768)
=4.982
= [(1/4.982)2]
= (0.201)2
=0.0404
Using the equation for Darcy Friction Factor,
Average hf= (0.008+ 0.023+ 0.058+ 0.107+ 0.355)/5
= 0.110
Average U= (0.138+ 0.277+ 0.414 + 0.552+ 0.831)/5
= 0.442 ms-1
= {*(0.110)(2)(9.81)(0.016)]/[(1.35)(0.442)2]}
= [(0.0345)/(0.264)]
=0.131
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-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
log()
log (Re)
Graph 1 showing logvs log Re for all three pipes
Cu pipe (18x1)
Cu pipe(28x1)
1/2'' St galvanized pipe
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
log()
log (Re)
Graph 1 showing logvs log Re for Cu pipe (18x1)
Cu pipe (18x1)
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-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
0.015 0.02 0.025 0.03 0.035 0.04 0.045
log()
log (Re)
Graph 1 showing logvs log Re for Cu pipe (28x1)
Cu pipe(28x1)
-1.6
-1.55
-1.5
-1.45
-1.4
-1.35
-1.3
-1.25
-1.2
0.015 0.02 0.025 0.03 0.035 0.04
log()
log (Re)
Graph 1 showing logvs log Re for all three pipes
1/2'' St galvanized pipe