ENGIN1002 Engineering Physics Assignment - Federation University, Australia
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Question 1 - Determine the pipe friction factor for flow of water through a 1m diameter old PVC pipe at an average velocity of 1.5 m/s with an equivalent sand grain roughness of 2 mm. State assumptions made and provide any charts used to arrive at the calculations.
Solution - Pipe friction factor = ? =f
Diameter = 1m
Average velocity = 1.5 m/s
Equivalent sand grain roughness = 2mm
Reynold Number = Re = pvD/μ
= 1000 x 1.5 x 1/ 8.9 x 0.0001 = 1685393 => Turbulent flow
Completely turbulent flow :
F = [1.14+2 log10(D/ε)]-2
= [1.14+2 log10(1000/2)]-2
[1.14+2 log10 500]-2 = 0.0234
Question 2 - A pipe reducer has dimensions of 300mm and 150mm at inlet and outlet. Find the force required to hold this in position if the pressure at the smaller exit end is 250 kPa for a discharge of 200 litres/sec. State assumptions made and provide diagram.
Solution - Bernoulli's equation:
We assume both inlet and outlet are at same height.
A1u1 = A2u2 = Q = 200L/s = 0.2 m3/s
P1+0.5pu12 = P2+0.5pu22
P1 = 252.16 kPa (By solving)
Force = P1A1 = 7.126 N
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Question 3 - Using the following pump characteristics, construct a Q-H and efficiency curve and determine how much power is required to drive the pump when Q = 0.08 m3/s.
Solution -
|
e(%)
|
H(m)
|
Q(m3/s)
|
|
|
|
|
0
|
56
|
0
|
|
25
|
55
|
0.01
|
|
45
|
54
|
0.02
|
|
60
|
52
|
0.03
|
|
64
|
49
|
0.04
|
|
62
|
42
|
0.05
|
|
48
|
34
|
0.06
|
|
32
|
20
|
0.07
|
|
18
|
8
|
0.08
|
QH Curve
Efficiency Curve:
Power needed = P = QHgp/n
Q= 0.08m3/s, H = 8m, p = density of water = 1000 kg/m3, n = efficiency = 18% = 0.18
P = 0.08*8*9.81*1000/0.18 = 34.88 kW
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