Q & A – Fluid Mechanics – Pump-Pipeline System Analysis & Design – Q.3

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Q & A – Fluid Mechanics – Pump-Pipeline System Analysis & Design – Q.3

Q & A – Fluid Mechanics – Pump-Pipeline System Analysis & Design – Q.3

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Question No.3

Topic : Pump-Pipeline System Analysis & Design

Calculate the steady discharge of water between the tanks in the system shown in the following figure and the power consumption. Pipe diameter Ds = Dd = 200 mm; length = 2,000 m; k = 0.03 mm (uPVC). Losses in valves, bends plus the velocity head amount to  6.2 v2 / 2g. Static lift = 10 m.

Pump Characteristics :

Discharge (l/sec)

0

10

20

30

40

50

Total Head (m)

25

23.2

20.8

16.5

12.4

7.3

Efficiency (per cent)

-

45

65

71

65

45

The efficiencies given are the overall efficiencies of the pump and motor combined.

Given :

  • Ds=Dd=200  mm=0.2  m
  • L=2,000  m
  • k=0.03  m
  • hminor=6.2v22g
  • Hs=10  m

Steps of solution :

The solution to such problems is basically to solve simultaneously the head-discharge relationships for the pump and pipeline :

For the pump, head delivered at discharge Q may be expressed by :

Hm=AQ2+BQ+C

For the pipeline, the head required to produce a discharge Q is given by :

Hm=Hs+hf+hminor

Hm=Hs+8fLπ2gD5Q2+Km2gA2Q2

A graphical solution is the simplest method and also gives the engineer a visual interpretation of the matching of the pump & pipeline.

First of all, we shall start with the system curve. Values of H corresponding to a range of Q values will be calculated.

To summarize the procedure for completing the previous table :

Flow velocity is calculated through :

v=QA=Qπ4D2 v=Qπ40.22

The kinematic viscosity for water is taken as :

ν=1.13106m2/sec

Reynolds number is calculated through :

Re=vDν=v0.21.13106

The roughness height for uPVC pipes is :

k=0.03  mm

To calculate the friction coefficient, Barr's equation is used :

1f=2logk/D3.7+5.1286Re0.89

The friction losses (using Darcy-Weisbach equation) occurring in the pipeline is calculated through :

hf=KQ2,K=8fLπ2gD5

To calculate the minor/secondary losses through the pipeline :

hminor=Km2gA2Q2

Finally, the total manometric head required is :

Hm=Hs+hf+hminor

The following graph shows the system curve for the previously tabulated values :

The following graph shows the pump characteristic curve (Head vs Discharge curve ) :

The computed system curve data and pump characteristic curve data are now plotted on the same graph as shown in the following figure :

The intersection point gives the operating conditions; in this case :

Qo=28  l/secHm=17.3  m

The operating efficiency is :

ηtotal=0.70

To calculate the power consumption :

Output  Power=γwQoHm=9,81028100017.3=4,751.964  Watt

ηtotal=Output  PowerInput  Power 0.70=4,751.964Input  Power

Input  Power=6,788.52  Watt=6.8  kW

 

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