Correct Answer - Option 4 : 17.75 lps
Concept:
Centrifugal pumps have a rotating impeller also known as a blade that is immersed in the liquid. Liquid enters the pump near the axis of the impeller, and the rotating impeller sweeps the liquid out toward the ends of the impeller blades at high pressure.
When two centrifugal pumps are connected in series, or connected along a single line, the head is added together and a high head is developed. This is because the fluid pressure increases as the continuous flow pass through each pump, much like how a multi-stage pump works. So pumps in series operation allow the head to increase.
When the Pumps in parallel operation increase the flow rate and head remains the same.
So as the pumps are in series the head will increase.
Manometric Head (Hm): The manometric head is defined as the head against which a centrifugal pump has to work. It is given by the following expressions:
- Hm = Suction Head (hs) + Delivery Head (hd) + Friction head loss in the suction pipe (hfs) + Friction head loss in the Delivery pipe (hfd) + Velocity head of water in the delivery pipe (V2/2g)
For flow to take place Total Manometric head available > Net Manometric head Required.
Calculation:
Here the pump is operated for various discharge and the discharge for which the Total available head is approximately equal to the Net Manometric head required will be the closest value of discharge. Doing tabular calculations for Total head and Net Manometric head required:
Q
|
Total Manometric head available
|
Net Manometric head Required = Static head + Head loss = 80 + Q2/120
|
12
|
50.2 + 42.4 = 92.6
|
81.2
|
14
|
52.8 + 38.8 = 91.6
|
81.63
|
16
|
51.3 + 35.7 = 87
|
82.13
|
18
|
50 + 32 = 82
|
82.7
|
20
|
30 + 25 = 55
|
83.33
|
From the table, the value of the Total available head and Net Manometric head required is closest in the discharge range 16 - 18.
For Q = 18 lps, the Net Manometric head > Total available head and hence this value cannot be adopted and adopting a smaller value of discharge, by hit and trial method, for Q = 17.5 lps
Required Net Manometric head corresponding to 17.5 lps,
\(H=80+\frac{{{17.5}^{2}}}{120}\)= 82.55
By linear interpolation, Total Manometric head available = 83.25 m
Increasing this discharge further will lead to Net Manometric head greater than 82.55 and Total Manometric head lesser than 83.25 which will be the most efficient condition.
The only correct option in the range is 17.75 lps.