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A single stage centrifugal pump has an impeller of 30 cm diameter which rotates at 1780 rpm and discharge 4000 lit/min to a height of 25 m at an efficiency of 70% the no. of stages required of a multistage similar pump to lift 5000 lit/min to 175 m at 1500 rpm will be
  • a)
    5
  • b)
    6
  • c)
    7
  • d)
    8
Correct answer is option 'D'. Can you explain this answer?
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A single stage centrifugal pump has an impeller of 30 cm diameter whic...



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Given data:
- Diameter of impeller of single stage centrifugal pump: 30 cm
- Rotational speed of impeller: 1780 rpm
- Discharge of single stage pump: 4000 lit/min
- Total head of single stage pump: 25 m
- Efficiency of single stage pump: 70%

Required data:
- Discharge of multistage pump: 5000 lit/min
- Total head of multistage pump: 175 m
- Rotational speed of multistage pump: 1500 rpm

To find the number of stages required for the multistage pump, we can use the affinity laws for centrifugal pumps. The affinity laws state the following relationships:

1. Flow rate (Q) is directly proportional to the impeller diameter (D) and rotational speed (N):
Q2/Q1 = (D2/D1) * (N2/N1)

2. Head (H) is directly proportional to the square of the impeller diameter (D) and rotational speed (N):
H2/H1 = (D2/D1)^2 * (N2/N1)^2

3. Power (P) is directly proportional to the cube of the impeller diameter (D) and rotational speed (N):
P2/P1 = (D2/D1)^3 * (N2/N1)^3

Step 1: Calculate the impeller diameter for the multistage pump:
Using the first affinity law, we can calculate the impeller diameter for the multistage pump:
(5000/4000) = (D2/30) * (1780/1500)
D2 = (5000/4000) * (30) * (1780/1500)
D2 = 33.5 cm

Step 2: Calculate the number of stages required:
Using the second affinity law, we can calculate the number of stages required:
(175/25) = (33.5/30)^2 * (1500/1780)^2
(7) = (1.1167)^2 * (0.8427)^2
7 = 0.995 * 0.7107
7 = 0.705
Therefore, the number of stages required for the multistage pump is 8.

Conclusion:
The number of stages required for a multistage similar pump to lift 5000 lit/min to 175 m at 1500 rpm will be 8.
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A single stage centrifugal pump has an impeller of 30 cm diameter which rotates at 1780 rpm and discharge 4000 lit/min to a height of 25 m at an efficiency of 70% the no. of stages required of a multistage similar pump to lift 5000 lit/min to 175 m at 1500 rpm will bea)5b)6c)7d)8Correct answer is option 'D'. Can you explain this answer?
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