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Two geometrically similar pumps are running at 1000 rpm speed (both). If one pump has impeller diameter of 0.3 m and discharges 20 lt/sec against 20 m head, and the other pump gives half of this discharge rate; calculate the head and diameter of second pump.
- a)12.5 m and 0.12 m
- b)10.5 m and 0.12 m
- c)10.5 m and 0.23 m
- d)12.5 m and 0.23 m
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two geometrically similar pumps are running at 1000 rpm speed (both)....
We know Q ? ND3
Substituting values gives us
D2 = 0.238
Similarly, H ? N2D2
H2 = 12.58
Most Upvoted Answer
Two geometrically similar pumps are running at 1000 rpm speed (both)....
To solve this problem, we can use the concept of similarity between the two pumps.
Given:
- The first pump has an impeller diameter of 0.3 m and discharges 20 liters/sec against 20 m head.
- The second pump has half the discharge rate of the first pump.
We need to find:
- The head and diameter of the second pump.
1. Discharge Rate:
Since the second pump has half the discharge rate of the first pump, the discharge rate of the second pump is 20/2 = 10 liters/sec.
2. Similarity between the Pumps:
The two pumps are geometrically similar, which means their corresponding dimensions are proportional. In this case, we can use the ratio of the impeller diameters to find the ratio of the heads.
3. Ratio of Impeller Diameters:
The ratio of the impeller diameters can be calculated as:
Diameter of second pump / Diameter of first pump = Discharge Rate of second pump / Discharge Rate of first pump
Let the diameter of the second pump be D.
D / 0.3 = 10 / 20
D = 0.15 m
4. Ratio of Heads:
The ratio of the heads can be calculated as:
Head of second pump / Head of first pump = (Diameter of second pump / Diameter of first pump)^2
Head of second pump / 20 = (0.15 / 0.3)^2
Head of second pump = 20 * (0.5)^2
Head of second pump = 20 * 0.25
Head of second pump = 5 m
Therefore, the head and diameter of the second pump are 5 m and 0.15 m respectively, which matches with option D.
Given:
- The first pump has an impeller diameter of 0.3 m and discharges 20 liters/sec against 20 m head.
- The second pump has half the discharge rate of the first pump.
We need to find:
- The head and diameter of the second pump.
1. Discharge Rate:
Since the second pump has half the discharge rate of the first pump, the discharge rate of the second pump is 20/2 = 10 liters/sec.
2. Similarity between the Pumps:
The two pumps are geometrically similar, which means their corresponding dimensions are proportional. In this case, we can use the ratio of the impeller diameters to find the ratio of the heads.
3. Ratio of Impeller Diameters:
The ratio of the impeller diameters can be calculated as:
Diameter of second pump / Diameter of first pump = Discharge Rate of second pump / Discharge Rate of first pump
Let the diameter of the second pump be D.
D / 0.3 = 10 / 20
D = 0.15 m
4. Ratio of Heads:
The ratio of the heads can be calculated as:
Head of second pump / Head of first pump = (Diameter of second pump / Diameter of first pump)^2
Head of second pump / 20 = (0.15 / 0.3)^2
Head of second pump = 20 * (0.5)^2
Head of second pump = 20 * 0.25
Head of second pump = 5 m
Therefore, the head and diameter of the second pump are 5 m and 0.15 m respectively, which matches with option D.
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Two geometrically similar pumps are running at 1000 rpm speed (both). If one pump has impeller diameter of 0.3 m and discharges 20 lt/sec against 20 m head, and the other pump gives half of this discharge rate; calculate the head and diameter of second pump.a) 12.5 m and 0.12 mb) 10.5 m and 0.12 mc) 10.5 m and 0.23 md) 12.5 m and 0.23 mCorrect answer is option 'D'. Can you explain this answer?
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Solutions for Two geometrically similar pumps are running at 1000 rpm speed (both). If one pump has impeller diameter of 0.3 m and discharges 20 lt/sec against 20 m head, and the other pump gives half of this discharge rate; calculate the head and diameter of second pump.a) 12.5 m and 0.12 mb) 10.5 m and 0.12 mc) 10.5 m and 0.23 md) 12.5 m and 0.23 mCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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