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For a hydraulic turbine operating at two different heads, the ratio of their speeds will be 3: 1. For the two heads, the ratio of the shaft power developed by the turbine will be:
  • a)
    9 : 1
  • b)
    243 :1
  • c)
    3 : 1
  • d)
    27 : 1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For a hydraulic turbine operating at two different heads, the ratio of...
In order to predict the behaviour of a turbine working under a varying condition of head, speed output, etc, the results are expressed in terms of quantities that may be obtained when the head on the turbine is reduced to unity.
The following are three important unit quantities.

Calculation:
Given:
N1/N2 = 3/1
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Most Upvoted Answer
For a hydraulic turbine operating at two different heads, the ratio of...
Ratio of Speeds:
The given ratio of speeds for the hydraulic turbine operating at two different heads is 3:1. This means that the speed of the turbine is three times higher at one head compared to the other head.

Ratio of Shaft Power:
When the speed of a turbine changes, the power developed by the turbine also changes. The power developed by a turbine is directly proportional to the cube of the speed. Therefore, if the speed of the turbine changes by a certain ratio, the power developed by the turbine will change by the cube of that ratio.

Calculating the ratio of shaft power:
Given that the ratio of speeds is 3:1, the ratio of the cube of speeds will be (3^3):(1^3) = 27:1. This means that the ratio of the shaft power developed by the turbine at the two different heads will be 27:1.
Therefore, the correct answer is option d) 27:1.
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For a hydraulic turbine operating at two different heads, the ratio of their speeds will be 3: 1. For the two heads, the ratio of the shaft power developed by the turbine will be:a)9 : 1b)243 :1c)3 : 1d)27 : 1Correct answer is option 'D'. Can you explain this answer?
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