The specific speed of a pump is defined as the speed of a unit of such...
The specific speed of a pump is defined as speed at which pump generates unit discharge under unit head.

where Q=discharge, H=head, N
s= specific speed, N= speed of pump.
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The specific speed of a pump is defined as the speed of a unit of such...
Specific Speed of a Pump
The specific speed of a pump is a dimensionless number that characterizes the geometry and performance of a centrifugal pump. It is defined as the speed of a unit of such a size that it discharges unit volume at unit head. In other words, it is the speed at which a pump would have to run in order to deliver a unit volume of fluid at a unit head.
Explanation:
a) Unit Discharge at Unit Power:
If the specific speed was defined as the speed at which a pump would have to run in order to discharge unit volume at unit power, it would mean that the pump is delivering a certain amount of power to move the fluid, regardless of the head. This would not be a suitable definition for specific speed because it does not take into account the head requirement.
b) Unit Work at Unit Head Loss:
If the specific speed was defined as the speed at which a pump would have to run in order to deliver unit work at unit head loss, it would mean that the pump is delivering a certain amount of work to overcome the head loss in the system, regardless of the discharge. This would not be a suitable definition for specific speed because it does not take into account the volume requirement.
c) Unit Discharge at Unit Head:
The correct definition of specific speed is the speed at which a pump would have to run in order to deliver unit discharge at unit head. This means that the pump is delivering a certain volume of fluid at a certain head, which is the most practical and relevant parameter for pump selection and performance evaluation. By using this definition, pumps of different sizes and capacities can be compared and analyzed based on their specific speed values.
d) Unit Volume at Unit Time:
If the specific speed was defined as the speed at which a pump would have to run in order to deliver unit volume at unit time, it would mean that the pump is delivering a certain volume of fluid in a certain amount of time, regardless of the head. This would not be a suitable definition for specific speed because it does not take into account the head requirement.
Therefore, the correct answer is option 'C' - unit discharge at unit head.