The answer to this question depends on many factors, such as the type of pump, the design of the pump, the drain line, how the valve is closed, the valve closed, and so on.
For industrial Centrifugal pump, minimum recirculation line is provided (highly recommended) from the pump discharge line to the suction vessel with control valve or RO (continuous recirculation). If discharge valve (not far from the pump) of such pump is closed, flow transmitter will sense that the flow is decreased in the pump discharge and it will open the control valve in the minimum recirculation line to maintain minimum flow from this pump. In this case there will be no effect of valve closure on the pump or on the discharge line.
For the Fire fighting pumps or similar other pumps which has comples network of pipeline in the whole plant and which dont have minimum recirculation line, we will see what will be the effect of valve closure. If we close the valve on the discharge line which is near to the pump, pump will run at its shut off head and it will increase the temperature of fluid which will result in cavitation. If we closed the valve, far away from the pump in the network where no other users are active, and speed of closure of valve is slow, pump will run at its shut off head and it will increase the temperature of fluid which will result in cavitation.
If we closed the valve, far away from the pump in the network where no other users are active, and that too very quickly, there is a huge chances of water hammering.
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