A pump motor is used to deliver water at a certain rate from a given pipe. To obtain ‘n’ times water from the same pipe in the same time, by what amount the power of the motor should be increased?

Question

Infinity Learn · Accepted Answer

If a liquid of density ρ is flowing through a pipe of $$cross-section$$ A at speed V, the mass coming out per second will be: (dmdt) $$=$$ AVρIn order to get n times water in the same time.(dmdt)' $$=$$ $$n(dmdt)$$ i.e.,A'V'ρ' $$=$$ nAVρBut as pipe and liquid are same, so ρ'$$=$$ ρ, A' $$=$$ A  v' $$=$$ NVSo F' F   $$=$$ V'(dmdt)V(dmdt) $$=$$ $$nV(ndmdt)V(dmdt)$$  $$=$$ $$n2or$$ F' $$=$$ $$n2F$$  P'$$P=$$ F'V'FV $$=$$ $$(n2F)(nV)FV$$ or P' $$=$$ $$n3P$$

A pump motor is used to deliver water at a certain rate from a given pipe. To obtain ‘n’ times water from the same pipe in the same time, by what amount the power of the motor should be increased?

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