Question

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 (a) the force (b) power of the motor be increased? Ans:(a) n^2. (b) n^3.

Answer 1

P=Work/time

We know,KE=0.5×m×v^2

mass of water pumped=

Area of C.S × velocity × time × density

=>A × p × v × t

Therefore total energy, i.e KE

=>0.5 × A ×p × v^3 × t

Power=K.E/t

This gives that Power

=0.5 × v^3 × p × A

Therefore Power is directly proportional to v^3.

So if water is made n times,

Velocity also becomes n times.

Therefore power is increased by n^3