A motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver n -times the water through the same pipe in the same time the power of the motor must be increased as follows :

Step-by-step solution

If the motor pumps water (density = ) continuously through a pipe of area of crosssection A with velocity v , then mass flowing out per second, m=A v ...(i) Rate of increase of kinetic energy = 1 2 m v^2= 1 2 (A v ) v^2 ..(ii) Mass m , flowing out per sec, can be increased to m^ by increasing v to v^ , then power increases from P to P^ . P^ P = 1 2 A v^3 1 2 A v^3 or P^ P = ( v^ v )^3 Now m^ m = A v^ A v = v^ v As m^ =n m, v^ =n v P^ P =n^3 P^ =n^3 P