Question

A motor is pumping water with a velocity of 20 ms-1 from a pump of area of cross section 20cm?Its average power is,
(A) 8 KW
(B) 12 kW
(C) 16 kW
(D) 4kW​

Answer 1

Power

Rate of doing work is called as power or we can say it as Capacity to do work. It is a scalar quantity. SI unit of Power is “Watt”, named after the scientist who discovered it. From definition we can write formula of power as :

$\\ \LARGE \bullet \boxed{\rm{Power\ =\ \dfrac{Work\ done}{time}}}$

Let's move ahead to given question,

• Velocity = 20 m/s
• Area = 20 cm = 0.2 m

$\longrightarrow$ P = Work Done/Time

$\longrightarrow$ P = Change in kinetic energy/time

$\longrightarrow$ P = [(1/2)mv²]/t

$\longrightarrow$ P = [1/2 * (volume * density) * v²]/t

$\longrightarrow$ P = [½ * (Area * length * density)*v²]/t

$\longrightarrow$ P = (½ * 20 * 1 * 1 * 20²)/1

$\longrightarrow$ P = (10 * 400)

$\longrightarrow$ P = 4000 W

$\longrightarrow$ P = 4000/1000

➾ Power = 4 kW