Question

How long does a 50 kW pump motor have to run to pump 500 cubic meters of water from a 180m deep mine

Answer 1

Answer:

t = 17658 s = 294.3 min = 4.9 h

Explanation:

The general formula for power is:

$P = \frac{W}{t}$

where,

P = Power of the Motor = 50 KW = 50000 W

W = Work Done by Motor = Change in P.E of Water = mgh

g = acceleration due to gravity = 9.81 m/s²

m = mass of  water = ρV

h = depth of water = 180 m

ρ = density of water = 1000 kg/m³

V = Volume of Water = 500 m³

t = time taken = ?

Therefore,

$P = \frac{mgh}{t}=\frac{\rho Vgh}{t}\\\\t = \frac{\rho Vgh}{P}\\\\t = \frac{(1000\ kg/m^3)(500\ m^3)(9.81\ m/s^2)(180\ m)}{50000\ W}$

t = 17658 s = 294.3 min = 4.9 h