In the mine at a depth of 100m, 4.3m3 of water is accumulated every minute.

In the mine at a depth of 100m, 4.3m3 of water is accumulated every minute. how much power does the pump need to pump it out?

h = 100 m.

g = 9.8 m / s2.

t = 1 min = 60 s.

V = 4.3 m3.

ρ = 1000 kg / m3.

N -?

We will express the pump power N by the formula: N = A / t, where A is the work of the pump to raise the water, t is the time of work.

If we consider the rise of water to be uniform rectilinear, then work A can be expressed by the formula: A = m * g * h, where m is the mass of water that was lifted, g is the acceleration of gravity, h is the depth of the mine.

We find the mass of water m by the formula: m = ρ * V, where ρ is the density of water, V is the volume of water that was raised.

A = ρ * V * g * h.

The formula for determining the pump power N will take the form: N = ρ * V * g * h / t.

N = 1000 kg / m3 * 4.3 m3 * 9.8 m / s2 * 100 m / 60 s = 70233 W.

Answer: to pump out water, you need a pump with a power of N = 70233 W.