What volume of water can a pump with a power of 50 kW pump out of a mine with a depth of 150 m in 1 hour?

Initial data: t (duration of pump operation) = 1 h (3600 s); N (pump power) = 50 kW (50 * 10 ^ 3 W); h (shaft depth) = 150 m.

Reference data: ρ (density of water pumped out of the mine) = 1000 kg / m3; g (acceleration due to gravity) ≈ 10 m / s2.

The volume of pumped water is determined from the formula: N = A / t = ΔEp / t = m * g * h / t = ρ * V * g * h / t, whence V = N * t / (ρ * g * h).

Calculation: V = 50 * 10 ^ 3 * 3600 / (1000 * 10 * 150) = 120 m3.

Answer: The pump will be able to pump 120 m3 of water out of the mine.