# From the dam of the hydroelectric power station, water falls every minute with a volume of 600 m

From the dam of the hydroelectric power station, water falls every minute with a volume of 600 m (3 degrees). The height of the dam is 8 m. Determine the power developed by the flow of falling water. The density of water is 1000 kg / m (3 degrees)

t = 1 min = 60 s.
V = 600 m ^ 3.
h = 8 m.
ρ = 1000 kg / m ^ 3.
g = 9.8 m / s ^ 2.
N -?
Power N is a physical quantity that characterizes the speed of performing work A and is determined by the formula: N = A / t, where t is the time of performing work A.
We will find work A by the change in the potential energy of water when it falls: A = ΔEp.
The change in potential energy ΔЕп is found by the formula: ΔЕп = m * g * h, m is the mass of the fallen water, g is the acceleration of gravity, h is the height of the fall of water.
We find the mass of water m by the formula: m = ρ * V.
The formula for determining the power will take the form: N = ρ * V * g * h / t.
N = 1000 kg / m ^ 3 * 600 m ^ 3 * 9.8 m / s ^ 2 * 8 m / 60 s = 784000 W.
Answer: the power of the dam is N = 784000 W.

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