A fountain consists of a large pool of water and a column of waterprojected upwa

Question

A fountain consists of a large pool of water and a column of waterprojected upward by means of a pump. The column has across-sectional area of 95 cm2at its base and reaches a height of 1.65m.
(a) Compute the speed of water as it leaves thepool.
1 m/s

Compute the flow rate of water as it leaves the pool.
2 liters/s

(b) Find the increase in mechanical energy per unit massE/m, as water starts from rest inthe pool and then is expelled by the pump.
3 J/kg

(c) Find the power supplied by the pump by computing the increasein mechanical energy per unit time.
4 W (a) Compute the speed of water as it leaves thepool.
1 m/s

Compute the flow rate of water as it leaves the pool.
2 liters/s

(b) Find the increase in mechanical energy per unit massE/m, as water starts from rest inthe pool and then is expelled by the pump.
3 J/kg

(c) Find the power supplied by the pump by computing the increasein mechanical energy per unit time.
4 W

Explanation / Answer

2 a s = 2 g s = vi2 v = (2 * 9.8 * 1.65) = 5.69 m/s V / t = A x / t = 95 cm2 *569 cm / sec / (1000 cm3 / L) = 54.1 L / s E = m * v2 / 2 E / m = v2 / 2 = 16.2 J / kg P = E / t = (m * v2 / 2) /t = (v2 / 2) * (m / t ) (m / t ) = V / t V / t = 1 kg / L * 54.1 L / s = 54.1 kg /sec P = (v2 / 2) * 54.1 kg /s = 876 J / sec = 876W v = (2 * 9.8 * 1.65) = 5.69 m/s V / t = A x / t = 95 cm2 *569 cm / sec / (1000 cm3 / L) = 54.1 L / s E = m * v2 / 2 E / m = v2 / 2 = 16.2 J / kg P = E / t = (m * v2 / 2) /t = (v2 / 2) * (m / t ) (m / t ) = V / t V / t = 1 kg / L * 54.1 L / s = 54.1 kg /sec P = (v2 / 2) * 54.1 kg /s = 876 J / sec = 876W

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