The pump in a water tower raises water with a density of rhow = 1.00 kg/liter from a filtered pool at the base of the tower up hT = 21 m to the top of the tower. The water begins at rest in the pool and comes to rest at the top of the tower. The pump is 100% efficient in lifting the water, and it raises a volume of Vw = 6.2 liters of water up the tower every second. The water tower sits on a mound that is Te = 75 m above sea level. Let gravitational potential energy be zero at ground level.

Calculate the power. Pp in Watts, of the pump

Question

Physics

Cynthia Dunn

28 November, 00:26

The pump in a water tower raises water with a density of rhow = 1.00 kg/liter from a filtered pool at the base of the tower up hT = 21 m to the top of the tower. The water begins at rest in the pool and comes to rest at the top of the tower. The pump is 100% efficient in lifting the water, and it raises a volume of Vw = 6.2 liters of water up the tower every second. The water tower sits on a mound that is Te = 75 m above sea level. Let gravitational potential energy be zero at ground level.

Calculate the power. Pp in Watts, of the pump

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Answers (1)

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Ronnie Shepard · Answer 1

mass of the water being lifted per second

m = volume x density

= 6.2 x 1 = 6.2 kg

height by which water being lifted

h = 75 - 21

= 54 m

increase in potential energy of water per second

mgh

6.2 x 9.8 x 54

= 3281.04 J / s

= 3281.04 W.