The pump in a water tower lifts water with a density of rho_w = 1.00 kg/liter fr

Question

The pump in a water tower lifts water with a density of rho_w = 1.00 kg/liter from a filtered pool at the bottom of the tower up h_T = 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 lifts a volume of V_w = 5.2 liters of water up the tower even second. The water tower sits on a hill that is T_e = 15 m above sea level. Let gravitational potential energy be zero at ground level. Calculate the power, P_p in Watts, of the pump. P_p = If the pump runs for 1.1 hours, calculate the increase in the potential energy, Delta U_w, in J, of the water in the tower. The water tower, when full, holds 10^6 liters of water. Calculate the gravitational potential energy of the water, U_w in J, of a full water tower relative to sea level.

Explanation / Answer

Part (a)

The pump lifts water of volume Vw = 5.2 liters every second.

So, mass of water lifted every second by the pump is m = Vww = (5.2 liter) (1 kg/liter) = 5.2 kg

The work done by the tower in lifitng mass m of water by a height h = 21 m is,

WT = mgh = (5.2 kg)(9.8 m/s2)(21 m)

or, WT = 1070.16 J

This mass is lifted every second, so power used by the pump is,

Pp = WT/(1 s) = 1070.16 J/s = 1070.16 W

or, Pp = 1070.16 Watts

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Part (b)

If the pump works for t = 1.1 hours = 3600X1.1 s = 3960 s, then energy used by the pump is,

E = Ppt = ( 1070.16 W)(3960 s)

or, E = 4.24X106 J

This energy is used to lift the water and the pump is 100% efficient, So total increase in potenrial energy of water is,

Uw = E

or, Uw = 4.24X106 J

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Part (c)

Mass of full tank of water is m = (106 liter)(1 kg/liter) = 106 kg

The water is at a height of H = (21 + 15)m = 36 m relative to sea level

So gravitational potential energy of water relative to sea level is,

Uw = mgH = (106 kg)(9.8 m/s2)(36 m)

or, Uw = 3.53X108 J

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This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....

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