Water is pumped from a lake to a storage tank 20 m above at a rate of 70 L/s whi

Question

Water is pumped from a lake to a storage tank 20 m above at a rate of 70 L/s while consuming 20.4 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine a) the overall efficiency of the pump-motor unit, b) the pressure difference between the inlet and the outlet of the pump, and c) if the diameter of the pipe is 9 cm, determine at 10 m above the lake the change in each component (i.e. kinetic energy, etc) of the mechanical energy with respect to their values at the outlet of the pump.

Explanation / Answer

just take one second. 70 L = 0.07 m³ = 69.9 kg The energy needed is E = mgh = 69.9 x 9.8 x 20 = 13700 J in that second, 20400 watts uses 20400 joules so the efficiency is 13700 / 20400 = 67% Pfluid = ?gh Pfluid is pressure in Pa or N/m² ? is the density of the fluid in kg/m³ density of water at 20C = 0.998 g/cm³ = 998 kg/m³ density of seawater = 1.025 g/cm³ = 1025 kg/m³ g is the acceleration of gravity 9.8 m/s² h is the height of the fluid above the object in m Pfluid = ?gh = 998x9.8x20 = 196000 Pa

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