Consider a 300-l storage tank of a solar water heating system initially filled with warm water at 45°c. warm water is withdrawn from the tank through a 2-cm diameter hose at an average velocity of 0.5 m/s while cold water enters the tank at 20°c at a rate of 5 l/min. determine the amount of water in the tank after a 20-minute period. assume the pressure in the tank remains constant at 1 atm.

160 Kg

Explanation:

This problem is solved by considering the mass balance. We know the density of water, which we will assume constant  , the volume of water originally in the tank and the flows of water entering and leaving the tank.

Let m₀ mass of water initially in the tank

m₁ mass of water entering the tank  and

m₂ mass of water exiting the tank

V  tank volume

then

m₀ = D x V = 1000 Kg x 0.30 m³ = 300 Kg

m₁ = D Vwater in x  time = 1000 Kg/m³ x 5 x 10⁻³ m /min  x 20 min = 100 Kg

m₂ = D x Area Hose x Vel exit x time =

     = 1000 Kg /m³ x 3.1416 x ( 0.02 m)² x 0.5 m/s x ( 20 min x 60 s/min)

     = 240 Kg

mass of water initially + mass water in - mass water out =

(300 + 100 - 240)  Kg = 160 Kg

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