Consider a 300-L storage tank of a solar water heating system initially filled with warm water at 45°C. Warm water is withdrawn from the tank through a 2-cm diameter hose at an average velocity of 0.5 m/s while cold water enters the tank at 20°C at a rate of 5 L/min.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