Consider the sketch A liquid of density 1100 kgm3 flows into

Consider the sketch. A liquid of density 1100 kg/m^3 flows into and out of a storage tank through several pipes. The volumetric flow rate of stream 1 is 25 liters/sec. The mass flow rate of stream 2 is 10 kg/s. The diameter of the exit pipe at 3 is 5 cm and the average velocity of the liquid at 3 is 12 m/s. Is the mass of liquid stored in the tank (its free surface is indicated in the sketch) increasing, decreasing or constant? If it is changing determine the rate of change (kg/s).

Solution

The mass flow rate through hole 1 is

m₁ = v₁ * (density)/1000

= 25*1100/1000 = 27.5 kg/s

The mass flow rate through hole 3 is

m₃ = V₃ * A₃ * densty

     = 12 * (/4*0.05²) * 1100

     = 25.91 kg/s

The rate of mass storage in the tank is

m = m₁ + m₂ – m₃

    = 27.5+10-25.91

    = 11.59 kg/s

Thus, the mass of liquid in the tank is increasing and at the rate of 11.6 kg/s.