The diameter of the ports in the accompanying figures are 10 cm, 5 cm, and 1 cm at port 1, 2, and 3 respectively. At a given instant, water enters the tank at port 1 with a velocity of 2 m/s and leaves through port 2 with a velocity of 1 m/s. Assuming air to be insoluble in water and density of water and air to remain constant at 1000 kg/m3 and 1 kg/m3 respectively, determine:
(a) The mass flow rate (m) of water in kg/s at the inlet,
(b) The rate of change of mass of water (dm/dt)W in the tank
(c) The rate of change of mass of air (dm/dt)A in the tank,
(d) The velocity of air port 3.