A mixing tank has two inlets and two exits Cold water enters

A mixing tank has two inlets and two exits. Cold water enters at 5degree C with a volumetric flow rate of 5.0 m^3/hour. Hot water enters at 98degree C with a volumetric flow rate of 2.0 m^3/hour. Warm water leaves the tank from two outlets, one with a mass flow rate of 1.00 kg/s, and the other with a mass flow rate of 0.50. Determine the change in the mass of water in the tank in 20 min? Specify whether it is an increase or decrease. (You may assume that the tank contains 1000 kg of water and is 1/4 full at the start of the process.)

Solution

Cold water inlet 1 = 5 m³/hr , 5^oC

Cold water inlet 2 = 2 m³/hr , 98^oC

Change in mass of water = Mass of water leaving - Mass of water entering

Mass of water leaving = mass flow rate x time

Mass of water entering = mass flow rate x time = density x volume flow rate x time

Mass of water leaving = 1.5 kg/s x 20 min x 60 s= 1800 kg

Mass of water entering = 999.96 kg/m³ x 5 m³/hr x 20/60 hr + 959.79 kg/m³ x 2 m³/hr x 20/60 hr = 1666.6 + 639.86

= 2306.46 kg

As mass of water entering is greater than the mass of water leaving the water level in the tank will increase.

Change in mass = 2306.46 - 1800 = 506.46 kg