1) A mixing tank initially contains 4500 kg of liquid water. The tank is fitted

Question

1) A mixing tank initially contains 4500 kg of liquid water. The tank is fitted with two inlet pipes: one delivering hot water at a volumetric flow rate of 1.5x10-3 m3/s and one delivering cold water at a mass flow rate of 2.2 kg/s. In addition, the tank has an outlet pipe with a diameter of 0.2 m through which water travels at 0.5 m/s.

How long does it take for the tank to empty assuming 1-D flow and constant mass flow rate in each of the pipes. Note: density of water is 1000 kg/m3.

What is the necessary outlet flow velocity to ensure steady state flow?

Explanation / Answer

kg of hot water coming in per second = 1.5*10^(-3) * 1000 kg = 1.5 kg

kg of cold water coming in per second = 2.2 kg

volume of water coming out of the tank in one second = pi * ( 0.2/2 )^2 * 0.5 m^3

kg of water coming out of the tank is = pi * ( 0.2/2 )^2 * 0.5 * 1000 kg

decrease in amount of water in kg in tank in one second = pi * ( 0.2/2 )^2 * 0.5 * 1000 - 1.5 - 2.2 = 12.008 kg

so total time in which tank will be empty is = 4500 / 12.008 seconds = 374.75 seconds

for steady state flow amount of water in kg flowing from the out let = total amount of water coming to tank in kg in one second

therefore,

for steady state flow amount of water in kg flowing from the out let = 2.2 +1.5 = 3.7 kg/seconds

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