The figure shows a tank which contains water at 15.6 o C and is being filled thr

Question

The figure shows a tank which contains water at 15.6oC and is being filled through section 1. Assume incompressible flow.

a. First derive an analytical expression for the water level change dh/dt in terms of arbitrary volume flows (Q1, Q2,Q3) and tank diameter, d.

b. If the water level, h, is constant, determine the exit velocity V2 for the given data V1 = 3 m/s and Q3=0.01 m3/s

The figure shows a tank which contains water at 15.6oC and is being filled through section 1. Assume incompressible flow. First derive an analytical expression for the water level change dh/dt in terms of arbitrary volume flows (Q1, Q2,Q3) and tank diameter, d. If the water level, h, is constant, determine the exit velocity V2 for the given data V1 = 3 m/s and Q3=0.01 m3/s

Explanation / Answer

a) dV/dt = Q1 + Q3 - Q2

=> A*dh/dt = Q1 + Q3 - Q2

=> dh/dt = (1/A)*(Q1 + Q3 - Q2)

b) when h is constant dh/dt = 0

so Q1 + Q3 = Q2

=> v1*A1 + Q3 = v2*A2

=> 3 * pi*(0.025)^2 + 0.01 = v2 * pi*(0.035)^2

=> v2 = 4.13 m/s

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