A Tank Shaped like a Vertical Cylinder Initially Contains Water to a Depth of 9m: Chemical Engineering Assignment, SIT, Singapore

Assignment Details:

A tank shaped like a vertical cylinder initially contains water to a depth of 9m. the bottom plug is pulled at time t = 0.  After 1h, the depth has dropped to 4m.

Determine how long will it take for all the water to drain from the tank if the rate of change of depth of water in the cylinder, y, is described by:

Where            

y is the depth of the water in the cylinder (m)

r is the radius of the cylinder (m)

t is the time (hr)

a is a constant.

The differential equation in the above can be derived using the Bernoulli Equation and the Mass Continuity Equation.

Bernoulli Equation:

P/r + 0.5v² + gz = 0

Mass Continuity Equation

Mass in – Mass out + Generation – Consumption = accumulation.

Derive the Differential Equation and express k in terms of the properties of the system.