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The diameter of a cylindrical water tank isD0 and its

Chapter 5, Problem 42P

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QUESTION:

The diameter of a cylindrical water tank is \(D_{0}\) and its height is H. The tank is filled with water, which is open to the atmosphere. An orifice of diameter D with a smooth entrance (i.e., negligible losses) is open at the bottom. Develop a relation for the time required for the tank (a) to empty halfway and (b) to empty completely.

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QUESTION:

The diameter of a cylindrical water tank is \(D_{0}\) and its height is H. The tank is filled with water, which is open to the atmosphere. An orifice of diameter D with a smooth entrance (i.e., negligible losses) is open at the bottom. Develop a relation for the time required for the tank (a) to empty halfway and (b) to empty completely.

ANSWER:

Step 1 of 5

Draw the figure as follows.

The flow rate,

\(\dot V = AV\)

where, \(A\) is the area, and \(V\) is the velocity of the fluid.

Then, the flow rate at the orifice,

\(\dot V = {A_2}{V_2}\)

\( = \left( {\frac{{\pi {D^2}}}{4}} \right){V_2}\;\;\;\;\;...\;\left( 1 \right)\)

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