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The diameter of a cylindrical water tank isD0 and its
Chapter 5, Problem 42P(choose chapter or problem)
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,
\(\dot V = {A_2}{V_2}\)
\( = \left( {\frac{{\pi {D^2}}}{4}} \right){V_2}\;\;\;\;\;...\;\left( 1 \right)\)