Chapter 14, Problem 14.1CYU

Check Your Understanding If the reservoir in Example 14.1 covered twice the area, but was kept to the same depth, would the dam need to be redesigned?

To determine

If the area of the reservoir is doubled but kept on the same height would the dam need to be redesigned?

Answer to Problem 14.1CYU

No, the dam does not require redesigning as the pressure and force on the dam is only dependent on the average depth of the reservoir.

Explanation of Solution

Consider the figure of the dam

Figure.1

Consider the formula of pressure

$P=\rho gh$

It is clear from the above formula that the pressure of a fluid with constant density is only dependent on the depth of the fluid.

Thus even if the reservoir cover twice the area there would be no change in the pressure as the reservoir is kept at the same height and there would be no need to redesign the dam.

Conclusion:

The pressure of the constant density fluid only depends on the depth of the fluid column.