Q. 13 - Calculus

Question

Strangely, the hydrostatic force exerted on the side wall of a pool does not depend on how much water is behind that wall, but only on the depth of the water. Explain why this makes sense. 

Step-by-Step Solution

Answer

The hydrostatic force exerted on the side wall of a pool does not depend on how much water is behind that wall, but only on the depth of the water because the force depends only on the water's average depth and the dimensions of the dam, not on the horizontal extent of the reservoir.  

Step 1. Explanation.

We know,

The hydrostatic force is given by,

$$\begin{gathered} F=\omega Ad \\ where \\ W\text{eight-density =}\omega \\ D\text{epth= }d \\ Area=a \end{gathered}$$

Step 2. Conclusion.

Now, we can observe,

The force depends only on the water's average depth and the dimensions of the dam, not on the horizontal extent of the reservoir.