The bottom of a cylindrical vessel has a circlular hole of radius r and at depth h below the water] level. If the diameter of the vessel is D, the find then speed with which the water level in the] vessel drops.

Explanation

To find the speed with which the water level in a cylindrical vessel drops due to a hole at the bottom, we can follow these steps:

### Step 1: Determine the velocity of efflux (v1)
The velocity of efflux (v1) through the hole at depth h can be calculated using Torricelli's theorem, which states:
\[ v_1 = \sqrt{2gh} \]
where:
- \( g \) is the acceleration due to gravity,
- \( h \) is the depth of the hole below the water level.
...