A cylinder of height 20m is completely filled with water. The velocity of effux of water `(in ms^(-1))` through a small hole on the side wall of the cylinder near its bottom is

Options

A. 10
B. 20
C. 25.5
D. 5

Explanation

To find the velocity of efflux of water through a small hole on the side wall of a cylinder filled with water, we can use Torricelli's theorem, which is derived from Bernoulli's principle.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Height of the water column (h) = 20 m
- Acceleration due to gravity (g) = 10 m/s² (approximate value)

2. **Apply Torricelli's Theorem:**
According to Torricelli's theorem, the velocity (v) of efflux of a fluid under the influence of gravity through a hole at a depth (h) is given by the formula:
\[ v = \sqrt{2gh} \]

3. **Substitute the Values:**
Substitute the known values into the equation:
\[ v = \sqrt{2 \times g \times h} = \sqrt{2 \times 10 \, \text{m/s}^2 \times 20 \, \text{m}} \]

4. **Calculate:**
\[ v = \sqrt{400} = 20 \, \text{m/s} \]

5. **Conclusion:**
The velocity of efflux of water through the hole is 20 m/s.

### Final Answer:
The velocity of efflux of water through the hole is **20 m/s**.