The velocity of efflux of a fluid through an orifice 15 cm below the fluid surface (which is open to the atmosphere) is [Take g = 10 m `s^(-2)`]

Options

A. `sqrt(3) m s^(-1)`
B. `3 m s^(-1)`
C. `(1)/(sqrt(3)) m s^(-1)`
D. `(1)/(3) m s^(-1)`

Answer

To solve the problem of finding the velocity of efflux of a fluid through an orifice that is 15 cm below the fluid surface, we can use Torricelli's theorem. According to this theorem, the velocity of efflux (V) of a fluid under the influence of gravity through an orifice is given by the formula:

\[ V = \sqrt{2gh} \]

where:
- \( g \) is the acceleration due to gravity (10 m/s² in this case),
- \( h \) is the height of the fluid column above the orifice (in meters).

### Step-by-Step Solution:

1. **Identify the given values**:
- The depth of the orifice below the fluid surface, \( h = 15 \) cm = \( 0.15 \) m.
- The value of \( g = 10 \) m/s².

2. **Substitute the values into the formula**:
\[ V = \sqrt{2gh} \]
Substituting the values of \( g \) and \( h \):
\[ V = \sqrt{2 \times 10 \, \text{m/s}^2 \times 0.15 \, \text{m}} \]

3. **Calculate the expression inside the square root**:
\[ V = \sqrt{2 \times 10 \times 0.15} = \sqrt{3} \, \text{m/s} \]

4. **Calculate the square root**:
\[ V \approx 1.732 \, \text{m/s} \]

5. **Final Result**:
The velocity of efflux of the fluid through the orifice is approximately \( 1.732 \, \text{m/s} \).