An open water tank has an orifice 10 cm below the surface of water. If there is no loss of energy, then what is the speed of efflux ? (Take g = 10 m `s^(-2)`)

Options

A. 1.414 m `s^(-1)`
B. 2.5 m `s^(-1)`
C. 6.32 m `s^(-1)`
D. 3.7 m `s^(-1)`

Answer

To find the speed of efflux from the orifice in the open water tank, we can use Torricelli's theorem, which states that the speed of efflux (V) of a fluid under the force of gravity through an orifice is given by the formula:

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

where:
- \( g \) is the acceleration due to gravity,
- \( h \) is the height of the fluid above the orifice.

### Step-by-Step Solution:

1. **Identify the height (h)**:
The problem states that the orifice is 10 cm below the surface of the water. Therefore, the height \( h \) is 10 cm.

2. **Convert height to meters**:
Since we need to use SI units, we convert 10 cm to meters:
\[ h = 10 \, \text{cm} = 10 \times 10^{-2} \, \text{m} = 0.1 \, \text{m} \]

3. **Substitute values into the formula**:
We know \( g = 10 \, \text{m/s}^2 \) and \( h = 0.1 \, \text{m} \). Now we can substitute these values into the formula:
\[ V = \sqrt{2gh} = \sqrt{2 \times 10 \times 0.1} \]

4. **Calculate the expression inside the square root**:
\[ 2 \times 10 \times 0.1 = 2 \]

5. **Take the square root**:
\[ V = \sqrt{2} \, \text{m/s} \]

6. **Approximate the value of \(\sqrt{2}\)**:
The approximate value of \(\sqrt{2}\) is about 1.41. Thus:
\[ V \approx 1.41 \, \text{m/s} \]

### Final Answer:
The speed of efflux is approximately \( 1.41 \, \text{m/s} \).