If the velocity head of a stream of water is equal to 10 cm, then its speed of flow is approximately

Options

A. `1.0 ms^(-1)`
B. `1.4 ms^(-1)`
C. `140 ms^(-1)`
D. `10 ms^(-1)`

Explanation

To find the speed of flow of water when the velocity head is given as 10 cm, we can use the following steps:

### Step-by-Step Solution:

1. **Understand the Concept of Velocity Head**:
The velocity head (h) is given by the formula:
\[ h = \frac{V^2}{2g} \]
where \( V \) is the speed of flow and \( g \) is the acceleration due to gravity.

2. **Convert the Velocity Head to Meters**:
Since the velocity head is given in centimeters, we need to convert it to meters:
\[ h = 10 \text{ cm} = 0.1 \text{ m} \]

3. **Rearrange the Velocity Head Formula**:
We can rearrange the formula to solve for \( V \):
\[ V^2 = 2gh \]
Thus,
\[ V = \sqrt{2gh} \]

4. **Substitute the Values**:
We know that \( g \approx 10 \text{ m/s}^2 \) (standard value for acceleration due to gravity), and we have \( h = 0.1 \text{ m} \). Substitute these values into the equation:
\[ V = \sqrt{2 \times 10 \text{ m/s}^2 \times 0.1 \text{ m}} \]

5. **Calculate the Value Inside the Square Root**:
\[ V = \sqrt{2 \times 10 \times 0.1} = \sqrt{2} \]

6. **Find the Square Root**:
The value of \( \sqrt{2} \) is approximately \( 1.414 \text{ m/s} \).

7. **Final Result**:
Therefore, the speed of flow is approximately:
\[ V \approx 1.4 \text{ m/s} \]

### Summary:
The speed of flow of the water stream is approximately **1.4 m/s**.