In a streamline flow if the gravitational head is h, then the kinetic and pressure heads are

Options

A. `1//2v^2//g" and "p//rho`
B. `1//2v^2//g" and "p//rhog`
C. `1//2v" and "p//rho`
D. `1//2v" and "p//rhog`

Explanation

To solve the problem, we need to determine the kinetic and pressure heads in a streamline flow when the gravitational head is given as \( h \). We will use Bernoulli's equation, which relates the pressure, kinetic energy, and gravitational potential energy in a fluid flow.

### Step-by-Step Solution:

1. **Understanding Bernoulli's Equation**:
The Bernoulli equation for a streamline flow can be expressed as:
\[ P + \frac{1}{2} \rho V^2 + \rho g h = \text{constant} \]
where:
- \( P \) is the pressure,
- \( \rho \) is the fluid density,
- \( V \) is the flow velocity,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height or gravitational head.

2. **Identifying the Heads**:
In the context of the problem:
- The **gravitational head** is represented by \( h \).
- The **kinetic head** is given by \( \frac{V^2}{2g} \).
- The **pressure head** is given by \( \frac{P}{\rho g} \).

3. **Expressing the Total Head**:
According to Bernoulli's principle, the sum of the pressure head, kinetic head, and gravitational head is constant along a streamline. Therefore, we can express the total head as:
\[ H = \frac{P}{\rho g} + \frac{V^2}{2g} + h \]
where \( H \) is the total head.

4. **Finding Kinetic and Pressure Heads**:
Since the gravitational head \( h \) is given, we can rearrange the equation to isolate the kinetic and pressure heads:
- **Kinetic Head**:
\[ \text{Kinetic Head} = \frac{V^2}{2g} \]
- **Pressure Head**:
\[ \text{Pressure Head} = \frac{P}{\rho g} \]

5. **Conclusion**:
In a streamline flow with a gravitational head \( h \), the kinetic head and pressure head can be calculated using the above formulas. The total head remains constant, and the values of kinetic and pressure heads will depend on the flow velocity \( V \) and the pressure \( P \).

### Final Result:
- Kinetic Head: \( \frac{V^2}{2g} \)
- Pressure Head: \( \frac{P}{\rho g} \)