Understanding Loss of Head at Pipe Exit
The loss of head at the exit of a pipe is a critical concept in fluid mechanics and hydraulic engineering. This phenomenon is primarily attributed to the conversion of pressure energy into kinetic energy when fluid exits a pipe.
Key Concept: Exit Loss
- When fluid flows through a pipe and exits into a lower-pressure environment (like the atmosphere), it experiences a loss of pressure energy.
- This transition results in a change in velocity, which is associated with a loss of head, calculated using the equation:
Loss of Head = V^2 / 2g
where:
- V = velocity of the fluid at the exit,
- g = acceleration due to gravity.
Explanation of the Correct Option 'D'
- The formula V^2 / 2g represents kinetic energy per unit weight of the fluid, which directly correlates to the loss of head.
- As the fluid exits, the kinetic energy increases, while the pressure energy decreases, leading to this specific relationship.
Why Other Options Are Incorrect
- Option A (V^3 / 2g) and Option B (V^3 / g) involve a velocity cubed term which does not apply in this context.
- Option C (V^2 / g) lacks the necessary factor of 2, which is essential for expressing energy per unit weight correctly.
Conclusion
Understanding the loss of head at the exit of a pipe is crucial for designing efficient piping systems. The correct expression, V^2 / 2g, highlights the relationship between velocity and energy loss, key for any civil engineering applications.