Question

Given the following data for a hydraulic jump, determine the power loss (in kW): 

 Given: - \( B = 5 \, \text{m} \) - \( Q = 15 \, \text{m}^3/\text{sec} \) - \( y_1 = 0.5 \, \text{m} \) - \( g = 9.81 \, \text{m/s}^2 \) - \( \rho_w = 1000 \, \text{kg/m}^3 \) - \( \alpha = 1.0 \) - Find Power loss in kW

• A. 0 kW
• B. 10 kW
• C. 5 kW
• D. 1 kW

Hint:

In hydraulic jump calculations, if the initial and final depths are the same, there is no power loss. Always check the energy relationship between the depths before performing calculations.

Answer 1

The Correct Option is A

Step 1: Formula for Power Loss
The power loss in a hydraulic jump can be calculated using the equation: \[ \text{Power Loss (kW)} = \frac{g \cdot Q \cdot (y_1 - y_2)}{1000} \] Where:
- \( Q \) is the discharge (in \( \text{m}^3/\text{sec} \)),
- \( y_1 \) and \( y_2 \) are the initial and final depths of flow (in meters),
- \( g \) is the acceleration due to gravity (in \( \text{m/s}^2 \)),
- The factor of 1000 is used to convert from Watts to kilowatts.
Step 2: Determine Final Depth \( y_2 \)
To determine \( y_2 \), we use the energy equation for a hydraulic jump: \[ y_2 = \alpha \cdot y_1 \] Substituting the given values: \[ y_2 = 1.0 \cdot 0.5 = 0.5 \, \text{m} \] Step 3: Calculate Power Loss
Now we can substitute the known values into the power loss equation: \[ \text{Power Loss (kW)} = \frac{9.81 \cdot 15 \cdot (0.5 - 0.5)}{1000} = 0 \, \text{kW} \] Thus, the power loss is \( \mathbf{0 \, \text{kW}} \).