Understanding Froude Number
The Froude number (Fr) is a dimensionless parameter used in fluid mechanics to compare inertial forces to gravitational forces. It is defined as the ratio of the flow velocity to the square root of the product of gravitational acceleration and a characteristic length.
Supercritical and Subcritical Flow
- Supercritical Flow: Occurs when Fr > 1, indicating that the flow is fast and has a lower depth.
- Subcritical Flow: Occurs when Fr < 1,="" indicating="" that="" the="" flow="" is="" slower="" and="" has="" a="" greater="" />
Hydraulic Jump and Froude Number Change
When a hydraulic jump occurs, the flow transitions from supercritical to subcritical. This change is characterized by a significant alteration in the flow's energy state.
Given Data
- Froude number after the hydraulic jump (subcritical flow): Fr = 0.2
Calculating the Supercritical Froude Number
To find the Froude number of the supercritical flow before the jump, we consider that hydraulic jumps occur at a specific relationship between the two states.
Relationship Between Froude Numbers
- For a hydraulic jump, the relationship can be simplified as:
- Fr_initial = √((1 + Fr_final^2)/Fr_final)
Where Fr_final is the Froude number after the jump (0.2).
Conclusion
- Using the above relationship, the Froude number of the supercritical flow can be calculated as follows:
Fr_initial = √((1 + 0.2^2)/0.2) = √(1.04/0.2) = √5.2 ≈ 2.28
Thus, the Froude number of the supercritical flow before the hydraulic jump is approximately 2.28.