What Is the Hydraulic Jump Sequent Depth & Energy Dissipation Calculator?
A hydraulic jump occurs when high-velocity supercritical water abruptly decelerates, creating intense turbulent rollers that dissipate kinetic energy.
How Does the Hydraulic Jump Sequent Depth & Energy Dissipation Calculator Work?
Equates specific force (momentum plus hydrostatic thrust) across the jump to solve for downstream subcritical sequent depth y2.
Hydraulic Jump Sequent Depth & Energy Dissipation Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
y_2 = rac{y_1}{2} left( sqrt{1 + 8 ext{Fr}_1^2} - 1
ight), quad Delta E = rac{(y_2 - y_1)^3}{4 y_1 y_2}, quad L approx 6.1 y_2Bélanger momentum equation for hydraulic jump sequent depth and head loss.
How to Use the Hydraulic Jump Sequent Depth & Energy Dissipation Calculator
- Input upstream supercritical depth y1 in meters and initial velocity V1 in m/s.
Step-by-Step Example Calculation
Spillway Apron Stilling Basin
Input Values:
upstreamDepthY1M:0.6
supercriticalVelocityV1MS:9.5
Worked Steps: Initial Froude Fr1 = 3.92, Sequent depth y2 = 3.03 m, Energy head loss = 2.01 m (38.6% dissipated), Basin length = 18.5 m.
Understanding Your Result
Displays required downstream sequent depth y2, dissipated energy head in meters, dissipation efficiency %, and recommended stilling basin length.
Factors That Affect the Result
- Optimum energy dissipation occurs when initial Froude number Fr1 is between 4.5 and 9.0 (steady, well-balanced jump).
When Should You Use This Calculator?
- Designing dam spillway aprons, USBR Type II/III stilling basins, drop structures, and open-channel flumes.
Assumptions & Limitations
- Applies to rectangular horizontal channels with negligible bed friction across the jump reach.
Frequently Asked Questions
Why is energy dissipation critical at dam spillways?+
Without hydraulic jump energy dissipation, high-velocity spillway flows would scour river beds, undermine dam foundations, and trigger catastrophic structural collapse.
What happens if tailwater depth is less than sequent depth y2?+
The jump gets swept downstream out of the reinforced stilling basin onto unprotected natural riverbeds, causing severe erosion.
Calculation Accuracy & Reference Note
Standard Bélanger momentum open-channel hydraulics formulation.