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Clemente Gotelli
Hydraulic Jump

Hydraulic Jump Calculator

Compute the sequent depth ($y_2$) for a hydraulic jump in a rectangular or trapezoidal channel using the momentum principle.

Trapezoidal Channel Schematic
Schematic of a trapezoidal channel showing channel width $b$, side slope $z$, upstream depth $y_1$, and discharge $Q$.

Depths

Upstream Depth $y_1$ (m)
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Sequent Depth $y_2$ (m)
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Depth Ratio $y_2/y_1$
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Velocities

Upstream Velocity $v_1$ (m/s)
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Downstream Velocity $v_2$ (m/s)
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Froude Numbers

Upstream $Fr_1$ (Hydraulic)
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Upstream $Fr_1$ (Depth)
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Methodology

This tool solves the general momentum equation for the sequent depth ratio $r = y_2 / y_1$ in a trapezoidal channel. The solution corresponds to the roots of the fourth-order polynomial derived by Sadiq Salman (2012):

$$ r^4 + B r^3 + C r^2 + D r + E = 0 $$

Coefficients $B, C, D, E$ are functions of the upstream section factor $k_1 = b / (z y_1)$ and the upstream Froude number $Fr_{D1} = v_1 / \sqrt{g D_1}$, where $D_1$ is the hydraulic depth.

Reference: Salman, S. M. (2012). Characteristics of the Hydraulic Jump in Trapezoidal Channel Section. Journal of Environmental Studies, 9(1), 53-63.

Header image: Viti, N., Valero, D., & Gualtieri, C. (2019). Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook. Water, 11(1), 28. https://doi.org/10.3390/w11010028