Hydraulic Jump Calculator

A hydraulic jump occurs when rapid supercritical flow abruptly transitions into slower subcritical flow, releasing significant energy. The underlying mechanics rely on mass conservation and momentum equations. The initial Froude number (F1) is defined as F1 = v1 / sqrt(g * y1), where v1 is incoming velocity, y1 is initial depth, and g is gravitational acceleration. The subsequent conjugate depth ratio (y2 / y1) is calculated using the momentum equation: y2 / y1 = 0.5 * (sqrt(1 + 8 * F1^2) - 1). Energy dissipation is evaluated through head loss, expressed as (y2 - y1)^3 / (4 * y1 * y2), while the physical length of the turbulent roller zone is approximated using empirical hyperbolic tangent relationships based on Froude number inputs.

Consider an open rectangular channel with a channel width (B) of 5 meters. The incoming flow velocity (v1) is 6 m/s, and the initial pre-jump depth (y1) is 0.5 meters, with acceleration due to gravity (g) at 9.81 m/s^2. First, we compute the initial Froude number: F1 = 6 / sqrt(9.81 * 0.5) = 2.71. Next, we determine the conjugate post-jump depth (y2) using the depth ratio formula: y2 = 0.5 * 0.5 * (sqrt(1 + 8 * (2.71)^2) - 1), yielding a downstream depth of approximately 1.68 meters. The resulting head loss across the jump is calculated as (1.68 - 0.5)^3 / (4 * 0.5 * 1.68) = 0.31 meters of energy head lost due to intense fluid turbulence.

Ensure that your input units remain consistent, preferably using standard SI units (meters, seconds) to avoid scaling errors in gravitational and velocity formulas. Always verify that your incoming Froude number exceeds 1.0; hydraulic jumps can only form under supercritical flow conditions where F1 > 1. When designing spillway dissipation basins, account for tailwater fluctuations to ensure the jump remains safely contained within the engineered structure.