Question 1

What conditions are required for a hydraulic jump to occur?

Accepted Answer

A hydraulic jump occurs when supercritical flow (Fr₁ > 1) transitions to subcritical flow (Fr < 1) in an open channel. This happens downstream of spillways, at the toe of steep slopes, or below sluice gates. The Froude number Fr₁ = v₁/√(g·y₁) must exceed 1.0 for a jump to form; stable jumps typically require Fr₁ > 1.7.

Question 2

How is the conjugate depth calculated for a hydraulic jump?

Accepted Answer

For a rectangular channel, the conjugate (sequent) depth ratio is given by the Bélanger equation: y₂/y₁ = (1/2)(√(1+8Fr₁²) − 1). This is derived by combining the continuity equation, momentum equation, and neglecting friction over the short jump length. For example, Fr₁ = 2 gives y₂/y₁ ≈ 2.56, and Fr₁ = 5 gives y₂/y₁ ≈ 6.85.

Question 3

How is energy loss computed in a hydraulic jump?

Accepted Answer

The specific energy is E = y + V²/(2g). The energy loss across the jump is ΔE = E₁ − E₂ = (y₂ − y₁)³/(4 y₁ y₂). This energy is dissipated as turbulence and air entrainment. Higher Fr₁ values result in greater energy dissipation — at Fr₁ = 5, roughly 50% of the upstream energy is lost. This principle is exploited in stilling basin design.

Question 4

How do you estimate the length of a hydraulic jump?

Accepted Answer

Empirical formulas are used since theoretical prediction is difficult. The most common is Lj ≈ 6.1 y₂ (Peterka, 1958), or Lj ≈ 5(y₂ − y₁). This simulator uses Lj ≈ 6 y₂ as a practical estimate. For design purposes, physical model tests or CFD (e.g., OpenFOAM with VOF free-surface method) provide more accurate values.

Hydraulic Jump Simulator

Theory