Free Hydraulic Jump Calculator

Understanding Open Channel Flow and Hydraulic Jumps

A hydraulic jump occurs when a supercritical stream abruptly transitions into a subcritical regime. This sudden change generates turbulence and dissipates a substantial amount of energy, which is crucial for designing stilling basins and preventing channel erosion. This comprehensive tool combines a Froude Number Calculator, Open Channel Flow Calculator, Conjugate Depth Calculator, Jump Length Calculator, and Hydraulic Jump Height evaluator to quickly determine all major properties of the jump, including upstream and downstream velocities, jump dimensions, and head loss.

Critical Depth and Flow Regimes

The key to classifying an open‑channel flow lies in the concept of critical depth — the depth at which the specific energy is minimized for a given discharge. When the actual depth is less than the critical value, the flow is supercritical (rapid, high‑velocity). When the depth exceeds the critical value, the flow is subcritical (slow, tranquil). The ratio of inertial to gravitational forces, expressed by the Froude number, provides a simple way to identify these regimes.

The Froude Number and Its Physical Meaning

For any open channel, the Froude number is defined as:

$$Fr = \dfrac{v}{\sqrt{g y}}$$

where:

• $v$ = mean flow velocity (m/s or ft/s)
• $g$ = gravitational acceleration ($\approx 9.81\; \text{m/s}^2$ or $32.17\; \text{ft/s}^2$)
• $y$ = flow depth (m or ft)

The denominator $\sqrt{g y}$ is the wave celerity — the speed at which a small surface disturbance propagates. Therefore, the Froude number compares the flow velocity with the speed of information transmission in the channel:

• Supercritical flow ($Fr > 1$): velocity exceeds celerity, disturbances are swept downstream.
• Subcritical flow ($Fr < 1$): velocity is less than celerity, disturbances travel upstream.
• Critical flow ($Fr = 1$): velocity equals celerity, disturbances stand still.

The built‑in Froude Number Calculator instantly performs this comparison.

Core Calculations for a Hydraulic Jump

The following formulas apply to a horizontal rectangular channel where the jump occurs from a supercritical upstream state (Fr1 > 1) to a subcritical downstream state (Fr2 < 1). The channel is assumed to be of constant width $B$.

1. Discharge (Flow Rate)
The volumetric flow rate $Q$ is conserved through the jump:

$$Q = v_1 y_1 B = v_2 y_2 B$$

2. Conjugate (Sequent) Depth
The depths before and after the jump are linked by a relation derived from the momentum equation:

$$\dfrac{y_2}{y_1} = \dfrac{\sqrt{1 + 8\, Fr_{1}^{2}} - 1}{2}$$

This Conjugate Depth Calculator uses this expression to find $y_2$ once the upstream conditions are known.

3. Head Loss
The energy dissipated across the jump, expressed as a head loss $\Delta E$, is:

$$\Delta E = \dfrac{(y_2 - y_1)^{3}}{4\, y_1 y_2}$$

Higher upstream Froude numbers lead to greater losses. The Head Loss Hydraulic Jump component reports this value directly.

4. Hydraulic Jump Length
The length of the turbulent roller region varies with flow conditions. Laboratory experiments suggest that the jump length $L_j$ can be approximated as $L_j \approx 6.1 y_2$ for typical steady jumps, though the actual value depends on factors such as bed roughness and inflow turbulence. The Jump Length Calculator provides a reasonable estimate using established empirical correlations.

5. Jump Height
The rise in water surface elevation is simply the difference between end depths:

$$h = y_2 - y_1$$

6. Jump Efficiency
The efficiency $\eta$ (ratio of energy after the jump to energy before the jump) decreases rapidly with increasing Fr1. While a closed‑form expression is complex, typical values indicate energy losses that can reach 70% for steady jumps and up to 85% for strong jumps.

Using the Hydraulic Jump Calculator

To obtain the full analysis, provide the channel width $B$, upstream depth $y_1$, and either the upstream velocity $v_1$ or the discharge $Q$. The tool then computes:

• Froude numbers (upstream and downstream)
• Downstream depth $y_2$ via the conjugate depth formula
• Jump height $h = y_2 - y_1$
• Jump length $L_j$ using empirical relations
• Head loss $\Delta E$
• Jump efficiency and type classification

All results update in real time, making it easy to explore how changes in upstream conditions affect the jump.

Classification of Hydraulic Jumps

The appearance and energy‑dissipating performance of a hydraulic jump depend strongly on the upstream Froude number Fr1. The table below summarizes the standard classes:

Fr1 Range	Jump Type	Characteristics	Approx. Energy Loss
< 1.7	Undular	Weak surface undulations, minimal turbulence	Very low
1.7 – 2.5	Weak	Small jump, low energy dissipation	Low
2.5 – 4.5	Oscillating	Irregular waves, moderate dissipation	Moderate
4.5 – 9	Steady	Well‑defined, stable roller; high dissipation	Up to 70%
> 9	Strong	High‑velocity jet, rough surface; maximum dissipation	Up to 85%

This Supercritical to Subcritical Flow transition analysis is automatically performed every time you use the calculator. Whether you are designing a channel transition, analyzing a spillway stilling basin, or studying the fundamentals of fluid mechanics, this all‑in‑one Hydraulic Jump Calculator provides the key results you need for a rectangular horizontal channel.