Understanding Hydraulic Jumps

A hydraulic jump is a sudden transition from fast, shallow, supercritical flow to slower, deeper, subcritical flow in an open channel. It typically occurs when high-velocity water from a spillway or sluice enters a calmer downstream reach. The abrupt rise in water surface level dissipates energy in the form of turbulence, eddies, and surface rollers. Engineers harness this phenomenon to protect channel beds from erosion and to estimate energy losses that affect downstream structures. The calculator above evaluates the sequent depth—the depth immediately after the jump—and the associated specific energy loss using idealized theory for a rectangular, horizontal channel.

The governing parameter for predicting a jump is the Froude number, the ratio of inertial to gravitational forces. In mathematical terms the upstream Froude number is . When is greater than unity the flow is supercritical and a jump can form; when it is below unity the flow is subcritical and stable. Our script computes this dimensionless quantity and reports it along with the downstream depth, offering insight into the flow regime.

The sequent depth relationship for a rectangular channel derives from conservation of momentum across the jump. Equating the momentum before and after and solving for the downstream depth yields . The calculator applies this formula to provide the depth following the jump, sometimes called the conjugate depth. Because the equation depends only on upstream conditions, it is widely used for preliminary design of stilling basins and energy dissipation structures at dams, culverts, and irrigation works.

Energy considerations complement the momentum analysis. The specific energy at a cross-section combines depth and velocity head as . During a hydraulic jump, specific energy decreases because turbulence dissipates mechanical energy into heat and sound. The idealized energy loss between sequent depths is . The calculator reports this loss in meters of head, illustrating how a jump can effectively reduce the energy of a fast-moving flow.

Hydraulic jumps are classified into several regimes depending on . For , a jump does not form. Between roughly 1 and 1.7 the jump is undular, characterized by gentle surface oscillations. Between 1.7 and 2.5 the jump is weak, producing small rollers. Values from 2.5 to 4.5 produce oscillating jumps with vigorous turbulence. Between 4.5 and 9 the jump is steady and well formed, ideal for dissipating energy in a controlled stilling basin. Beyond 9 the jump becomes strong and highly turbulent, demanding robust structural protection. Understanding these regimes helps engineers select basin dimensions and slab reinforcements that can withstand the associated forces.

In real channels factors such as bed slope, channel width, inflow roughness, and air entrainment modify the ideal equations. Nevertheless, the sequent depth relation remains a valuable first approximation. Designers often adjust the computed value with safety factors or refer to more detailed numerical models and physical experiments when constructing large hydraulic structures. Field observations reveal that the jump length typically scales with multiple times the sequent depth, and that air entrained in the roller can lower effective density, influencing scour patterns downstream.

The inputs requested by this calculator—upstream depth and velocity—are quantities usually measured in the field or obtained from hydraulic models. The computed sequent depth guides the placement of end sills, baffle blocks, or other energy-dissipating devices. The reported energy loss helps determine whether additional structures are necessary to achieve desired downstream conditions. Because open-channel flows can carry sediment and debris, the calculator assumes clear water and ignores sediment transport, though in reality sediment can affect both jump location and stability.

The Froude number also signals how responsive the flow is to downstream controls. In supercritical conditions information cannot travel upstream, so structures downstream have little influence until a hydraulic jump forces the flow to slow down. This property is exploited to stabilize flows exiting spillways by designing tailwater levels that trigger a jump in a controlled location. The kinetic energy lost within the roller reduces velocities that might otherwise erode the riverbed.

The table below summarizes typical Froude number ranges and qualitative descriptions of hydraulic jump behavior. While the boundaries are not rigid and vary with channel geometry, they provide a useful reference for interpreting the calculator’s output.

Froude Number F₁	Jump Classification
< 1	No jump (subcritical flow)
1 – 1.7	Undular jump
1.7 – 2.5	Weak jump
2.5 – 4.5	Oscillating jump
4.5 – 9	Steady jump
> 9	Strong jump

By integrating theoretical relations, practical design guidance, and qualitative behavior, this calculator serves as an educational aid for students of fluid mechanics and a quick reference for practicing engineers. Hydraulic jumps are not merely textbook curiosities; they are essential to energy dissipation in spillways, stormwater outlets, wastewater treatment basins, and irrigation canals. A solid grasp of their properties enables safer and more cost-effective hydraulic structures.