Hydraulic Jump Calculator

When a fluid flow transitions from supercritical to subcritical, a hydraulic jump occurs. This change in flow characteristics is accompanied by significant energy losses as well as flow turbulence. To further grasp the Hydraulic Jump, one must first understand supercritical and subcritical flows. Before learning about these, you should first understand what critical depth is. Critical Depth is the flow depth for which the energy is lowest at a given discharge Q.

Supercritical Flow or Rapid Flow - When the depth is less than the critical depth, it is referred to as Supercritical Flow or Rapid Flow.

Subcritical Flow or Slow Flow - When the depth exceeds the critical depth, it is referred to as Subcritical Flow or Slow Flow.

The Froude Number Fr1 greatly influences the sort of hydraulic jump. The ranges below represent several sorts of jumps with various flow patterns.

Undular Jump(Fr₁ < 1.7): This is a very low-energy jump that produces minor surface undulations.

Weak Jump(1.7 < Fr₁ < 2.5): This Jump is quite modest and dissipates very little energy.

scillating Jump(2.5 < Fr₁ < 4.5): The waves in this jump are erratic, and there are significant energy losses.

Steady Jump(4.5 < Fr₁ < 9): It is limited to a single point and has energy losses of up to 70%.

Strong Jump(Fr₁ > 9): Supercritical jets emerge in these jumps, and the difference between upstream and downstream velocities is relatively large, with energy dissipation reaching up to 85%.

Rather than spending time examining the flow, hydraulic engineers frequently use the Froude number equation to determine if the flow is supercritical or subcritical. The formula Fr = v / √(g * D) can be used to determine it for any open channel.

• Where, Fr = Froude Number of the Flow
• V = Flow Velocity
• g = gravitational acceleration
• D = Flow Depth

The wave propagation velocity, or wave celerity, is represented by the value in the denominator √(g * D). Consider tossing a pebble into the water, and the ripples generated by the celerity cause them to propagate on the surface.

The flow velocity is larger than the celerity in a supercritical flow (Fr > 1). Waves or flow disruptions are propagated downstream as a result of this. If the flow is subcritical (Fr < 1), the flow velocity is less than the celerity, and waves or disturbances are conveyed upstream. When a critical flow occurs, the Froude Number equals Celerity, and the waves do not move upstream or downstream, remaining stationary.

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The Hydraulic Jump has various properties, and we've given the jump efficiency equation. All of the formulas are only valid under particular conditions, which are listed below.

• The channel is one with an open flow.
• There is no slope in the channel, which is rectangular and horizontal.
• The transition from supercritical to subcritical flow occurs.

Formula for Flow Rate: The discharge Q is equal to the flow velocity v multiplied by the channel cross-section surface area in both upstream and downstream flows. In the case of a non-varying rectangular channel, Q = v * y * B is the formula

• Where Q is the discharge, which is measured in m^3/s or cu ft/s.
• The flow velocity, V, is measured in m/s or ft/s.
• The flow depth, y, is measured in m or ft.
• The Channel width is measured in m or ft.

Equation for Conjugate Depth: Momentum Upstream and downstream flow depth functions are equivalent. The depths y1 and y2 are conjugate depths, and the formula y₂/y₁ = 0.5 * [√(1 + 8 * Fr₁²) - 1] is used.

• Where The depth ratio is denoted by y₂/y₁
• The Froude Number of Upstream is Fr₁

Head Loss Formula: Although momentum is retained in a hydraulic jump, some energy is lost. This is known as Head Loss and is calculated using the formula ΔE = (y₂ - y₁)³ / (4 * y₁ * y₂)

Hydraulic Jump Length Equation: Several investigations have shown the equation for determining the length of a hydraulic jump. However, this is an estimate, and the actual duration of the hydraulic jump may differ depending on numerous parameters such as flow turbulence, i.e. L = 220 * y₁ * tanh[(Fr₁ - 1) / 22]

Hydraulic Jump Height Formula: Hydraulic Jump Height is the difference between downstream and upstream flow depth. Because the flow is supercritical, the flow depth is always lower and is given by the formula h = y₂ - y₁.

Jump Efficiency Equation: Using the Froude Number of Upstream Flow Fr₁, you may determine how much energy is lost in a hydraulic jump. En = [[√(8 * Fr₁² + 1)] ³ - 4 * Fr₁² + 1] / [8 * Fr₁² * (2 + Fr₁²)] * 100% is the equation for it.

1. What is the formula for calculating hydraulic jump?

Because of the turbulence in the hydraulic jump, there will always be a frictional head loss. The frictional head loss, hL, is determined using the following formula: hL = y1 + V12/2g - (y2 + V22/2g).

2. What is the hydraulic jump's length?

It is defined as the distance between two parts, one of which is taken before the hydraulic jump and the other after the hydraulic jump. According to an experiment, the length of a hydraulic jump in a rectangular channel is 5 to 7 times the height of the hydraulic jump.

3. In which cases is it possible to perform a hydraulic jump?

When the beginning speed is less than the crucial speed, hydraulic jumping is not possible. During the transformation, a transition is created. As an undulating wave, the changeover appears. The transition becomes more sudden as the initial flow increases.

4. In a hydraulic jump, what is alternate depth?

The depths of flow in open channels that have the same specific energy are referred to as alternate depths. The computation of alternate depths is required to solve problems involving transitions in the width and bottom of channels.