Hydraulic Jump Calculator

Hydraulic Jump Occurs if a fluid flow changes from Supercrticial to Subcritical. This change in the flow characteristics is accompanied by substantial ebergy losses along with turbulence in the flow.

To understand the Hydraulic Jump in a better way one needs to know about the supercritical and subcritical flows. Before learning about these firstly know what exactly is critical depth. Depth of flow for which the energy is minimum at a given discharge Q is called Critical Depth.

• Supercritical Flow - If the depth is lower than the critical depth then it is said to be Supercritical Flow or Rapid Flow.
• Subcritical Flow - If the depth is greater than the critical depth then it is said to be Subcritical Flow or Slow Flow.

Rather than investing time in analyzing the flow hydraulic engineers mostly prefer froude number equation to check if it is a supercritical flow or subcritical flow. We can calculate it for any open channel using the formula Fr = v / √(g * D)

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

If the Froude Number is greater than 1 then the flow is considered as Supercritical Flow and if it is less than 1 it is treated as subcritical flow. Looking at the Froude Number Equation closely we can say the denominator needs to have the units meters per second or feets per second.

The value in the denominator √(g * D) indicates the wave propogation velocity or wave celerity. Imagine you throw a pebble in the water and the ripples caused propogates on the surface due to the celerity.

In case of supercritical flow(Fr > 1) velocity of the flow is higher than the celerity. Due to this the waves or disturbances in the flow gets transmitted downstream. On the contrary if flow is subcritical (Fr < 1) Velocity of the flow is smaller than the celerity and the waves or disturbances gets transmitted upstream. In case of a critical flow the Froude Number is equal to Celerity and the waves neither move upstream nor downstream but stays in one place.

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Hydraulic Jump has several characteristics and we have included the equation for jump efficiency. All the formulas are only valid for certain assumptions and they are as under

• The Channel is an Open Flow One
• The Channel is Rectangular and Horizontal and doesn't contain any slope.
• Jump happens from supercritical flow to subcritical flow

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

• Where Q is the discharge and is measured in units m³/s or cu ft/s
• V is the flow velocity and is expressed in units m/s or ft/s
• y is the flow depth and has units m or ft
• B is the Channel width and its units are m or ft

2. Conjugate Depth Equation: Momentum Functions of flow depths upstream and downstream are equal. We can say that the depths y₁ and y₂ are conjugate depths and uses the formula y₂/y₁ = 0.5 * [√(1 + 8 * Fr₁²) - 1]

• Where y₂/y₁ is the depth ratio
• Fr₁ is the Froude Number of Upstream

3. Head Loss Formula: In Hydraulic Jump although momentum is conserved certain energy is lost. This Energy Loss is known as Head Loss and is given by the formula ΔE = (y₂ - y₁)³ / (4 * y₁ * y₂)

4. Hydraulic Jump Length Equation: The Equation to determine the length of a hydraulic jump is found in several experiments. However, this is an approximation and the real length of hydraulic jump may vary based on several factors such as flow turbulance i.e. L = 220 * y₁ * tanh[(Fr₁ - 1) / 22]

5. Hydraulic Jump Height Formula: Hydraulic Jump Height is nothing but the difference between flow depth downstream and upstream. Since the flow is supercritical it is always a lower flow depth and is given by formula h = y₂ - y₁

6. Jump Efficiency Equation: You can estimate what percent of energy is lost in a Hydraulic Jump and it depends on the Froude Number of Upstream Flow Fr₁. Its equation is given by En = [[√(8 * Fr₁² + 1)]³ - 4 * Fr₁² + 1] / [8 * Fr₁² * (2 + Fr₁²)] * 100%

The type of Hydraulic Jump majorly depends on the Froude Number Fr₁. The Below ranges indicates different types of jumps having different flow patterns.

• Undular Jump(Fr₁ < 1.7): This Jump is Minimal and results in small undulations on the surface and has very low energy loss.
• Weak Jump(1.7 < Fr₁ < 2.5): This Jump is quite small and has quite low energy dissipation.
• Oscillating Jump(2.5 < Fr₁ < 4.5): In this Jump Waves are irregular and energy losses are in considerable amount.
• Steady Jump(4.5 < Fr₁ < 9): This Jump is confined to single location and has energy losses upto 70%.
• Strong Jump(Fr₁ > 9): In these kind of jumps supercritical jets are formed and the difference between up and downstream velocities are comparitively high and the energy dissipation reaches upto 85%.

1. How do you Calculate the Hydraulic Jump?

You can calculate the hydraulic jump by smply finding the difference between flow depth downstream and upstream.

2. What is the Jump Efficiency Equation?

Jump Efficiency Equation is given by En = [[√(8 * Fr₁² + 1)]³ - 4 * Fr₁² + 1] / [8 * Fr₁² * (2 + Fr₁²)] * 100%

3. What are the types of Hydraulic Jump?

The Types of Hydraulic Jumps are Undular jump, Weak Jump, Oscillating Jump, Steady Jump, Strong Jump, etc.

4. What is Froude Number Equation?

Froude Number Equation is given by the formula Fr = v / √(g * D)