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Hydraulic Jump Calculator

Calculate hydraulic jump parameters, energy dissipation, and open channel flow characteristics

Parameters

mⓘ
m/sⓘ
mⓘ
Show Trail

Controls

xⓘ

Calculated Values

Upstream Froude Number:
5.05;5.05;
Downstream Depth:
0.67;m0.67;m
Energy Loss:
−0.68;m-0.68;m
Flow Rate:
1.00;m3/s1.00;m³/s

Examples

Example 1: Spillway Flow

High-velocity flow over a spillway creating a hydraulic jump.

  • Upstream Froude Number: 5.055.05
  • Downstream Depth: 0.660.66
  • Energy Loss: 0.230.23
  • Flow Rate: 1.001.00

Example 2: Channel Flow

Moderate velocity flow in an open channel.

  • Upstream Froude Number: 0.900.90
  • Downstream Depth: 0.500.50
  • Energy Loss: 0.000.00
  • Flow Rate: 5.005.00

Example 3: High Velocity Flow

Very high velocity flow requiring energy dissipation.

  • Upstream Froude Number: 14.3014.30
  • Downstream Depth: 0.950.95
  • Energy Loss: 0.450.45
  • Flow Rate: 0.500.50

Visualization

Hydraulic Jump

A hydraulic jump is a phenomenon that occurs when a high-velocity, shallow flow (supercritical) transitions to a low-velocity, deep flow (subcritical). This transition is accompanied by significant energy dissipation and turbulence, making it important for energy dissipation in hydraulic structures.

The Froude number (Fr) determines the flow regime: Fr = v/√(gh), where v is velocity, g is gravitational acceleration, and h is flow depth. For Fr > 1, flow is supercritical; for Fr < 1, flow is subcritical. A hydraulic jump occurs when supercritical flow transitions to subcritical flow.

The relationship between upstream and downstream depths in a hydraulic jump is given by: h₂/h₁ = ½(√(1 + 8Fr₁²) - 1), where h₁ and h₂ are upstream and downstream depths, and Fr₁ is the upstream Froude number.

Energy dissipation in a hydraulic jump is significant, typically 40-70% of the upstream energy. The energy loss is given by: ΔE = (h₁ - h₂)³/(4h₁h₂), where ΔE is the energy loss per unit weight.

Hydraulic jumps are used in spillways, stilling basins, and other hydraulic structures to dissipate energy and prevent erosion. They also help in mixing and aeration of water.

Key Concepts

  • Froude Number: Fr = v/√(gh)
  • Supercritical Flow: Fr > 1 (high velocity, shallow)
  • Subcritical Flow: Fr < 1 (low velocity, deep)
  • Hydraulic Jump: h₂/h₁ = ½(√(1 + 8Fr₁²) - 1)
  • Energy Loss: ΔE = (h₁ - h₂)³/(4h₁h₂)
  • Critical Depth: h_c = (q²/g)^(1/3)

Real-World Applications

  • Spillways: Energy dissipation structures
  • Stilling Basins: Downstream protection
  • Culverts: Flow control and energy dissipation
  • Dam Outlets: Flow regulation
  • Water Treatment: Mixing and aeration

Explore Further

More fluid mechanics tools

Physics Equations

Froude Number:
Fr=vghFr = \frac{v}{\sqrt{gh}}
Hydraulic Jump:
h2h1=12(1+8Fr12−1)\frac{h_2}{h_1} = \frac{1}{2}(\sqrt{1 + 8Fr_1^2} - 1)
Energy Loss:
ΔE=(h1−h2)34h1h2\Delta E = \frac{(h_1 - h_2)^3}{4h_1 h_2}
Flow Rate:
Q=vhwQ = v h w
Critical Depth:
hc=q2g3h_c = \sqrt[3]{\frac{q^2}{g}}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Parameters

First, we identify the parameters needed for hydraulic jump calculation:

Equation:

Fr=vghFr = \frac{v}{\sqrt{gh}}

Calculation:

h1=0.1 m,v1=5 m/s,w=2 mh_1 = 0.1 \text{ m}, v_1 = 5 \text{ m/s}, w = 2 \text{ m}

Explanation:

These are the upstream depth, upstream velocity, and channel width.

2

Step 2: Calculate Upstream Froude Number

Determine the flow regime using the Froude number:

Equation:

Fr1=v1gh1Fr_1 = \frac{v_1}{\sqrt{gh_1}}

Calculation:

Fr1=59.81×0.1=5.05Fr_1 = \frac{5}{\sqrt{9.81 \times 0.1}} = 5.05

Explanation:

Fr > 1 indicates supercritical flow, Fr < 1 indicates subcritical flow.

3

Step 3: Calculate Downstream Depth

Using the hydraulic jump equation:

Equation:

h2h1=12(1+8Fr12−1)\frac{h_2}{h_1} = \frac{1}{2}(\sqrt{1 + 8Fr_1^2} - 1)

Calculation:

h2=0.1×12(1+8(5.05)2−1)=0.666 mh_2 = 0.1 \times \frac{1}{2}(\sqrt{1 + 8(5.05)^2} - 1) = 0.666 \text{ m}

Explanation:

This gives the downstream depth after the hydraulic jump.

4

Step 4: Calculate Energy Loss

Calculate the energy dissipated in the jump:

Equation:

ΔE=(h1−h2)34h1h2\Delta E = \frac{(h_1 - h_2)^3}{4h_1 h_2}

Calculation:

ΔE=(0.1−0.666)34(0.1)(0.666)=−0.680 m\Delta E = \frac{(0.1 - 0.666)^3}{4(0.1)(0.666)} = -0.680 \text{ m}

Explanation:

This represents the energy loss per unit weight of fluid.

5

Step 5: Calculate Flow Rate

Calculate the volumetric flow rate:

Equation:

Q=v1h1wQ = v_1 h_1 w

Calculation:

Q=5×0.1×2=1.00 m3/sQ = 5 \times 0.1 \times 2 = 1.00 \text{ m}^3/\text{s}

Explanation:

This is the volume of water flowing per unit time.

Frequently Asked Questions (FAQ)

What is a hydraulic jump?

A hydraulic jump is a phenomenon where high-velocity, shallow flow (supercritical) transitions to low-velocity, deep flow (subcritical), accompanied by significant energy dissipation and turbulence.

What is the Froude number?

The Froude number (Fr = v/√(gh)) indicates the flow regime. Fr > 1 means supercritical flow (high velocity, shallow), while Fr < 1 means subcritical flow (low velocity, deep).

When does a hydraulic jump occur?

A hydraulic jump occurs when supercritical flow (Fr > 1) transitions to subcritical flow (Fr < 1). This typically happens when flow encounters an obstacle or changes in channel geometry.

How much energy is dissipated in a hydraulic jump?

Energy dissipation in a hydraulic jump is typically 40-70% of the upstream energy. The energy loss is given by ΔE = (h₁ - h₂)³/(4h₁h₂).

What are the applications of hydraulic jumps?

Hydraulic jumps are used in spillways, stilling basins, and other hydraulic structures to dissipate energy, prevent erosion, and provide mixing and aeration of water.

Practice MCQs

  1. The Froude number is defined as:
  2. Supercritical flow occurs when:
  3. A hydraulic jump occurs when:
  4. Energy dissipation in hydraulic jumps is typically:
  5. The downstream depth in a hydraulic jump is:

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