Hydraulic Jump Calculator
Calculate hydraulic jump properties including depth ratio, head loss, and jump efficiency
Calculate Hydraulic Jump Properties
Flow depth before the hydraulic jump
Width of the rectangular channel
Flow rate through the channel
Hydraulic Jump Results
Froude number must be greater than 1 for a hydraulic jump to occur. Current Fr₁ = 0.000
Key Formulas Used
Froude Number: Fr = v / √(g × y)
Conjugate Depth: y₂/y₁ = ½(-1 + √(1 + 8Fr₁²))
Head Loss: ΔE = (y₂ - y₁)³ / (4y₁y₂)
Jump Length: L = 220y₁ × tanh((Fr₁ - 1)/22)
Example Calculation
Open Channel Flow Example
Upstream depth (y₁): 0.5 m
Channel width (B): 2.0 m
Discharge (Q): 4.0 m³/s
Upstream velocity: v₁ = Q/(y₁×B) = 4.0/(0.5×2.0) = 4.0 m/s
Froude number: Fr₁ = 4.0/√(9.807×0.5) = 1.81
Results
Downstream depth: y₂ = 0.5 × ½(-1 + √(1 + 8×1.81²)) = 0.95 m
Jump height: h = 0.95 - 0.5 = 0.45 m
Jump type: Weak jump (Fr₁ = 1.81)
Jump Types by Froude Number
Fr₁ < 1.7
Undular Jump
Small undulations, very low energy loss
1.7 < Fr₁ < 2.5
Weak Jump
Small jump, low energy dissipation
2.5 < Fr₁ < 4.5
Oscillating Jump
Irregular waves, considerable losses
4.5 < Fr₁ < 9
Steady Jump
Steady, confined, up to 70% loss
Fr₁ > 9
Strong Jump
Water jets, up to 85% loss
Flow Conditions
Supercritical Flow
Fr > 1, high velocity, shallow depth
Critical Flow
Fr = 1, minimum energy for given discharge
Subcritical Flow
Fr < 1, low velocity, deep flow
Understanding Hydraulic Jumps
What is a Hydraulic Jump?
A hydraulic jump is a phenomenon that occurs when flowing water changes from supercritical to subcritical flow. This abrupt transition is characterized by a sudden increase in flow depth, decrease in velocity, and significant energy dissipation.
Key Characteristics
- •Transition from high-velocity, shallow flow to low-velocity, deep flow
- •Conservation of momentum but significant energy loss
- •Formation of turbulent mixing zone
- •Used for energy dissipation in hydraulic structures
The Froude Number
Fr = v / √(g × D)
- Fr: Froude number (dimensionless)
- v: Flow velocity (m/s)
- g: Gravitational acceleration (9.807 m/s²)
- D: Flow depth (m)
Applications
- •Spillway design for dams
- •Stilling basin design
- •Open channel flow analysis
- •Hydraulic structure optimization