Froude Number Calculator
Calculate Froude number to characterize fluid flow in open channels and determine flow regime
Calculate Froude Number
Area of the channel cross-section perpendicular to flow
Width of the channel at the water surface
Average velocity of fluid flow
Standard Earth gravity is 9.81 m/s²
Calculation Results
Formula: Fr = u / √(g × Hd), where Hd = A / W
Input values: A = 0 m², W = 0 m, u = 0 m/s, g = 9.81 m/s²
Flow Analysis
Example Calculation
Open Channel Flow Example
Channel: Rectangular open channel
Cross-section area (A): 1.0 m²
Channel width (W): 0.5 m
Flow velocity (u): 1.0 m/s
Gravity (g): 9.81 m/s²
Calculation Steps
Step 1: Hydraulic depth: Hd = A / W = 1.0 / 0.5 = 2.0 m
Step 2: Froude number: Fr = u / √(g × Hd)
Step 3: Fr = 1.0 / √(9.81 × 2.0) = 1.0 / √19.62 = 0.2258
Result: Fr = 0.2258 (Subcritical flow)
Flow Classifications
Subcritical
Fr < 1
Tranquil flow, upstream influence
Critical
Fr = 1
Transition state, minimal energy
Supercritical
Fr > 1
Rapid flow, shooting flow
Applications
Open channel flow design
Hydraulic jump analysis
Ship hydrodynamics
Spillway and weir design
River and irrigation systems
Understanding the Froude Number
What is the Froude Number?
The Froude number is a dimensionless parameter that characterizes the flow regime in open channel flow and ship hydrodynamics. It represents the ratio of inertial forces to gravitational forces acting on the fluid.
Physical Significance
- •Determines flow stability and behavior
- •Predicts possibility of hydraulic jumps
- •Indicates energy dissipation characteristics
- •Critical for spillway and channel design
Mathematical Formulation
Fr = u / √(g × Hd)
Hd = A / W
- Fr: Froude number (dimensionless)
- u: Flow velocity (m/s)
- g: Gravitational acceleration (m/s²)
- Hd: Hydraulic depth (m)
- A: Cross-sectional area (m²)
- W: Channel width (m)
Note: For ship applications, hydraulic depth is replaced by the characteristic length (waterline length).