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

m

Width of the channel at the water surface

m/s

Average velocity of fluid flow

m/s²

Standard Earth gravity is 9.81 m/s²

Calculation Results

Hydraulic Depth
0.000 m
Hd = A / W
Froude Number
0.0000
Fr = u / √(g × Hd)

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

<1

Subcritical

Fr < 1

Tranquil flow, upstream influence

=1

Critical

Fr = 1

Transition state, minimal energy

>1

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).