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Froude Number

Reference data and engineering information about froude number for fluid mechanics applications.

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Overview

The Froude number (FrFr) is a dimensionless number comparing inertial forces to gravitational forces in open channel flow. It determines the flow regime — subcritical, critical, or supercritical.

Variables

Symbol Description Unit
FrFr Froude number —
vv Flow velocity m/s
gg Gravitational acceleration m/s²
DhD_h Hydraulic depth m

Formula

Fr=vg⋅LFr = \frac{v}{\sqrt{g \cdot L}}

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Notes

  • Results are approximate and should be verified for critical applications
  • Input values should be within reasonable engineering ranges

Critical Flow Conditions

When the Froude number equals 1 (Fr = 1), the flow velocity is equal to the velocity of shallow-water wave propagation. This defines critical flow.

  • For Fr < 1, the flow is subcritical. Gravity waves can travel upstream, and flow is influenced by downstream conditions.
  • For Fr > 1, the flow is supercritical. Gravity waves cannot travel upstream, and flow is influenced by upstream conditions.

This criterion is essential for the design and analysis of hydraulic structures like spillways, weirs, and transitions in open channels.

Hydraulic Mean Depth

The hydraulic mean depth (h_m) is a characteristic length used specifically in the context of open channel flow to calculate the Froude number.

hm=ATh_m = \frac{A}{T}

Where:

  • A is the cross-sectional area of the flow (m²).
  • T is the top width of the channel's free surface (m).

Note: This is distinct from the hydraulic radius (R_h), which is the cross-sectional area divided by the wetted perimeter and is more commonly used with the Manning equation and Reynolds number in pipe flow.

Example Calculation: For a rectangular channel 10 m wide with a water depth of 2 m: hm=AT=(10 m×2 m)10 m=2 mh_m = \frac{A}{T} = \frac{(10 \text{ m} \times 2 \text{ m})}{10 \text{ m}} = 2 \text{ m}

Practical Significance

The Froude number is a primary scaling parameter for simulating open-channel flows in hydraulic models. Maintaining similitude in Fr ensures that the ratios of inertial to gravitational forces are correctly represented in the model and prototype. It is also crucial for predicting wave formation, sediment transport, and the transition from tranquil to rapid flow.

References