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# Froude Number

## Introduction to the Froude Number.

In open channel hydraulics, the Froude number is a very important non-dimensional parameter.

The Froude Number is a dimensionless parameter measuring the ratio of "the inertia force on a element of fluid to the weight of the fluid element" - the inertial force divided by gravitational force.

The Froude Number can be expressed as

Fr = v / (g hm ) 1/2 (1)

where

Fr = Froude number

v = velocity (m/s)

g = acceleration of gravity (9.81 m/s2)

hm = hydraulic mean depth or characteristic length  (m)

The Froude Number is relevant in fluid dynamic problems where the weight (gravitational force) of the fluid is an important force.

In general this is the situation for free surfaces like cold windows and hot radiators - or flow in open conduits like water channels, sewer pipes . It is used when calculating momentum transfer in general and open channel flow and wave and surface behavior in particular.

The Froude Number is important when analyzing flow in spillways, weirs, channel flows, rivers and in ship design.

Water measurement in open channel flow generally requires the Froude number to be less than 0.5 to prevent waves disturbing accurate head readings.

When the Froude number is 1 the velocity is equal to the velocity of wave propagation and downstream waves or pressure disturbances cannot travel upstream. A Froude number of 1 defines critical mean depth vs. critical velocity.

### Hydraulic Mean Depth

Hydraulic mean depth can be calculated as

hm = A / T                 (2)

where

hm = hydraulic mean depth (m)

T = width of conduit or channel  open surface (m)

A = cross sectional area of filled flow in conduit or channel (m2)

Note that the hydraulic radius (or diameter) commonly used in fluid mechanics and relates flow area to wetted perimeter .

#### Example - Hydraulic Mean Dept in an Open Rectangular Channel

The width of an open channel is 10 m . The depth of the water in the channel is 2 m . The mean dept can be calculated as

hm = ((10 m) * (2 m)) / (10 m)

= 2 m

For a conduct with an irregular shape - estimate the fluid flow area and the conduct surface width - and make the calculation above.

## Related Topics

• ### Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

• ### Dimensionless Numbers

Physical and chemical dimensionless quantities - Reynolds number, Euler, Nusselt, and Prandtl number - and many more.
• ### Drag Coefficient

The drag coefficient quantifies the drag or resistance of an object in a fluid environment.
• ### Manning's Formula and Gravity Flow

Calculate cross-sectional average velocity flow in open channels.
• ### Open Channel Weirs - Volume Flow Measurements

Weirs can be used to measure flow rates in open channels and rivers - common for water supply and sewage plants.
• ### Technical Terms in Fluid Mechanics

Some commonly used technical terms in fluid mechanics.

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## Citation

• The Engineering ToolBox (2004). Froude Number. [online] Available at: https://www.engineeringtoolbox.com/froude-number-d_578.html [Accessed Day Month Year].

Modify the access date according your visit.

7.8.15

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