# 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 h_{m})^{1/2}(1)

where

Fr = Froude number

v = velocity (m/s)

g = acceleration of gravity (9.81 m/s^{2})

h= hydraulic mean depth or characteristic length (m)_{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

*h _{m} = A / T (2)*

*where *

*h _{m} = hydraulic mean depth (m)*

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

*A = cross sectional area of filled flow in conduit or channel (m ^{2}) *

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

*h _{m} = ((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.