Calculating Channel Froude Numbers for Flumes and Weirs

We often talk about how flumes and weirs accelerate sub-critical flow to a supercritical state and how that in turn develops the level-to-flow relationships that are used to determine the flow rate. In the past we’ve defined the various stages of critical flow by the Froude number (Fr).

F_r < 1, flow is sub-critical
F_r = 1, flow is critical
F_r > 1, flow is super-critical

We've also stated before that the Froude number should generally not exceed 0.5, as above this number standing surface waves are prone to form.

But what we haven’t delved into is how exactly we determine the Froude number.

Froude Number Equation

The Froude number is defined as follows:

Equation — Froude Number Equation

Fr = Froude number
V = average velocity of the liquid in a channel (feet/second OR meters/second)
g = acceleration due to gravity (32.17ft/sec2 OR 9.81 m/sec2)
D = hydraulic depth

Example

A rancher needs to install a flume in a channel to measure his water right and he knows the following information:

Channel shape: Rectangular
Channel depth: 1-feet (at maximum flow)
Channel width: 3-feet
Flow rate: 9-cubic feet/sec (which gives us a velocity of 3-cubic feet/sec as Q (flow rate) = A (area) * V (velocity), A = 3*1)

From this the Froude number can be calculated as: