Froude Number and Flow States
The Froude number, Fr, is a dimensionless value that describes different flow regimes of open channel flow. The Froude number is a ratio of inertial and gravitational forces.
· Gravity (numerator) - moves water downhill
· Inertia (denominator) - reflects its willingness to do so.
V = Water velocity
D = Hydraulic depth (cross sectional area of flow / top width)
g = Gravity
Fr = 1, critical flow,
Fr > 1, supercritical flow (fast rapid flow),
Fr < 1, subcritical flow (slow / tranquil flow)
The Froude number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.
The denominator represents the speed of a small wave on the water surface relative to the speed of the water, called wave celerity. At critical flow celerity equals flow velocity. Any disturbance to the surface will remain stationary. In subcritical flow the flow is controlled from a downstream point and information is transmitted upstream. This condition leads to backwater effects. Supercritical flow is controlled upstream and disturbances are transmitted downstream.
Wave propagation can be used to illustrate these flow states: A stick placed in the water will create a V pattern of waves downstream. If flow is subcritical waves will appear in front of the stick. If flow is at critical waves will have a 45o angle. If flow is supercritical no upstream waves will appear and the wave angle will be less than 45o.
Note: Critical flow is unstable and often sets up standing waves between super and subcritical flow. When the actual water depth is below critical depth it is called supercritical because it is in a higher energy state. Likewise actual depth above critical depth is called subcritical because it is in a lower energy state.