Froude Number
In addition to the effects of fluid viscosity and inertial forces, gravity also plays a role in fluid flow because gravity influences the way a fluid transmits surface waves. [1] The velocity with which small gravity waves move in shallow water is given by the expression √(gL), where g is gravitational acceleration and L is water depth. [1]
The Froude number Fr is the ratio between inertial and gravity forces, expressed as: [1]
Fr = U / √(gL)
where U is the mean velocity of flow and L is water depth in the case of water flowing in an open channel. [1] Like the Reynolds number, the Froude number is a dimensionless value and therefore very useful in modelling studies. [1]
Subcritical Flow (Fr < 1)
When the Froude number is less than 1, the velocity at which waves move is greater than flow velocity, and waves can travel upstream - that is, waves in a stream move upstream in the direction opposite to current flow. [1] Flow under these conditions is called tranquil, streaming, or subcritical. [1]
In a subcritical flow, any disturbance on the water surface - a stone thrown in, an obstruction on the bed - sends ripples upstream as well as downstream. The upstream travel of those waves is only possible because waves move faster than the current. A slowly flowing river is typically subcritical, and you can observe this directly: ripples from a disturbance spread in all directions rather than being swept entirely downstream.
Supercritical Flow (Fr > 1)
If the Froude number is greater than 1, waves cannot be propagated upstream and flow is said to be rapid, shooting, or supercritical. [1] In supercritical flow, the current moves faster than waves can travel, so any surface disturbance is carried entirely downstream. Supercritical flow occurs where a channel steepens abruptly - in rapids, at the lip of a waterfall, or in certain high-velocity channels - and is associated with distinctive bedforms in the upper flow regime.
Critical Velocity and Flow Regime Transitions
The Froude number can be used to define the critical velocity of moving water at which flow at a given depth changes from tranquil to rapid, such as the change from tranquil flow in a stream channel with a gentle slope to rapid flow where the channel becomes steeper, or vice versa. [1]
The transition from subcritical to supercritical flow - and back - is visible in natural streams wherever the slope changes. The hydraulic jump, a turbulent transition zone where supercritical flow abruptly becomes subcritical, is a familiar feature below steep chutes. Sedimentologically, the Froude number also has a relationship to flow regimes, which are defined by characteristic bedforms - such as ripples - that develop during fluid flow over a sediment bed. [1] Lower-regime bedforms (ripples, dunes) develop under subcritical flow; upper-regime bedforms (upper-plane bed, antidunes) develop under supercritical conditions.
Related Topics
Fluid Viscosity
Fluid viscosity is a measure of the ability of fluids to flow - fluids with low viscosity flow readily and fluids with high viscosity flow sluggishly.{/* SRC: Boggs p.19: "Fluid viscosity is a...
Reynolds Number
The fundamental differences in laminar and turbulent flow arise from the ratio of inertial forces to viscous forces within a moving fluid.{/* SRC: Boggs p.22: "The fundamental differences in...
Ripples
Ripples are the smallest bedform produced by fluid flow, and they are among the most widespread sedimentary structures in both modern environments and the ancient rock record. They form in...
Bedforms
Bedforms are the repeating surface features that develop on a sandy bed under fluid flow - ripples, dunes, flat surfaces, and the upstream-migrating antidunes that form under the most energetic...
References & Citations
- 1.Principles of Sedimentology and Stratigraphy Boggs, Sam Jr.
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