Froude number

The Froude number (symbol: Fr) is a dimensionless parameter of physics. It is named after William Froude (1810-1879) and is a measure of the ratio of inertial forces to gravity forces within a hydrodynamic system Represent ( free surface flow ) is used, for example, in hydrodynamics influence on the free liquid surface. The Froude number in addition to the Reynolds number of the coefficients of the non-dimensional Navier-Stokes equation.

Definition

The Froude number is defined as

With:

In meteorology, a definition is in the consideration of mountain overtopping used that takes into account the stratification of the atmosphere:

With:

A rigid body and a model of the body that cause waves by moving through a fluid, or the waves of a liquid are exposed, have on the earth exactly then same Froude number, the ratio of the length to the square of the velocity identical is.

When forces only have a minor influence due to viscosity, one can represent the behavior of a solid to the liquid surface in the model test at the same Froude number and convert the different measured variables as follows:

• Lengths with the length scale
• Times the square root of the length scale
• Forces ( assuming equal fluid density ) with the cube of the length of the scale.
• Accelerations are equal in model and full-scale.

It should be noted the analogy with the Mach number.

Froude number in open channels

Substituting the water depth of open channel for the characteristic length L a, the Froude number is the ratio of flow velocity and the velocity of propagation of a wave (more precisely, a shallow water wave). This causes the flow state of open channel is characterized.

• Resting state of flow ( Fr = 0): An error (eg, a wave that is created when a stone is thrown into the water ) spreads evenly in all directions, ie from circular. The descriptive differential equation is called elliptic (special case of the flowing state ). Example: See.
• Pouring flow regime ( Fr < 1): disturbances propagate both upstream and downstream from. The wave propagation shows a parabolic pattern. The flow is described by a parabolic equation. Example: flow.
• Limit runoff / drainage critical (Fr = 1): The wave propagation speed is now consistent exactly with the flow rate. Waves can not propagate against the flow itself. The facing upstream wavefront remains at the site of disorder "stand" ( analogous to the sound barrier ). In this state, the maximum amount of water to be removed in the present energy level. This is used as a drainage control in hydraulic engineering. Example: flow over a weir.
• Shooting flow regime ( Fr> 1): The flow rate now exceeds the propagation speed. A disturbance propagates now only downstream. Propagation patterns and zugehörigere differential equation are called hyperbolic. Example: mountain stream.