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The Froude number is based on the speed–length ratio which he defined as: [2] [3] = where u is the local flow velocity (in m/s), g is the local gravity field (in m/s 2), and L is a characteristic length (in m). The Froude number has some analogy with the Mach number.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
When the Froude number grows to ~0.40 (speed/length ratio ~1.35), the wave-making resistance increases further from the divergent wave train. This trend of increase in wave-making resistance continues up to a Froude number of ~0.45 (speed/length ratio ~1.50), and peaks at a Froude number of ~0.50 (speed/length ratio ~1.70).
To help visualize the relationship of the upstream Froude number and the flow depth downstream of the hydraulic jump, it is helpful to plot y 2 /y 1 versus the upstream Froude Number, Fr 1. (Figure 8) The value of y 2 /y 1 is a ratio of depths that represent a dimensionless jump height; for example, if y 2 /y 1 = 2, then the jump doubles the ...
The parameter is known as the Froude number, and is defined as: = where is the mean velocity, is the characteristic length scale for a channel's depth, and is the gravitational acceleration. Depending on the effect of viscosity relative to inertia, as represented by the Reynolds number , the flow can be either laminar , turbulent , or ...
The essence of the actuator-disc theory is that if the slip is defined as the ratio of fluid velocity increase through the disc to vehicle velocity, the Froude efficiency is equal to 1/(slip + 1). [2] Thus a lightly loaded propeller with a large swept area can have a high Froude efficiency.
The Froude number is not necessarily a constant, and may depend on the height of the flow in when this is comparable to the depth of overlying fluid. The solution to this problem is found by noting that u f = dl / dt and integrating for an initial length, l 0. In the case of a constant volume Q and Froude number Fr, this leads to