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Topic: Froude number

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Richardson number

Dimensionless number

Rayleigh number

Fluid Dynamics

Reynolds number

Grashof number

Knudsen number

William Froude

Friction factor

Boussinesq approximation

Prandtl number

Laminar flow

Potential flow

Boundary layer

Mach number

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	Low Drag Rowing Shells: E. O. Tuck and L. Lazauskas
		For the case with no form drag, the volumetric Froude numbers corresponding to these speeds are 0.100, 0.125,...,0.675; 0.680, 0.685,...,0.700; 0.725, 0.750...,0.900; 0.905, 0.910...,0.925; 0.950, 0.975; 0.980, 0.985,...,1.0; 1.025, 1.050,...,1.2; and 1.3, 1,4,...,4.0.
		This volumetric Froude number of 1.8 corresponds to a conventional (actual length-based) Froude number of 0.38, or a speed of 11 knots for a one-tonne vessel.
		Instead, the length-based Froude number passes (quite rapidly) through the value where wave resistance is maximal, but the proportion of wave resistance is nevertheless kept sufficiently low to achieve an optimal design because of the large boatlength.
	www.cyberiad.net /library/rowing/misbond/misres.htm (2613 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		Froude's observations led him to derive the Wave-Line Theory which first described the resistance of a shape as being a function of the waves caused by varying pressures around the hull as it moves through the water.
		The Froude number is thus the hydrodynamic equivalent to the Mach number.
		The Froude number is the reciprocal of the square root of the Richardson number.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Froude_number (417 words)

	Froude number - Biocrawler
		In fluid dynamics, the Froude number (named after William Froude) is the reciprocal of the square root of the Richardson number.
		Strictly, this is known as the densimetric Froude number.
		The densimetric Froude number is usually preferred by modellers who wish to nondimensionalize a speed preference to the Richardson number which is more commonly encountered when considering stratified shear layers.
	www.biocrawler.com /encyclopedia/Froude_number (172 words)

	McNeil Alexander's Analysis of Animal Running
		This relationship was found by fitting a regression line to the logarithms of the Froude numbers and relative strides for his data sample.
		With this relationship McNeil Alexander was able to compute the Froude number for the dinosaurs for which he had data on relative stride.
		The relative stride length determines the maximum angle between the legs and, consequently, the variation in height of the center of gravity during the course of a stride.
	www.sjsu.edu /faculty/watkins/alexander.htm (908 words)

	Significance of the Froude number
		By substituting C into the definition of the Froude number, we see that the Froude number is the ratio of flow velocity to the celerity of a wave at the top of the flow (Fr = U/C).
		When the Froude number equals 1, the flow velocity equals the wave celerity and the wave is stationary at the water surface (Middleton and Southard, 1984).
		Second, the Froude number can be used to classify the energy state of a flow and how the flow reacts to perturbations in the bed (Middleton and Southard, 1984).
	www.es-designs.com:16080 /antidune/chapter1/froude.html (1048 words)

	Froude number - Facts, Information, and Encyclopedia Reference article (Site not responding. Last check: )
		In fluid dynamics, the Froude number (named after William Froude) is the reciprocal of the square root of the Richardson number.
		The Froude number give the ratio of inertial forces to gravitational forces, and is used by ship designers to determine the size and speed of models for tank testing, when wave-making behaviour is the primary interest and frictional forces may be neglected.
		The densimetric Froude number is usually preferred by modellers who wish to nondimensionalize a speed preference to the Richardson number which is more commonly encountered when considering stratified shear layers.
	www.startsurfing.com /encyclopedia/f/r/o/Froude_number.html (232 words)

	Froude_number - The Wordbook Encyclopedia (Site not responding. Last check: )
		The Froude number is a dimensionless number used to quantify the resistance of an object moving through water, and compare objects of different sizes.
		Froude's observations led him to derive the Wave-Line Theory which first described the resistance of a shape as being a function of the waves caused by varying pressures around the hull as it moves through the water.
		In fluid dynamics, the Froude number is the reciprocal of the square root of the Richardson number.
	www.thewordbook.com /Froude_number (410 words)

	Are Fast-Moving Elephants Really Running?
		In elephants, the dimensionless speed or Froude number, a ratio of the kinetic energy (or inertial forces) and potential energy (or gravitational forces) during locomotion, reaches values as high as 3.4.
		Theoretically, at Froude numbers greater than 1.0 animals should have to switch from walking to running, as the forces drawing them off their circular (pendular) path exceed the gravitational forces pulling them down.
		For the Froude number, think about it this way: if you are late for the bus and start walking faster as you realize that you might miss it, at some speed you cannot walk any faster.
	www.rvc.ac.uk /Aboutus/staff/jhutchinson/ResearchInterests/Elephants/FAQ.cfm?display=print&display=print&display=print&display=print&display=print&display=print&display=print&display=print&display=print&display=print&display=print&display=print&display=print&display=print& (2280 words)

	Methods (Site not responding. Last check: )
		Second, the use of Froude numbers provided a means to extrapolate the habitat classification system beyond the low flow discharges where it was possible to test habitat significance with biological sampling.
		While our Froude number based criterion were derived independently from field data collected at Ratcliff Ford (Figure 2.6), it is interesting to note the concurrence between this classification system and that derived by Jowett (1993).
		Jowett used a Froude number of 0.2 to delineate between pools and runs and a froude number of 0.4 to delineate between runs and races.
	www.cerc.usgs.gov /rss/rfmodel/2-Methods/methods.htm (2466 words)

	88.06.04: The Continuity Equation, the Reynolds Number, the Froude Number
		Two of the ratios are the ratio of inertial force to viscous force which is called the Reynolds number and the ratio of inertial force to gravitational force which is called the Froude number.
		While experimenting with the scale models he noticed that the wave patterns were the same in number along the hull when their ratios of speed to square root of length were the same.
		The residual resistances varied as the displacements when the Froude number for both the model and the prototype were equal.
	www.yale.edu /ynhti/curriculum/units/1988/6/88.06.04.x.html (4165 words)

	Physics News Graphics: Flutter and Tumble
		What determined whether the falling strips predominantly oscillated from side-to-side (flutter) or rotated end-over-end (tumble) was the Froude number, in this case the ratio of the time it takes for the strip to fall its own length to the time it takes for the strip to move from side to side.
		In that case, the Froude number describes the interplay between the swinging energy of the legs and the pull of the earth's gravity on the legs.
		For values just above the critical number, the strip would sometimes reverse its rotation direction randomly as it tumbled, but this was not observed enough times for the experimentalists to confirm that the culprit was chaos, in which small variations in the starting conditions lead in a well-defined way to unpredictable outcomes.
	www.aip.org /png/html/paper.htm (1529 words)

	Flow Regimes
		The Reynolds number (Re) is the ratio of inertial resistance to viscous resistance for a flowing fluid.
		The Mach number (Ma) is a ratio of inertia to compressibility.
		The Froude number (Fr) is the ratio of the inertial forces to the gravitational forces.
	hypertextbook.com /physics/matter/turbulence (1428 words)

	Chapter 8 - HEC 14 - Hydraulics - Engineering - FHWA (Site not responding. Last check: )
		To increase the Froude number as the water flows from the culvert to the basin, an expansion and depression is used as is shown in Figure 8.1.
		The Froude number used to determine jump efficiency and to evaluate the suitability of alternative stilling basins as described in Table 8.1 is defined in Equation 8.1.
		The number of chute blocks is determined by Equation 8.15a and rounded to the nearest integer.
	www.fhwa.dot.gov /engineering/hydraulics/pubs/06086/hec14ch08.cfm (6021 words)

	Met Office: Gravity wave drag
		When the Froude number is large, all the low-level flow passes over the sub-grid orography and all the drag is attributed to gravity waves.
		When the Froude number reduces to order unity, some of the drag is also attributed to flow blocking.
		In practice, the Froude number tends to be much less than unity, and so the majority of the drag is attributed to flow blocking.
	www.metoffice.gov.uk /research/nwp/numerical/physics/gravity.html (159 words)

	William Froude Summary
		Froude's most important work was in determining the amount of force that water exerts on a body passing through it.
		Froude conducted a great deal of laboratory research before developing Froude's law, which is a tool used to determine the amount of force required to pull an object against the retarding wave that is built up in front of it as it travels.
		Froude was the first to formulate reliable laws for the resistance that water offers to ships (such as the hull speed equation) and for predicting their stability.
	www.bookrags.com /William_Froude (468 words)

	Fluids In Motion, Alaska Science Forum
		In the case of the car and the wind tunnel, a factor called the "Reynolds number" dictates that the dimensions of the model must vary in inverse proportion to the wind velocity.
		In this situation, a factor called the "Froude number" outweighs the Reynolds number, and the scaling factor depends largely on the weight of the water that must be moved.
		To maintain a constant Froude number between model and full-size ship (which would result in the same wave pattern from both), the dimensions of the model must vary in proportion to the square of the velocity ratio.
	www.gi.alaska.edu /ScienceForum/ASF7/727.html (446 words)

	Eighteenth Symposium on Naval Hydrodynamics (Site not responding. Last check: )
		Figure 2a are visualizations of the surface deformation and underwater flow at a Froude number F/(g R3)1l2 = 0.252 where His the circulation of the vortex ring, g is the gravitational acceleration and R is the radius of the ring before interaction.
		For the cases shown in Figure 3 the core size parameter Rle, where e is the core radius, was 4.9 for the low Froude number case and 2.7 for the high Froude number case.
		Figure 4 is a plot of the normalized maximum elevation at the center, hlR, as a function of Froude number, F/(g R3J]/, for all the cases tested in the h/R.1 1 r/(g R3)1/2.01 / laboratory.
	www.nap.edu /books/0309045754/html/479.html (7020 words)

	Stream Habitat Quantification by Use of the Froude Number
		The Froude number (Fr) is used by hydraulic engineers to describe types of flow.
		Consequently, the Froude number can be computed by measuring channel width, cross sectional area, and discharge at specific stream cross sections.
		Froude number longitudinal and frequency distributions at 31 cross sections at two sites on Onondaga Creek, Tully, New York.
	www.stream.fs.fed.us /news/streamnt/jan96/jan96a3.htm (790 words)

	Generation of the Denver Cyclone. (Site not responding. Last check: )
		If the Froude number of the flow based on the height of the Palmer Divide (an east-west ridge to the south of Denver) is small then a vortex forms over the Denver region.
		Idealized experiments of low Froude number flow past a bell-shaped hill are also performed to explore the connection between lee vortices and the stagnation aloft predicted by linear theory.
		This experiment suggests that the intense, concentrated vorticity that develops in the lee of obstacles at low Froude numbers is due to the tilting of horizontal vorticity as gravity waves overturn and break.
	www.rap.ucar.edu /staff/crook/denver.html (298 words)

	Froude number - Definition, explanation
		In fluid dynamics, the Froude number (named after William Froude) is the reciprocal of the square root of the Richardson number.
		Strictly, this is known as the densimetric Froude number.
		The densimetric Froude number is usually preferred by modellers who wish to nondimensionalize a speed preference to the Richardson number which is more commonly encountered when considering stratified shear layers.
	www.calsky.com /lexikon/en/txt/f/fr/froude_number.php (173 words)

	Trapezoidal Open Channel Design Calculations, Software. Manning equation. Rivers, streams
		g is used in the equation for Froude number.
		However, if you wish to simulate a rectangular channel, you can set one of them to 0.0 and the other to a very small positive number such as 0.00001.
		Triangular channels can be modeled by setting the bottom width, b, to a very small positive number such as 0.001 m or as low as 10
	www.lmnoeng.com /Channels/trapezoid.htm (959 words)

	The Bridgenorth Esker - abstract
		From the calculated palaeovelocity values, Reynolds number, Froude number and bed shear stress were then calculated.
		The observed dependence of inferred velocity upon the esker width is, however, consistent with the expected hydraulic behaviour of the meltwater.
		Most Reynolds numbers indicated turbulent flow (using 500 as threshold), while most Froude numbers indicated subcritical flow.
	www.bridgenorthesker.ca /abstract.shtml (274 words)

	Kayak design comparison - wave and viscous drag
		This chart really shows the relative efficiency of the hulls adjusted for displacement (that is why the volumetric Froude number as the horizontal x-axis).
		The interpretation is different (than with speed) and may be a little confusing because the volumetric Froude number takes into consideration BOTH speed AND volume at the same time.
		This Froude number is essentially the "speed / length" ratio so often talked about in relation to prismatic coefficient, 'hull speed' and wave resistance.
	www.oneoceankayaks.com /kayakpro/kayakgrid.htm (1356 words)

	Ferry Wash Project Homepage
		Due to the ability of fast ferries to operate in shallow water with high speeds the influence of the ratio of water depth to ship velocity becomes the major parameter in analyzing the wash. This parameter is described in common as the Depth delimited Froude number, defined as:
		The wave pattern is called super critical as it occurs for all ship velocities with a Froude number >1.
		The crests and troughs are long continuously curved lines in contrast to the short crests and troughs in the sub critical wave pattern.
	www.qub.ac.uk /waves/fastferry/hsc/fast_ferry_hp.htm (213 words)

	Fluid Mechanics
		An introduction to and a definition of the Froude Number
		The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity
		An introduction to and a definition of the Weber Number
	www.engineeringtoolbox.com /fluid-mechanics-t_21.html (1370 words)

	Froude number -- CFD-Wiki, the free CFD reference
		Froude number -- CFD-Wiki, the free CFD reference
		The Froude number is the ratio of the flow speed to the speed of infinitesimal (incompressible) gravity waves in the same medium.
		It has application in phenomena such as Hydraulic Jump.
	www.cfd-online.com /Wiki/Froude_number (57 words)

	UTas ePrints - A High Froude Number Time Domain Strip Theory Applied to the Seakeeping of Semi-SWATHs
		This is a low Froude number theory, and although it is still being used, often successfully, for fast ships there is no rational justification for its validity in these cases.
		As speeds are increasing it is becoming imperative that an equivalent analysis tool suitable for higher Froude numbers be developed.
		This thesis proposes such a theory, based on calculation of two dimensional hydrodynamic potentials in a fixed reference frame in place of the traditional moving one.
	eprints.utas.edu.au /269 (528 words)

	Flutter and tumble in fluids (April 1999) - Physics World - PhysicsWeb
		For a falling object the Froude number measures the ratio between the typical timescales of falling and of swinging.
		Moreover, recent studies of the transition from walking to running in bipeds, or to a brisk trot in quadrupeds, occur at a critical Froude number of 0.8; the transition from a trot to a gallop in quadrupeds then occurs at around a Froude number of 3.
		In our experiments, the Froude number is proportional to the square root of the mass and inversely proportional to the length of the strip.
	www.physicsweb.org /articles/world/12/4/7/1 (3121 words)

	Savage Research
		With an increase number of missions to Mars over the next several years, research of the Martian atmosphere is vital for future missions.
		High Froude number flow simulations over a Martian mountain indicate little blocking and is comparable with flow found on Earth.
		Medium Froude number flow simulations over a Martian mountain indicate the basic flow is strong enough to overcome marginal blocking.
	mesolab.meas.ncsu.edu /~lcsavage/Mars.html (620 words)

	On Instabilities and Turbulence in Strongly Stratified Flows
		There are many situations involving smaller-scale, quasi-horizontal atmospheric and oceanic flows in which the local Froude number is of order 1 or less, so that the effects of stable density stratification are important or even dominant.
		It is found that, in the low Froude number regime, the wake ultimately will evolve into remarkably stable, quasi-horizontal vortex patches of alternating sign, suggesting a possible behavior of atmospheric and oceanic flows.
		The Reynolds number in the low Froude number regime in the experiments is rather low, however, raising the question of whether the results scale up to geophysical scales and truly represent atmospheric and oceanic flows.
	www.galcit.caltech.edu /Seminars/Fluids/PastFluids/2003-2004/Riley_abs.html (417 words)

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