Information about Froude Number
The Froude number is a dimensionless number comparing inertial and gravitational forces. It may be used to quantify the resistance of an object moving through water, and compare objects of different sizes. Named after William Froude, the Froude number is based on his speed/length ratio.
The quantification of the resistance of floating objects is generally credited to Froude, who used a series of scale models to measure the resistance each model offered when towed at a given speed. 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 Naval Constructor Ferdinand Reech had put forward the concept in 1832 but had not demonstrated how it could be applied to practical problems in ship resistance. Speed/length ratio was originally defined by Froude in his Law of Comparison in 1868 in dimensional terms as:
where:
The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did. It is sometimes called Reech-Froude number after Ferdinand Reech.
is an average velocity , and 
is the propagation velocity of a shallow water wave. The Froude number is thus the hydrodynamic equivalent to the Mach number.
is equal to the square root of gravitational acceleration times cross-sectional area divided by free-surface width, i.e.
and so the Froude number can often be simplified to
The Froude number is the reciprocal of the square root of the Richardson number.
where g' is the reduced gravity
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. For example, the leading edge of a gravity current moves with a front Froude number of about unity.
In free-surface flow, the nature of the flow (supercritical or subcritical) depends upon whether the Froude number is greater than or less than unity.
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Origins
)
The hulls of swan (above) and raven (below). A sequence of 3, 6 and 12 (shown in the picture) foot scale models were constructed by Froude and used in towing trials to establish resistance and scaling laws.
where:
- v = speed in knots
- LWL = length of waterline in feet
The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did. It is sometimes called Reech-Froude number after Ferdinand Reech.
Dimensionless form
The dimensionless Froude number is defined as
is an average velocity , and is the propagation velocity of a shallow water wave. The Froude number is thus the hydrodynamic equivalent to the Mach number.
is equal to the square root of gravitational acceleration times cross-sectional area divided by free-surface width, i.e.
and so the Froude number can often be simplified to
The Froude number is the reciprocal of the square root of the Richardson number.
Densimetric Froude Number
When used in the context of the Boussinesq approximation the densimetric Froude number is defined as
where g' is the reduced gravity
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. For example, the leading edge of a gravity current moves with a front Froude number of about unity.
Uses
The Froude number is used to compare the wave making resistance between bodies of various sizes and shapes.In free-surface flow, the nature of the flow (supercritical or subcritical) depends upon whether the Froude number is greater than or less than unity.
See also
Dimensionless numbers in fluid dynamics |
|---|
| Archimedes • Bagnold • Bond • Brinkman • Capillary • Damkhler • Dean • Deborah • Eckert • Ekman • Etvs • Euler • Froude • Galilei • Grashof • Hagen • Knudsen • Laplace • Lewis • Mach • Magnetic Reynolds • Marangoni • Nusselt • Ohnesorge • Pclet • Prandtl • Rayleigh • Reynolds • Richardson • Rossby • Rouark • Schmidt • Sherwood • Stanton • Stokes • Strouhal • Taylor • Weber • Weissenberg • Womersley |
External Links
- More than 300, freely available, published research articles on open channel flow, hydraulic engineering and related topics by Professor Hubert Chanson, Department of Civil Engineering, The University of Queensland
- http://www.qub.ac.uk/waves/fastferry/reference/MCA457.pdf
In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number.
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William Froude (November 28, 1810, Dartington, Devon, England - May 4, 1879, Simonstown, South Africa) was an engineer, hydrodynamicist and naval architect. He was the first to formulate reliable laws for the resistance that water offers to ships (such as the hull speed equation)
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Mach number (Ma) (pronounced: [mɑːk], [mɑx], [mæk], see IPA) is a dimensionless measure of relative speed.
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The Richardson number is named after Lewis Fry Richardson (1881 - 1953). It is the dimensionless number that expresses the ratio of potential to kinetic energy [1]
where g is the acceleration due to gravity, h
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where g is the acceleration due to gravity, h
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In fluid dynamics, the Boussinesq approximation (named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow. It states that density differences are sufficiently small to be neglected, except where they appear in terms multiplied by g
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The Richardson number is named after Lewis Fry Richardson (1881 - 1953). It is the dimensionless number that expresses the ratio of potential to kinetic energy [1]
where g is the acceleration due to gravity, h
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where g is the acceleration due to gravity, h
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In fluid dynamics, a gravity current is a primarily horizontal flow in a gravitational field that is driven by a density difference. Typically, the density difference is small enough for the Boussinesq approximation to be valid.
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Wave making resistance is a form of drag that effects surface Watercraft, such as boats and ships, and reflects the energy required to push the water out of the way of the hull. This energy goes into creating the wake.
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A supercritical flow is when the flow velocity is larger than the wave velocity. The analogous condition in gas dynamics is supersonic.
Information travels at the wave velocity, this is the velocity at which waves travel outwards from a pebble thrown into a lake.
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Information travels at the wave velocity, this is the velocity at which waves travel outwards from a pebble thrown into a lake.
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In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number.
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Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion).
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An Archimedes number (not to be confused with Archimedes' constant, π), named after the ancient Greek scientist Archimedes, to determine the motion of fluids due to density differences, is a dimensionless number in the form:
where:
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where:
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The Bagnold number, named after Ralph Alger Bagnold, used in granular flow calculations, is defined by
where is the mass, is the grain diameter, is the surface tension and
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where is the mass, is the grain diameter, is the surface tension and
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In fluid mechanics, the Bond number, notated Bo, is a dimensionless number expressing the ratio of body forces (often gravitational) to surface tension forces:
where
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where
- is the density,
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The Brinkman Number is a dimensionless group related to heat conduction from a wall to a flowing viscous fluid, commonly used in polymer processing. There are several definitions; one is
Where
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Where
- NBr = the Brinkman Number
- η
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In fluid dynamics, the capillary number represents the relative effect of viscous forces versus surface tension acting across an interface between a liquid and a gas, or between two immiscible liquids.
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The Dean number is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels. It is named after the British scientist W. R. Dean, who studied such flows in the 1920's (Dean, 1927, 1928).
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The Deborah number is a dimensionless number, used in rheology to characterize how "fluid" a material is. Even some apparent solids "flow" if they are observed long enough; the origin of the name, coined by Prof.
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The Eckert number is a dimensionless number used in flow calculations. It expresses the relationship between a flow's kinetic energy and enthalpy, and is used to characterize dissipation. It is named for the late professor Ernst R. G. Eckert.
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The Ekman number, named for V. Walfrid Ekman, is a dimensionless number used in describing geophysical phenomena in the oceans and atmosphere. It characterises the ratio of viscous forces in a fluid to the fictitious forces arising from planetary rotation.
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The Euler number is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop over e.g. a restriction and the kinetic energy per volume, and is used to characterize losses in the flow.
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In fluid dynamics, the Galilei number (Ga), sometimes also referred to as Galileo number (see discussion), is a dimensionless number named after Italian scientist Galileo Galilei (1564-1642).
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The Grashof number is a dimensionless number in fluid dynamics which approximates the ratio of the buoyancy to viscous force acting on a fluid. It is named after the German engineer Franz Grashof.
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The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid.
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The Laplace number (La), also known as the Suratman number (Su), is a dimensionless number used in the characterization of free surface fluid dynamics. It is represents a ratio of surface tension to the momentum-transport (especially dissipation) inside a fluid.
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Lewis number is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transfer by convection.
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Mach number (Ma) (pronounced: [mɑːk], [mɑx], [mæk], see IPA) is a dimensionless measure of relative speed.
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