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In continuum mechanics, the Froude number (Fr) is a dimensionless number defined as the ratio of the flow inertia to the external field (the latter in many applications simply due to gravity). Named after William Froude, the Froude number is based on the speed–length ratio as defined by him, and is defined as:〔(Shih, 6.Incompressible fluid flow, p.7 )〕〔Frank M. White, Fluid Mechanics, 4th edition, McGraw-Hill (1999), 294.〕 : where ''u''0 is a characteristic flow velocity, ''g''0 is in general a characteristic external field, and ''l''0 is a characteristic length. The Froude number has some analogy with the Mach number. In theoretical fluid dynamics the Froude number is not frequently considered since usually the equations are considered in the high Froude limit of negligible external field, leading to homogeneous equations that preserve the mathematical aspects. For example homogeneous Euler equations are conservation equations. However, in naval architecture the Froude number is a very significant figure used to determine the resistance of a partially submerged object moving through water, and permits the comparison of similar objects of different sizes, because the wave pattern generated is similar at the same Froude number only. The Denny Ship Model Experiment tank in Dumbarton, Scotland, has a bust of Froude near the front door. ==Origins== In open channel flows, Bélanger (1828) introduced first the ratio of the flow velocity to the square root of the gravity acceleration times the flow depth. When the ratio was less than unity, the flow behaved like a fluvial motion (i.e., subcritical flow), and like a torrential flow motion when the ratio was greater than unity. thumbaven'' (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.]] Quantifying resistance of floating objects is generally credited to William 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 1852 for testing ships and propellers. Speed/length ratio was originally defined by Froude in his ''Law of Comparison'' in 1868 in dimensional terms as: where: :''u'' = flow speed :LWL = length of waterline The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did. In France, it is sometimes called Reech–Froude number after Ferdinand Reech.〔Chanson (2004), p. xxvii.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Froude number」の詳細全文を読む スポンサード リンク
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