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Chapter02 - Dimensional Analysis Dimensional This technique...

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Dimensional Analysis Dimensional Analysis z This technique is useful in all branches of science and engineering z Basic premises are 1. Physical quantities have dimensions 2. All equations developed from basic laws of physics are dimensionally homogeneous z We can develop a useful theory from this information
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Dimensions Dimensions - - 1 1 z Consider viscosity, μ, which has SI units kg/(m•sec) and USCS units slug/(ft •sec) z We write z [ μ ] means “dimensions of μ ” while M , L and T denote dimensions of mass, length and time, respectively z If temperature is relevant, we denote its dimension by Θ z M , L , T and Θ are called independent dimensions
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Dimensions Dimensions - - 2 2 z All dimensions can be expressed in terms of the independent dimensions z For example, consider pressure, p , which has dimensions of force per unit area…appealing to Newton’s law, we have z Thus, for dimensional analysis purposes, pressure has SI units of kg/(m•sec 2 ) and USCS units of slug/(ft•sec 2 )
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Dimensional Homogeneity Dimensional Homogeneity - - 1 1 z Universal equations are valid regardless of the choice of units z Counter-example… theoretical hull speed for a sailboat (single hull, non-surfing) U hull = Sailboat speed in knots L w = Hull length at the waterline in feet
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