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DIMENSIONAL ANALYSIS

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What it is: In science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions.

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What it is: In science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of (up to) 7 fundamental dimensions which describe it. – Ex: speed has the dimension length per time, and volume has dimensions of length cubed.

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What it is: In science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the 7 fundamental dimensions which describe it. – Ex: speed has the dimension length per time, and volume has dimensions of length cubed. Dimensional analysis is based on the fact that a physical law must be independent of the units used to measure the physical variables.

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What it is: In science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the 7 fundamental dimensions which describe it. – Ex: speed has the dimension length per time, and volume has dimensions of length cubed. Dimensional analysis is based on the fact that a physical law must be independent of the units used to measure the physical variables. It follows that any meaningful equation must have the same dimensions in the left and right sides. Checking this is the basic way of performing dimensional analysis.

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EXAMPLE I

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EXAMPLE II

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IDEAL GAS LAW (cont’d)

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EXAMPLE III

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EXAMPLE III (cont’d)

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EXAMPLE IV

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EXAMPLE IV (cont’d)

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Procedure to check dimensionality 1.Eliminate all constants (numbers without units), by “dropping” them out of the equation. That is, re-write the equation, leaving the constants out.

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Procedure to check dimensionality 1.Eliminate all constants, by “dropping” them out of the equation. That is, re-write the equation, leaving the constants out. 2.Replace all quantities by their SI dimensions, on both sides of the equation.

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Procedure to check dimensionality 1.Eliminate all constants, by “dropping” them out of the equation. That is, re-write the equation, leaving the constants out. 2.Replace all quantities by their SI dimensions, on both sides of the equation. 3.Simplify both sides.

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Procedure to check dimensionality 1.Eliminate all constants, by “dropping” them out of the equation. That is, re-write the equation, leaving the constants out. 2.Replace all quantities by their dimensions, on both sides of the equation. 3.Simplify both sides. 4.Compare both (simplified) sides. If they have the same dimension, the equation is dimensionally correct.

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CAUTION!

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THE END Lilian Wehner ©

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