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Unformatted text preview: v = C ( ) a ( p ) b , with C a dimensionless constant. 4. Substitute units from 2 and combine exponents. [ L ][ T ]1 [ M ] a [ L ]3 a [ M ] b [ L ]b [ T ]2 b = [ L ][ T ]1 [ M ] a + b [ L ]3 ab [ T ]2 b 5. Equate exponents of [ M ], [ L ], [ T ] on left and right sides of 4 and solve the resulting equations simultaneously. [ M ]: 0 = a + b [ L ]: 1 =3 ab [ T ]:1 =2 b = b = 1 / 2 = a =1 / 2 = answer: v = C q p / 6. Always check your results by plugging back into the equations. 0 =1 / 2 + 1 / 2 1 =3 (1 / 2)1 / 2 = 3 / 21 / 2 1 =2 1 / 2 If you have identied the most relevant quantities, the (undetermined!) dimensionless coecient will typically be of order unity (e.g., between 1/3 and 3). C 1 . 2 for air!...
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 Spring '11
 Furnstahl
 Quantum Physics

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