Unformatted text preview: v = C ( ρ ) 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 /ρ 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 identiﬁed the most relevant quantities, the (undetermined!) dimensionless coeﬃcient 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, Elementary algebra

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