Example Solutions Homework 11

1 x c2 c2 0 t 0 1 x b2 b2 0 l 0 1 1 x

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Unformatted text preview: 2 b2 = 0 L: 0 = 1 + (1) x a2 + (-3) x c2 a2 = -1 + (3)c2 a2 = -1 (d) Substitute the exponents back into the original equation: Π D d t ρ Therefore, Π D d Generate 3: (a) Multiply another of the remaining independent variables by the repeating variables: Π γ d t ρ (b) Set the left hand side exponents equal to the right hand exponents (dimensionally): M L t M Lt L t M L (c) Solve for the exponents by forcing x,y, and z to be zero, in turn: M: 0 = 1 + (1) x c3 c3 = -1 t: 0 = -2 + (1) x b3 b3 = 2 L: 0 = -2 + (1) x a3 + (-3) x c3 a3 = 2 + (3) x (-1) a3 = -1 (d) Substitute the exponents back into the original equation: Π γ d t ρ Therefore, Π γt dρ Generate 4: (a) Multiply the remaining independent variable by the repeating variables: Π h d t ρ (b) Set the left hand side exponents equal to the right hand exponents (dimensionally): M L t L L t M L (c) Solve for the exponents by forcing x,y, and z to be zero, in turn: M: 0 = (1) x c4 c4 = 0 t: 0 = (1) x b4 b4 = 0 L: 0 = 1 + (1) x a4 + (-3) x c4 a4 = -1 + (3)c4 a4 = -1 (d) Substitute the exponents back into the original equation: Π h d t ρ Therefore, Π h d 6) Given that 1 is a function of 2-k, the formulation would appear as follows: Π Π ,Π ,Π T...
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