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Unformatted text preview: .................................................................................................. .................................................................................................................................................................................................................................. σ µ ρg h Solution: The dimensional quantities and their dimensions are [h] = L, [µ] = M , LT [U ] = L T ML M F MLT −2 M = = 2 , [ρg ] = 3 2 = 2 2 [σ ] = L L T LT LT This problem has 5 dimensional quantities and 3 independent dimensions (M, L, T ). Hence, the Buckingham Π Theorem tells us that the number of dimensionless groupings is 2. Using the indicial method, the appropriate dimensional equation is [h] = [µ]a1 [U ]a2 [σ ]a3 [ρg ]a4 Substituting the dimensions for each quantity yields L = M a1 L−a1 T −a1 La2 T −a2 M a3 T −2a3 M a4 L−2a4 T −2a4 = M a1 +a3 +a4 L−a1 +a2 −2a4 T −a1 −a2 −2a3 −2a4 Thus, equating exponents, we arrive at the following three equations. 0 =...
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