Theorem: Reynolds number Re = rho*U*L/mu is dimensionless; exponent sums (M,L,T) = (0,0,0)

Theorem (Vaschy-Buckingham Reynolds-number dimensionless verification): Reynolds number Re = rho * U * L / mu where [rho] = M L^{-3}, [U] = L T^{-1}, [L] = L, [mu] = M L^{-1} T^{-1}. Exponent sums in each primitive dimension: M: +1 (rho) -…