If the dimensions of the critical velocity v_c of a liquid flowing through a tube are expressed as [η^xρ^yγ^z], where η, ρ and γ are the coefficient of viscosity of the liquid, the density of the liquid and the radius of the tube respectively, then the values of x, y and z are given by

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(3) 1, -1, -1. [η]=[ML⁻¹T⁻¹], [ρ]=[ML⁻³], [γ]=[L] [v_c]=[LT⁻¹]=[ML⁻¹T⁻¹]^x[ML⁻³]^y[L]^z Idea: match the exponents of M, L and T one at a time. Time: -x=-1⇒ x=1 Mass: x+y=0⇒ y=-1 Length: -x-3y+z=1⇒ -1+3+z=1⇒ z=-1 So x=1, y=-1, z=-1, giving the familiar v_c=(kη)/(ργ).

If the dimensions of the critical velocity v_c of a liquid flowing through a tube are expressed as [η^xρ^yγ^z], where η, ρ and γ are the coefficient of viscosity of the liquid, the density of the liquid and the radius of the tube respectively, then the values of x, y and z are given by

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