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

1 , -1 , -1

c = [$η^xρ^yr^z$]

Put dimensions of various quantities,

[M⁰LT^-1] = [ML^-1T^-1]^x [ML^-3T⁰]^y [M⁰LT⁰]^z
                = [M^{x + y} L^{- x - 3y + z} T^{- x}]

Equating power both sides, we get

x + y = 0;
- x - 3y + z = 1;
- x = - 1

On solving, we get

x = 1, y = -1, z = -1