In dimension of critical velocity v c, of liquid following through a tube are expressed as (${\mathrm{\eta }}^{\mathrm{x}}{\mathrm{\rho }}^{\mathrm{y}}{\mathrm{r}}^{\mathrm{z}}$) , where $\mathrm{\eta },\mathrm{\rho }$ and rare 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 :

$$\begin{gathered} {\mathrm{\nu }}_{\mathrm{c}}\propto \left[{\mathrm{\eta }}^{\mathrm{x}}{\mathrm{\rho }}^{\mathrm{y}}{\mathrm{r}}^{\mathrm{z}}\right] \\ \left[{\mathrm{L}}^1{\mathrm{T}}^{-1}\right]\propto {\left[{\mathrm{M}}^1{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}\right]}^{\mathrm{x}} {\left[{\mathrm{M}}^1{\mathrm{L}}^{-3}\right]}^{\mathrm{y}}{\left[{\mathrm{L}}^1\right]}^{\mathrm{z}} \\ \left[{\mathrm{L}}^1{\mathrm{T}}^{-1}\right]\propto \left[{\mathrm{M}}^{\mathrm{x}+\mathrm{y}}\right]\left[{\mathrm{L}}^{-\mathrm{x}-3\mathrm{y}+\mathrm{z}}\right]\left[{\mathrm{T}}^{-\mathrm{x}}\right] \end{gathered}$$
Taking comparison on both sides
x+y=0, -x-3y+z=1, -x=-1
$\Rightarrow$x= 1,y=-1,z=-1

ALTERNATE SOLUTION:

REYNOLDS NUMBER    R=$\frac{D v \rho }{\eta }=M^0{L}^0{T}^0$ 

V $\alpha \eta r^{-1}{\rho }^{-1}$  v is critical velocity D = DIAMETER OF the TUBE , r= radius of the tube.