In dimension of critical velocity ${\text{v}}_{\text{c}}$ of liquid flowing through a tube are expressed as $\left({\eta }^x,{\rho }^y,r^z\right)$ where $\eta ,\rho \text{\hspace{0.17em}and\hspace{0.17em}r}$ 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: