Question

The critical velocity (v) depends on 
1)coefficient of viscosity
2)density of liquid
3)radius
derive an expression of velocity

Answer 1

Let us dimension analysis.
Critical Velocity  = Vc = K  *  coeff of viscocity^a  * density^b   *  radius^c
        L T^-1 =  K  *  (M L^-1 T^-1)^a    *  (M L^-3)^b    *  L^c
                  =  K    *  M^(a+b)    L^(-a-3b+c)    T^-c
         So      a+b =0  a = -b        -a -3b +c = 1      a = 1      So b = -1      c = -1

  Vc  =  K .  (coeff of visocity) / (density * radius)