Problem $3$ The terminal rise velocity of a spherical shaped particle in a fluid is a function of diameter of the particle $d_p,$ viscosity of the fluid $$ and weight of the particle in the fluid, $W_f.$ Through dimensional analysis, represent the functional relationship in terms of two characteristic dimensionless groups ${}_1-K({}_2{)}^n.$ If Stokes flow regime is applicable what is the numerical value of $K$ and $a$ in the above $?$