Drag force fD=f(D,V,P,$\mu)$

fD=$k-D^{a}.V^{b}.P^{c}.\mu^{d}$

substituting the dimensions on both sides

$MLT^{2}=k(L)^{a}.(LT^{-1})^{b}.(ML^{-2})^{c}.(ML^{-1}T^{-1})^{d}$

on equating the dimensions on both sides

Power of M:1=c+d

Power of L:=1=a+b-3c-d

Power of T=-2=-b-d

We have only three equation whereas we have unknowns therefore the values of the power abcd cannot be determined out of these any …