i know there are 5 products in here are 3 fundamental dimension of MLT in here i was able to get the the liner system of equation however i was not able to solve it as it seems hard and was wondering if you could check to see if it actually correct leading to that point . my attmept so far https://ibb.co/hBmprn9
The dimensions are $[E]=L^2MT^{-3},\,[D]=L,\,[f]=T^{-1},\,[\mu]=L^{-1}MT^{-1},\,[m]=M$, so as long as we get rid of the $M$ power we can tidy up with $D,\,f$ later. There are two ways to cancel the $M$ in $\mu$, one with $E$, one with $m$. So $\frac{D^3f^2\mu}{E}$ is dimensionless, as is $\frac{D\mu}{mf}$.