v α λa ρb gc ⇒ v = K λa ρb gc
Where K is the dimensionless constant).
Writing the dimensional formulae of various quantities involved in equation (i) we have
[M0LT-1] = [L]a [ML-3]b [LT-2]c
= [Mb La-3b +c T-2c]
Comparing the powers of M,L and T, we get a - 3b +c = 1 ...(ii)
-2c = -1
or ,c = 1/2 ....(iii)
b = 0
Again from (iii), (ii) and (iv), we get
a - 3b = 1 -1/2 = 1/2
or, a - 0 = 1/2 ⇔ a = 1/2 ...(iv)
Substituting the values of a, b and c in (i), we get