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Let R = K rho^a upsilon^b eta^c D^1 …. (...

`Let R = K rho^a upsilon^b eta^c D^1 …. (i)`
where a, b, c are the dimensions and K is dimensionless constant. Writing the dimensions in(i) we get
`[M^0 L^0 T^0] = [ML^(-3)]^1 (LT^(-1)^b (ML^(-1))^c L^1`
`= M^(a+c) L^(-3a +b +1-c) T^-b-c`
Applying the principle of homogeneity of dimensions, we get
a +c = 0, c= -a
-3a +b +1 -c =0 .... (ii)
-b-c = 0 or b= -c
From (ii) -3a - c+1 -c = 0
-3a - 2c =-1 or -3a +2a = -1 or a= 1
c = -a =-1, b=-c =1
Putting these values in (i) we get
`R = K rho^1 upsilon^1 eta^(-1) D^1`
`R = K (rho upsilonD)/(eta)`

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