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Bernolli's equation


Hello!

My name is Saeed, and i have a problem which i hope you can help me to solve.
The problem is as follows:

Having Bernolli's equation 
(1/2)*u^2+(1/(Gamma-1)*a^2-G*M/r=(1/(Gamma-1))*ainf^2
i would like to write it as dimensionless equation using parameters below
x \equiv r/(G*M/ainf^2), v \equiv u/a, z \equiv rho/rhoinf =
(a/ainf)^(2/Gamma-1), eliminating z from the result using \dot M =
4*Pi*r^2*rho*u and \dot M = 4*Pi*lambda*(G*M/ainf^2)^2*rhoinf*ainf.

The question is how can i substitute these parameters in Bernolli's equation
in order to obtain desired result using Mma 3.0. 

Any help appreciated.

Thakns



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