Sonic Velocity & Mach No.
 

Hi Guys, does anyone know how to determine the (dimensionless) sonic velocity of a flow purely in terms of the upstream mach number?

I am reading a paper at the moment and the author uses

U_s = { 1 + [ 2(1-M^2) / (gm+1)M^2 ] }^(1/2)

where M is the mach number and gm is the ratio of heat capacities.

I have no idea where this equation comes from but would be very grateful if someone could shed some light on the matter.

Many thanks, Frank

worked it out
 

Doh!

sorry guys I was being a bit slow - I worked out the solution to this easy question.

The answer for the interested reader is to use the conservation of total enthalpy - non-dimensionalise using the upstream velocity (which gives a 1/M_inf^2 term). The equation I mentioned in my first post then comes from setting the local flow velocity equal to the local sound speed and easy algebraic changes.

Thanks for those who read my post Frank