Absolute or Gauge pressure? NS and Equation of state
Hi All,
Are those pressure used in NS equations the same as in equation of state? My understanding has always been that the former gauge pressure, the latter absolute one. But how come most of the references use the same symbol to refer to these two different variables. Or is ot just a convention?? Thanks. 
The NavierStokes equations include just the pressure gradient, therefore it doesn't matter which one you use since their gradients are the same.

Thanks! But I knew this. I should use governing or conservation equations instead of NS equations. In the conservation of engergy, there are u(dp/dx) and p(du/dx), if we use total enthalpy as the conservative, which rise with the relation between energy and enthalpy:h=e+p/rho. What is the pressure here then?

If you are using pressure to define enthalpy you should use absolute pressure since the use of gauge pressure would make the definition of enthalpy and terms like p(du/dx) arbitrary (and possibly negative!).

Thanks.
Some references ignore the acoustic pressure Pa, and decompose the pressure into the thermodynamic pressure Pt and hydrodynamic pressure Ph. Pt is used for equation of state, not the total pressure, and Ph for momentum. In this case, what is the absolute pressure? If acoustic pressure is included, which part of pressure does it fit into? On other words, how is pressure decomposed? 
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