Absolute or Gauge pressure? NS and Equation of state

cici · October 10, 2012, 10:59

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.

cdegroot · October 10, 2012, 12:47

The Navier-Stokes equations include just the pressure gradient, therefore it doesn't matter which one you use since their gradients are the same.

cici · October 10, 2012, 13:23

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?

cdegroot · October 10, 2012, 13:34

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!).

cici · October 11, 2012, 09:52

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?

October 10, 2012, 10:59	Absolute or Gauge pressure? NS and Equation of state	#1
cici New Member Join Date: Jul 2011 Posts: 25 Rep Power: 14	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.

October 10, 2012, 12:47		#2
cdegroot Senior Member Chris DeGroot Join Date: Nov 2011 Location: Canada Posts: 414 Rep Power: 17	The Navier-Stokes equations include just the pressure gradient, therefore it doesn't matter which one you use since their gradients are the same.

October 10, 2012, 13:23		#3
cici New Member Join Date: Jul 2011 Posts: 25 Rep Power: 14	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?

October 10, 2012, 13:34		#4
cdegroot Senior Member Chris DeGroot Join Date: Nov 2011 Location: Canada Posts: 414 Rep Power: 17	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!).

October 11, 2012, 09:52		#5
cici New Member Join Date: Jul 2011 Posts: 25 Rep Power: 14	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?