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 Beginner April 13, 2005 08:30

the pressure in Momentum eq.

What is the unit of pressure term in the Momentum equation? It is the absolute pressure or relative pressure? for the close cavity wall flow, the result is in -20~20 ... Do not know whether it is correct? Thanks in advance

 m. malik April 13, 2005 08:55

Re: the pressure in Momentum eq.

Well, pressure unit is Pa or psi. In the momentum equations, it appears as derivatives of spatial coordinates (and not as such).

 Beginner April 13, 2005 09:14

Re: the pressure in Momentum eq.

Thank you for your information. It should be the absolute pressure value, isn't it? That pressure range -20~20 pa is for low Ra and laminar flow.

 Tom (different one) April 13, 2005 09:25

Re: the pressure in Momentum eq.

As the earlier poster suggests the value of the pressure in the Navier-Stokes equation is a relative quantity - the actual numeric value is pretty much meaningless; i.e. replace P by P+f(t) in the equations for any function (f) of time and the solution will be unchanged.

The only time when the actual value of P is important is when you have boundary condition which specifies the (atmospheric) value of P.

 Jonas Holdeman April 13, 2005 09:43

Re: the pressure in Momentum eq.

The above responses are appropriate for incompressible flow. The pressure units should be compatible with the system of units used for the density and velocity. For compressible flow, the pressure also appears in the equation of state for the fluid. This is a thermodynamic pressure and the units will depend on the approximation used for the equation of state (and the units used for the compressibility).

 Mani April 13, 2005 14:21

Re: the pressure in Momentum eq.

That's right. The absolute pressure is of significance in compressible flow. We cannot answer your question because we don't know in which form your momentum equation is used. It could be using dimensional or non-dimensional quantities. Since you indicated negative pressure values, you must be using some kind of relative pressure... I am guessing that you indeed solve incompressible flow.

Even in the incompressible case, the units of dp/dx may still be of interest to you. You should be able to determine the units by analyzing your equation (provided that you know the units of the other quantities like mass, time, length...). In case of non-dimensionalization you need to find out which reference values are used.

 Beginner April 13, 2005 23:30

Re: the pressure in Momentum eq.

Thank you for your valueable advices. It is incompressible flow and I am using the non-dimensional governing equations.

Best Regards

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