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P' is the hydrostatic pressure while P is the static pressure. If gravity is off, this term would fall out, but if gravity is on and if you define a density in the operating conditions, then this would be the density used in the rho*g*r term. This could be negative if P is less than rho*g*r, but that could only happen if P was a gauge pressure. Absolute pressure can't be negative (if the numerics run away, that's another story, but physically it can't happen).
What I was describing was the use of gauge vs. absolute pressure.
Pgauge = Pabsolute - Preference
If gravity is on and you define a reference point, then the absolute pressure would be adjusted so that the gauge pressure at the reference location is 0 (only for incompressible fluids without a pressure inlet BC). So if gravity were on and there was no (or very little) fluid motion, you'd be right, then anything "above" this location would have a negative static pressure, and anything "below" this location has a positive pressure. |
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