This is a general fluid mechanics question: Suppose that we have a venturi conduit (entry segment of radius R1 reducing linearly to R2; middle segment of steady radius R2; exit segment of radius R2 and increasing linearly to R1) . Say now that we have an incompressible flow throughout the conduit and the flow exits the conduit at an ambient pressure say p0. Is it possible to reduce the diameter of the middle segment (R1) in such a scale so at some point in the middle segment the pressure would be less than p0 or even negative?

This is something I came accross while simulating a venturi flow and taking dimensionless p0=1. It would give me negative pressure in the middle segment. Would that have any sense?

thanks for your time

Pressure is a relative value in fluid mechanics, so there's no problem with negative pressure. In your case, it makes sense.

For incompressible flow, pressure is defined only upto a constant. This is because pressure only appears as a gradient in the fluid equations for incompressible flow. You talk of pressure differences only so that the constant does not matter. Of course in reality you must look out for cavitation.

one way to simplify this is to take a condition such that value of pressure at any one node is taken as zero and the other values are all relative to it and u can take a contour plot of the same to see ur output