In the flow screen, should there be a buildup of pressure before a pipe narrowing?

[samreid]

A client wrote:

I would like to show that partial occlusion of a vein/artery results in increased pressure behind the occlusion/narrowing. I understand, that at the point of occlusion/narrowing, the pressure actually decreases, however, I was under the impression that the pressure behind that point would actually increase as there is still fluid entering and there is limited space for it to exit (i.e. like putting your thumb over the end of the hose). If you physically limit the amount of space for the fluid to pass – at some point – the pressure behind the occlusion must increase and this would also lead to increased fluid flow through the narrowed region. I tried to do this on the program. I put two pressure readouts in the normal state (picture below) and then I narrowed the pipe, but all pressures (and flow) stayed the same. I wonder whether you are interested in this question, as I hope that it is relevant.. can the edges of the pipe be brought even closer together to demonstrate this?

[brettfiedler]

The simulation uses the incompressible Bernoulli equation, which is an approximation for "ideal" conditions (constant density, incompressible fluid/gas, nonviscous, laminar flow - i.e. a nice Newtonian fluid) and steady-state flow. (see http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html)

The pressure before a constriction is often higher than after thanks to friction and a loss of kinetic energy in the system resulting from Poisseiulle's law (http://hyperphysics.phy-astr.gsu.edu/hbase/pber2.html#c4). However, the beginning pressure is not higher than the initial pressure.

The client is asking to place real, physical constraints on the system that bring us out of equilibrium, which requires you to simulate outside of ideal conditions, which could be accounted for in blood vessels by factors such as:

• Variable volumes due to arterial wall stretching
• Density, viscosity changes due to local cell concentrations around a constriction (compressibility).
• Turbulent flow
• Oscillating input pressure (heartbeat) All which might briefly knock you out of equilibrium around the constriction, but should re-establish pretty quickly.

In the ideal equation, if you change the pipe height/volume, something else has to change about the liquid to increase the pressure rather than decrease it. That being said, this equation is a HUGE approximation, so they are probably right. However, we'd need to add some more variables and consider this as a non-equilibrium problem.

[samreid]

I pointed the client to this issue and will self-unassign until I hear back.