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Forgive me for my ignorance. What would be the method to determine the pressure a non compressible fluid creates when forced though an orifice? Keep in mind this orifice does not have a constant diameter. I know the volume of fluid, the area squared of the orifice and the flow rate. I'm not a mathematician, any information you can provide will be helpful.

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    $\begingroup$ That doesn't seem to be a matter of mathematics. (You'll need to know at least the viscosity of the fluid, too). $\endgroup$ – Henning Makholm Oct 30 '14 at 12:49
  • $\begingroup$ Its blood. forty over one hundred units of millipoise. $\endgroup$ – Eric Oct 30 '14 at 13:11
  • $\begingroup$ You say you know the area of the orifice, but it does not have constant diameter. That's confusing. $\endgroup$ – Mike Dunlavey Oct 30 '14 at 13:52
  • $\begingroup$ Related question by someone also called Eric: physics.stackexchange.com/q/127954/2451 $\endgroup$ – Qmechanic♦ Feb 5 '15 at 16:14
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According to this doc flow rate is area times velocity times a correction factor $$Q = AVK$$ where $K$ depends on the orifice geometry, and for blood through a heart valve I suspect it is as large as possible, $1.55$. ($K$ is basically the ratio between the area of the actual flow and the measured area of the orifice - they are not the same.)

Pressure is related to velocity by Bernoulli's equation. My favorite explanation is this where pressure essentially boils down to $$1/2 \rho V^2$$ where $\rho$ is density (about 1 for blood). Then all you gotta do is get the units right.

BTW there's a calculator here.

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