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.
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.