# Fluid flow through an orifice

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.

• That doesn't seem to be a matter of mathematics. (You'll need to know at least the viscosity of the fluid, too). Oct 30 '14 at 12:49
• Its blood. forty over one hundred units of millipoise.
– Eric
Oct 30 '14 at 13:11
• You say you know the area of the orifice, but it does not have constant diameter. That's confusing. Oct 30 '14 at 13:52
• Related question by someone also called Eric: physics.stackexchange.com/q/127954/2451 Feb 5 '15 at 16:14

## 1 Answer

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.