I hated pump curves. Fluids was one of my least favorite classes actually, but it ends up being a big part of my thesis. Go figure!
Ok, so if you're fascinated, I'll tell you more about it, hopefully this doesn't get too boring . The full title of my thesis is ... The Roles of Mechanical Conditioning in the Development of an Bioartificial Artery. The basic idea is to subject artificial artery tissue to the types of mechanical forces they would experience in the body and see how they affect tissue growth. I think you can imagine that blood flow in arteries is pretty much pipe flow. Not quite that simple, but basically its the same thing. One of the most important forces in arterial system is the wall shear stress that acts on the cells that line your arteries and veins (endothelial cells). These cells are very sensitive to the shear stress so controlling it is really important. That means breaking out things like the Navier-Stokes equations to calculate it. Flow regime is really important since the cells only respond to laminar flow so the Reynolds number comes into play. And to get all this to happen I need pumps to make the fluid go.
So there you go, fluid mechanics and arteries in a nutshell. Hope that wasn't to horrible to read.
Feel free to ask away. I don't mind answering questions about it, especially if people are genuinely interested as you seem to be.
To answer your question ... well first, what you do mean by "model an artery"? Physically? Mathematically?
The N-S equations are pretty daunting, but in most situations nearly all of the terms drop out leaving fairly simple equations to solve. We really don't do much modeling since the flow profile is simple enough that it can be adequately estimated by the Poiseuille assumption (steady laminar flow in a pipe), which you may or may not have studied yet. If you really wanted to model it, it would quite difficult. A lot of people have tried, but still not gotten it right. Trying to take into account pulsatile flow , nonlinear viscoelastic artery wall mechanics, and shear-thinning blood means you are in for a world of hurt in the math department.
Ok, so if you're fascinated, I'll tell you more about it, hopefully this doesn't get too boring
So there you go, fluid mechanics and arteries in a nutshell. Hope that wasn't to horrible to read.
To answer your question ... well first, what you do mean by "model an artery"? Physically? Mathematically?
The N-S equations are pretty daunting, but in most situations nearly all of the terms drop out leaving fairly simple equations to solve. We really don't do much modeling since the flow profile is simple enough that it can be adequately estimated by the Poiseuille assumption (steady laminar flow in a pipe), which you may or may not have studied yet. If you really wanted to model it, it would quite difficult. A lot of people have tried, but still not gotten it right. Trying to take into account pulsatile flow , nonlinear viscoelastic artery wall mechanics, and shear-thinning blood means you are in for a world of hurt in the math department.