according to EK, bp is highest in arteries (small area) and lowest in capillaries (largest area when all of them are combined)
It's implying that pressure and velocity are directly related, and inversely related to area
However, benoulli's principle states that velocity and pressure are inversely proportional in a closed system
I'm confused. The reason I'm asking is that I've seen different test prep companies do things differently
I've seen some test prep companies use Bernoulli's law in circulatory system "passages"
EK, on the other hand, states that opposite and says that they are incompatible...
So, from my understanding as an engineer (maybe diff. than md's?):
Bernoulli's law in it's absolute sense is really a variation of Conservation of Energy. If you multiply its components by Volume, you will get all energy units:
P + rho*g*h + (1/2)*rho*velocity^2 = Constant becomes
PV + mass*g*h + (1/2) * mass * velocity^2 = Constant or
"Pressure" Energy + Potential Energy + Kinetic Energy (bulk flow) = Constant
To make this fit with what you asked about EK......the "Pressure" Energy is analogous to the Bee stinging analogy in EK Physics on page 85. Personally, I only loosely endorse this analogy....but whatever works for you.
In any case, the Bern. equation is therefore simply a conservation of this energy in fluid flow; given the following caveats:
1. fluid flow is inviscid
2. is laminar / irrotational
3. is incompressible.
The circulatory system is clearly not inviscid. Clearly there is a drag force / frictional force/ non-conservative force as the blood flows from the aorta, through the circulatory system and back to the major veins.
Berns. Equation does not apply directly in this case because there cannot be a conservation of energy! Energy is being "leaked"
P + 1/2*rho*g + 1/2*rho*v^2 DOES NOT = Constant (the value is continually diminshing)
In engineering terms this is called the pressure drop through the system, and an alternate equation such as Darcy-Weisbach equation can be used to calculate the pressure drop, though I would never imagine this would ever be on the MCAT.
The only other question then becomes, why does a dialation of an artery then lower the local blood pressure. I submit this is because there is magnitude factor differrence between the volume flow and the surface area as dialation occurs....namely a factor of r (r^3 vs. r^2).
Hope that helps.
