Ek bernoullis principle

[Meredith92]

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In ek bio p 142 it says " although bernoullis equation tells us that pressure is inversely related to cross sectional area it is evident in figure 7-7 that this is not the case w blood vessels"

However I thought in bernoullis equation area and pressure are directly related
A1v1=A2v2
So if area increases v decreases
Then in bernoulis equation a decrease in v leads to an increase in P

This makes P and A directly proportional right? Or Am I misunderstanding something?
Thanks!

 

[Clinicall]

I could be way off but I think in vessels it's not technically a closed system.

 

[SKaminski]

I believe that EK says that the circulatory system is a closed system, and that the lymphatic system was an open system.

Not saying thats the truth, though.

 

[Meredith92]

Thanks for your help but I'm specifically asking about how they describe bernoullis principle. They say Area is inversely related to pressure... But using the continuity equation area is directly proportional to pressure right?

 

[slz1900]

Pressure = F/A. It's an inverse relationship assuming force is constant. Also, the continuity equation doesn't apply when talking about blood vessels since blood doesn't behave like an ideal fluid.

 

[Meredith92]

Ah now im really confused...
Could someone help me with bernoulli's/ continuity equation? This is a question totally separate from blood vessels...

so in the continuity equation A1v1=A2v2
So lets say that area increases, which from this equation means that velocity decreases
Lets say we want to see how this affects pressure.. I THOUGHT we did this by seeing how the this decrease in velocity affects Bernoulli's principle:
P+1/2v^2 +densityxgxheight
If you have a decrease in velocity here that increases pressure in bernoulli's equation (as vdecreases P increases in the equation)

But now I think I'm doing this totally wrong. if you want to know the effect of a change in area in pressure, do we just use P=F/A or do you go through all the steps I went through (continuity and bernoullis) they give you completely opposite effects

Thank you!!

 

[Meredith92]

Also, I believe that the continuity equation does work with blood flow. According to EK, since the cross-sectional area of the capillaries are very large, the velocity is the slowest in the capillaries. They show a graph supporting this. I believe that usually the continuity equation works with blood vessels. Sometimes, the Bernoulli's equation can work for blood vessels as well.

 

[slz1900]

If you look at the entire vascular system it applies, but for an individual blood vessel that constricts, a smaller blood volume will flow through. A1V1 = A2V2 is assuming that volume is constant. With a smaller velocity, there is greater pressure because of Bernoulli's principle, but that works with ideal fluids, which blood is not.