Very confused about blood pressure, resistance and Velocity

[Astra]

So This is what I understand.

When radius decreases, pressure increases. Due to P = F/A and area decreases.

When pressure increases, velocity decreases? I am confused as to why.

Is it due to the fact that resistance increases and this causes velocity to decrease?

But according to the continuity equation, AV= AV,
if
(10)x = 5(2), the initial velocity will be 1m/s while the pressure would be lower as well.

In this picture, why is the 1st region having a higher pressure? Shouldn't it have a lower pressure due to having a cross sectional area?

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[theonlytycrane]

Use bernoulli's equation for your diagram above. The middle term (density * g * height) is the same in all sections of your diagram. In the regions with larger cross sectional area, velocity will decrease because the fluid doesn't need to flow as fast to get through a larger space. In the region with a smaller cross sectional area, velocity will increase because the fluid will need to flow faster to get through a smaller space. Using bernoulli's equation above, pressure will be inversely proportional to velocity to keep the equation constant.

 

[NextStepTutor_2]

So This is what I understand.

When radius decreases, pressure increases. Due to P = F/A and area decreases.

When pressure increases, velocity decreases? I am confused as to why.

Is it due to the fact that resistance increases and this causes velocity to decrease?

But according to the continuity equation, AV= AV,
if
(10)x = 5(2), the initial velocity will be 1m/s while the pressure would be lower as well.

In this picture, why is the 1st region having a higher pressure? Shouldn't it have a lower pressure due to having a cross sectional area?

Your confusion is understandable, and too many MCAT students simply memorize away without understanding. If your problem is with P=F/A "contradiction you should realize there is no problem with it. The physics behind it is well beyond what is expected on the MCAT but what is likely the source of the confusion is your thinking is that you're not realizing the force F changes too.

Let's recap what happens in your situation:

1. There's a change in cross-sectional area: A2 < A1
2. Thanks to conservation of mass, (1) implies v2 > v1
3. Thanks to Bernoulli (conservation of energy), we know p2 < p1

Now take a look at this diagram

The dark blue rectangle on the left is what we call an element. Like the rest of the flow in the bigger section, it flows with velocity v1. v1 is delimited left and right by faces with area A1. Note that, since the liquid left and right of it has pressure p1, this element is compressed by forces F1=p1A1 on each side.

Now to the element on the smaller section, which flows faster. Its cross-sectional area is smaller. The pressure left and right of it is also smaller. As a result, the forces compressing it, F2=p2A2, are also smaller.

So, P =F/A still holds. Yes, when the situation changes, A is smaller, which by itself would make p bigger. However, as we saw above, then new F is smaller than the old one too, which by itself would make p smaller. The net effect of p2 < p1 (which we know beforehand from Bernoulli) means, therefore, simply that F'>F has diminished more than A'>A did.

This is still a simplification of what's truly happening (advection and diffusion of fluids)

Hope this helps, good luck!

 

[aldol16]

You should approach these problems with conservation of energy in mind. Fluids can have kinetic energy (velocity) and/or potential energy (pressure). When you lower cross-sectional area, velocity increases by the continuity equation. If velocity increases, then pressure must decrease because that's just an interconversion of energy. Put another way, you can't just magically make velocity increase without providing a particle with energy - that's equivalent to saying that you can't make a ball move unless you push on it. It won't just spontaneously increase its speed.

Your concern about P = F/A is valid, but you're just not applying it correctly here. You're right in saying that as A increases, P decreases but you didn't realize that this occurs only in the limited case that F is constant. If F isn't constant, then you cannot predict any relationship between F and A.