Blood Flow

[shefv]

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A blood platelet is moving along through an artery that is partially blocked by deposits, though there is no accumulation or leakage of blood in the artery. Which of the following best describes the speed and pressure of the platelet as it moves from the narrow region (the region partially blocked by deposits) to the wider region?


Can someone explain why pressure would increase in this situation?

I get that speed is decreasing using A1v1 = A2v2
So going to a wider region, A2 is higher, thus v2 must be lower

For pressure, I am thinking P1 = P2 which is F1/A1 = F2/A2
So a higher A2 should result in a lower P2, but the answer is saying that the pressure increases. I am confused.

 

[Cawolf]

For pressure, I am thinking P1 = P2 which is F1/A1 = F2/A2

This does not apply here.

Consider Bernoulli's equation and the relationship of velocity and pressure when VFR is constant.

 

[shefv]

Thanks! I see how you can get the answer from Bernoulli's Principle.

Can you elaborate on when to use which equation? I am a little unclear on that. Thanks!

 

[Cawolf]

P1 = P2 is used to describe the pressure going into a closed pipe and out of a closed pipe.

The most common application of that will be a hydraulic system, where a pipe with moveable end plates is filled with an ideal fluid.

Bernoulli's describes the energy of a fluid flowing through closed system and is used to see the effects of changes in height (potential energy) or velocity (kinetic energy). This also applies to things like lift in wings. The top of the wing has a longer path for air to travel, so it moves faster over the wing than under the wing. Bernoulli's equation shows us that a greater velocity results in decreased pressure, and the net upwards pressure provides the lift force.

 

[NextStepTutor_3]

Yes exactly! P1 = P2 is Pascal's principle, which 1) doesn't appear as often on the MCAT, and like @Cawolf said, is mainly exemplified by hydraulic lifts, and 2) applies to a closed system where fluid ISN'T flowing. In systems like blood vessels, where fluid is flowing, Bernoulli's is the equation to use.

As a side note, personally, I like to use conservation of energy whenever possible. It really ties physics concepts together! And Bernoulli's equation simply describes conservation of energy in a fluid system. Because of this, it's often a good idea to try Bernoulli's equation first in any scenario. Consider a case where you actually DID have to use Pascal's principle - in other words, a static, closed system. Even if you "wrongly" tried to use Bernoulli's (which, for the sake of simplicity, we'll write here as P1 + KE1 + PE1 = P2 + KE2 + PE2), you could still find the correct answer! Since the fluid isn't flowing, the KE term can be dropped from both sides. Hydraulic lift questions generally don't involve weird changes in height, so the PE term is also the same on both sides of the equation. What are we left with? P1 = P2, the exact equation we should have used in the first place!