Fluid Pressure increase or decrease with increasing cross-sectional Area?

[MelBl]

https://www.reddit.com/r/Mcat/search?q=flair_name:"Question 🤔🤔"&restrict_sr=1
Hi everyone. Blood pressure increases by vasoconstriction(narrowing blood vessels). But according to Bernoulli's equation, P & velocity have inverse relationship with eo=> P & A have direct rel(based on A1v1=A2v2). Can someone plz explain this contradiction? Thank you!

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[SeitenKishi]

The supposed "contradiction" is because pressure is measured at two different points. However in both cases, flow is assumed to be constant.

In the first case, assuming blood flow is constant, pushing blood into a narrower blood vessel (vasoconstricted thus smaller cross-sectional area) results in a HIGHER pressure proximal to the constricted vessel. For example, if precapillary sphincters are constricted, arteries will have higher pressure.

In the second case, assuming blood flow is constant, pushing blood into the narrowed segment (e.g. precapillary sphincters) results in a LOWER pressure in that segment itself. For example, pressure in the precapillary sphincters will be lower than the arteries.

Another way to think about blood flow is electricity from physics, where V = IR. Think of V as pressure, I as flow, and R as resistance. Vasoconstriction increases R, and then see what happens to voltages before and after the resistor, when flow is constant.

I hope this helps.

 

[MelBl]

So are you saying that the first case is more of a DIFFERENCE in pressure between the constricted vessel & the vessel next to it? Please correct me if I got it wrong, but does that mean that the vasoconstricted vessel itself would have a low pressure because of its narrowness?

 

[SeitenKishi]

The first case is a difference in pressure between the constricted vessel and the vessel coming BEFORE it (not parallel to it). This is formally termed a pressure gradient.

And yes, the constricted vessel itself would have a lower pressure because of its narrowness. A lower pressure relative to the vessels coming BEFORE it.

Sorry if this seems complicated. Bernoulli's principle does not consider fluid resistance / friction in a vessel and so does not tell the whole story. If you are interested, I would recommend looking into the Hagen–Poiseuille equation.

Read 4th paragraph of wiki here:

Hagen–Poiseuille equation - Wikipedia

en.wikipedia.org

 

[Dochopeful13]

reddit.com: search results - flair_name:"Question "
Hi everyone. Blood pressure increases by vasoconstriction(narrowing blood vessels). But according to Bernoulli's equation, P & velocity have inverse relationship with eo=> P & A have direct rel(based on A1v1=A2v2). Can someone plz explain this contradiction? Thank you!

Following

 

[MelBl]

The first case is a difference in pressure between the constricted vessel and the vessel coming BEFORE it (not parallel to it). This is formally termed a pressure gradient.

And yes, the constricted vessel itself would have a lower pressure because of its narrowness. A lower pressure relative to the vessels coming BEFORE it.

Sorry if this seems complicated. Bernoulli's principle does not consider fluid resistance / friction in a vessel and so does not tell the whole story. If you are interested, I would recommend looking into the Hagen–Poiseuille equation.

Read 4th paragraph of wiki here:

Hagen–Poiseuille equation - Wikipedia

en.wikipedia.org

Thank you so much!

 

[PapaGuava]

Thread moved to appropriate subsection.