Flow Rate and Cross-Sectional Area

[collegelife101]

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Hello everyone! I am thoroughly confused on flow rate and its relationship to cross-sectional area. TPR says that according to the continuity equation, as a tube narrows the flow speed will increase. But then EK says that the shorter and fatter the tube, the greater the flow rate. Can someone help distinguish between the two?

If that's the case, then why does blood flow decrease when the blood vessels constrict?

Many thanks in advance!

 

[Teleologist]

Hello everyone! I am thoroughly confused on flow rate and its relationship to cross-sectional area. TPR says that according to the continuity equation, as a tube narrows the flow speed will increase. But then EK says that the shorter and fatter the tube, the greater the flow rate. Can someone help distinguish between the two?

If that's the case, then why does blood flow decrease when the blood vessels constrict?

Many thanks in advance!

What does into a hose comes out. The continuity equation says that the volume flow rate into the hose is equal to the volume flow rate anywhere else in the tube, such as the other end.

Now, volume is anything is cross sectional area multiplied by its height. Volume flow rate takes this a step further since it's also a rate, so volume flow rate, a constant for a particular tube, is cross-sectional area * velocity. Through dimensional analysis we can see that the units are correctly m^3/s, or volume per unit time.

So TPR is correct that as one changes cross sectional area, the velocity increases. The flow speed increases. You are confusing flow speed/velocity with volume flow rate. EK is similarly correct in that physically changing the tube changes the volume flow rate just as changing your car leads to a different ride.

About blood flow, what decreases is not volume flow rate but rather flow velocity. The amount of blood in your system is constant and stays that way until you start cutting yourself.

 

[DrknoSDN]

Common questions. Both are right and saying the same thing. A fluid has to push on the fluid in front of it to continue moving foward (continuity). So as the area of the (rigid) pipe decreases then velocity must increase to have a constant flow.

When talking about resistance to flow then a larger pipe will let the fluid move more easily through the pipe and flow "could" be greater. This is a classic straw scenario. A small straw vs a big straw in a viscous milkshake. Same applies to the length, if you had a 5 inch straw or a 50 in straw the longer straw would have more resistance to flow and a lower rate (all else equal).

EkamKrackers audio: Flow rate can change over time, but at any two points in the system it will be the same.

These scenarios are using a rigid system that does not have any reservoirs or elasticity. Lots of threads attempt to explain why comparisons should not be made.
Czarcasm linked this search result in another thread showing how often it comes up.:
https://www.google.com/search?q=student doctor blood pressure bernoulli site:forums.studentdoctor.net&espv=210&es_sm=93&biw=1746&bih=869#q=blood pressure bernoulli site:forums.studentdoctor.net
http://forums.studentdoctor.net/threads/blood-pressure-vs-physics.1064120/#post-15108664

 

[NextStepTutor_1]

I agree wholeheartedly with what everyone else said, but I also wanted to talk about the blood pressure/blood flow issue that you mentioned. When blood vessels constrict, the blood flow rate doesn't change. That's because your cardiovascular system is a closed system, which means there is no outlet for the blood to leave the system. Thus, if the blood vessels constrict, the blood flow rate would stay the same, and the flow speed would increase (causing high blood pressure) to adjust for the decrease in cross sectional area.

 

[Czarcasm]

I agree wholeheartedly with what everyone else said, but I also wanted to talk about the blood pressure/blood flow issue that you mentioned. When blood vessels constrict, the blood flow rate doesn't change. That's because your cardiovascular system is a closed system, which means there is no outlet for the blood to leave the system. Thus, if the blood vessels constrict, the blood flow rate would stay the same, and the flow speed would increase (causing high blood pressure) to adjust for the decrease in cross sectional area.

I understand that the volume of blood in our body is relatively constant (assuming no blood loss, about 5L), but isn't that subject to changing based on our heart rate? For instance, if you're walking home and being chased by a dog, your heart would be pumping blood faster, and so the volume per time is changing (a change in flow rate essentially). If instead we were comparing the flow rate of a hose attached to a faucet, or a pipe at the bottom of a container, I can understand how flow rate wouldn't change because change in volume per unit time is constant. But, this confuses me.

Also, with regard to the contradiction in blood vessels: assuming flow rate is constant as blood pumps through the capillaries, a decrease in cross-sectional area would indicate an increase in the flow velocity of blood at the capillaries. But we know that's not the case, and I believe the apparent contradiction for this has to do with the fact that collectively, the entire cross sectional area of the blood capillaries combined, is larger than the blood leaving the arterioles, hence a decrease in blood velocity as we'd expect.

Also, maybe you can correct me if I'm wrong, but the cardiovascular system presents a situation of non-ideal flow, where resistance, viscosity, and pressure differentials are a factor and therefore, the more appropriate expression to use to compare flow rate changes at a given location is Poiseulle's law. This also explains why throughout our cardiovascular system, the flow rate is not constant. However, I think in your explanation you instead were referring to a particular area of blood flow (ie. the arterioles, capillaries, venules), not the whole cardiovascular system collectively.

EDIT: Okay, so Poiseulle's law is an applicaton of ideal flow, so clearly, I still have a lot of learning to do lol.

 

[DrknoSDN]

Poiseulle's law is also likely to come up on "experimental" questions for current MCATs. It is listed as a specific topic for the 2015 version of the exam.

Just remember they can put anything they want on the MCAT and some of the real questions do not even apply to your overall score.

 

[Czarcasm]

Poiseulle's law is also likely to come up on "experimental" questions for current MCATs. It is listed as a specific topic for the 2015 version of the exam.

Just remember they can put anything they want on the MCAT and some of the real questions do not even apply to your overall score.

Interesting. Do you have a link to this?

 

[DrknoSDN]

Interesting. Do you have a link to this?

https://www.aacu.org/meetings/annualmeeting/AM12/documents/riegelman2015previewguide.pdf
Content category 4B, or just search Poiseuille.



https://www.aamc.org/students/download/63060/data/mcatessentials.pdf
Search "Experimental"
Says: "Note: Each of the three scored multiple-choice sections includes some experimental items. Experimental items, as well as questions contained in the Trial Section, do not count toward your score."

http://www.mcat2015.com/what-do-i-need-to-know/

 

[DrknoSDN]

6 Hours instead of 3 hours. Verbal now has zero physical science based passages (all humanities and social sciences). Adding Biochem, Psychology, and sociology... Sounds like fun. 😵