[aamc 8] ps #31

[480225]

I'm having trouble with Poiseuille's Law as it applies both here and to blood flow in capillaries.

The formula is Q=(P1-P2) (pie)(r^4)/8(eta)L

So for capillaries, blood flow is slow (the slowest) because the radius decreases and every decrease in radius is accompanied by a (decrease^4) modification to flow rate. In this question it asks about where the flow rate is the greatest so using the previous thought process I assumed it would be at the wide end.

Question: If the valve is opened to drain the tank, where is the speed of the flowing water the greatest?
A: At the narrow end of the pipe. (Given answer, For a given volume flow rate, the speed of fluid flow is inversely proportional to the cross-sectional area through which the fluid flows.)

Why would it be at the narrow end? Doesn't this contradict the notion that Q is directly proportional to r^4?

Cheers.

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[Jepstein30]

I'm having trouble with Poiseuille's Law as it applies both here and to blood flow in capillaries.

The formula is Q=(P1-P2) (pie)(r^4)/8(eta)L

So for capillaries, blood flow is slow (the slowest) because the radius decreases and every decrease in radius is accompanied by a (decrease^4) modification to flow rate. In this question it asks about where the flow rate is the greatest so using the previous thought process I assumed it would be at the wide end.

Question: If the valve is opened to drain the tank, where is the speed of the flowing water the greatest?
A: At the narrow end of the pipe. (Given answer, For a given volume flow rate, the speed of fluid flow is inversely proportional to the cross-sectional area through which the fluid flows.)

Why would it be at the narrow end? Doesn't this contradict the notion that Q is directly proportional to r^4?

Cheers.

I'm pretty sure I used the continuity equation (or something) where Q = Av

Flow rate is constant everywhere in fluids so largest area = slowest velocity and vice versa. Therefore, highest velocity will be smallest cross sectional area.

Not entirely sure how to get around the conflict with capillaries that you pointed out but I think Q = Av only applies to ideal fluids.. which blood is not? Idk

 

[sciencebooks]

I'm pretty sure I used the continuity equation (or something) where Q = Av

Flow rate is constant everywhere in fluids so largest area = slowest velocity and vice versa. Therefore, highest velocity will be smallest cross sectional area.

Not entirely sure how to get around the conflict with capillaries that you pointed out but I think Q = Av only applies to ideal fluids.. which blood is not? Idk

The continuity equation still applies to blood, but Bernoulli's doesn't (relating pressure) because, like you said, it's not ideal.

The trick with the blood passages is that in capillaries, while individual radius is smaller, the NET area of the whole capillary system (all the branches) is GREATER so (like you said above), greater area = slower.

Maybe what OP included refers to an INDIVIDUAL capillary?

 

[Jepstein30]

The continuity equation still applies to blood, but Bernoulli's doesn't (relating pressure) because, like you said, it's not ideal.

The trick with the blood passages is that in capillaries, while individual radius is smaller, the NET area of the whole capillary system (all the branches) is GREATER so (like you said above), greater area = slower.

Maybe what OP included refers to an INDIVIDUAL capillary?

Right.. knew that.

Capillaries have the largest surface area... giving it the lowest blood pressure and slowest blood flow.

 

[Jepstein30]

The continuity equation still applies to blood, but Bernoulli's doesn't (relating pressure) because, like you said, it's not ideal.

The trick with the blood passages is that in capillaries, while individual radius is smaller, the NET area of the whole capillary system (all the branches) is GREATER so (like you said above), greater area = slower.

Maybe what OP included refers to an INDIVIDUAL capillary?

OP is referring to a passage on AAMC 8 where there was (IIRC) a tank of water with a pipe coming out of one end that got smaller and smaller..

 

[sciencebooks]

OP is referring to a passage on AAMC 8 where there was (IIRC) a tank of water with a pipe coming out of one end that got smaller and smaller..

Oh, so that equation they listed was just one memorized? I assumed it was given for some reason?

 

[Jepstein30]

Oh, so that equation they listed was just one memorized? I assumed it was given for some reason?

yea wasn't given so probably not wise to use it.

It's one of those that will be given if necessary IMO.

 

[480225]

It was not given; I was just using the formula to try and understand. I was also referring to a single capillary because I would think moving from large arteries to smaller capillaries would cause an increase. I was just thoroughly confused.

 

[Jepstein30]

It was not given; I was just using the formula to try and understand. I was also referring to a single capillary because I would think moving from large arteries to smaller capillaries would cause an increase. I was just thoroughly confused.

Well do you understand our explanations? Let me know if u dont

 

[ThirdEye]

They're asking about "velocity"

Q is flow rate not velocity.

Q is volume per time and is proportional to area for ideal(Q=AV), and r^4 for non ideal.

V is meters per second and is inversely proportional to area(V=Q/A).

 

[sciencebooks]

They're asking about "velocity"

Q is flow rate not velocity.

Q is volume per time and is proportional to area for ideal(Q=AV), and r^4 for non ideal.

V is meters per second and is inversely proportional to area(V=Q/A).

Lol, in with another obviously easy way to think about things. I over-think/justify things to myself way too much sometimes instead of looking at the obvious.

 

[Singhp03]

They're asking about "velocity"

Q is flow rate not velocity.

Q is volume per time and is proportional to area for ideal(Q=AV), and r^4 for non ideal.

V is meters per second and is inversely proportional to area(V=Q/A).

I second this, looks like your confusing flow rate with velocity, also keep in mind that Poiseuille's law is for non-ideal fluids(viscosity, non laminar flow etc.)

 

[NonTraditional3]

Flow Rate Q = velocity * area of cross section.