Poiseuille's Law Confused

[kobe-in-a-labcoat]

Can someone clarify...According to continuity equation, if a section of a pipe has twice the radius, then the velocity will be 1/2 original velocity. Flow rate should remain constant. I didn't see Poiseuille's in my MCAT prep but I remember it from physics and am vaguely aware that increasing radius by a factor of 2 leads to a 2^4=16 fold increase in flow rate. Is it the case that, Poiseuille's applies to different tubes, while the continuity equation to only one tube.

Is there any thing besides knowing that there is a 4th power relationship that is important for poiseuilles for the mcat?

Can some one help me reconcile this conceptual mistake I am making.

Thanks guys!!!

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[erythrocyte666]

Poisseuille's law applies to fluid flow rate (i.e. units would be like mL/s) while continuity eqn applies to fluid velocity (i.e. units of m/s). doubling radius will halve the fluid velocity and decrease resistance of tube by factor of 16. so for the latter, if you still have constant pressure before and after pipe thickening then fluid flow rate will increase by factor of 16.
in short different equations for each: for continuity the familiar Av = constant; but for Poisseuille's: pressure = fluid flow rate X resistance (think Ohm's law)

 

[Labrat07]

Add on question regarding to continuity law.

Do you have to account for area of other pipes in the same plane as well?? for example: 1 pipe split into 3 pipes. Do i have to consider the 3 pipes area when trying to find velocity.

I'm trying to relate to capillaries velocity regarding to this law?? or is this the exception??

 

[Cawolf]

@Labrat07

Yes, the total cross sectional area is accounted for - this is the perfect concept to relate to the capillaries.

Even though each capillary has a tiny cross sectional area, there are so many more that their total area is much greater than the aorta. This explains mathematically why the velocity of blood is slowest in the capillaries (arterial system-wise).

 

[Labrat07]

@Labrat07

Yes, the total cross sectional area is accounted for - this is the perfect concept to relate to the capillaries.

Even though each capillary has a tiny cross sectional area, there are so many more that their total area is much greater than the aorta. This explains mathematically why the velocity of blood is slowest in the capillaries (arterial system-wise).

Thank you. Good to learn that.

 

[kobe-in-a-labcoat]

Perfect. Thanks!

 

[Mantis Toboggin]

@Labrat07

Yes, the total cross sectional area is accounted for - this is the perfect concept to relate to the capillaries.

Even though each capillary has a tiny cross sectional area, there are so many more that their total area is much greater than the aorta. This explains mathematically why the velocity of blood is slowest in the capillaries (arterial system-wise).

A caveat for people reading this-- our circ system isn't an ideal fluid. While our blood follows the continuity equation well (capillaries have lowest blood velocity), it doesn't follow Bernoulli's as well. Bern's eq. would suggest that pressure would be highest at the capillaries, but it is quite low there too.

For the purposes of the MCAT remember that pressure is highest from where the circuit starts in the heart. That is, aorta, then arteries, thenarterioles, then capillaries, and finally the pressure is lowest in the veins.


Tiny side question though-- OP mentions that doubling the radius halves the velocity. However if we are assuming a circular pipe, doesn't doubling the radius quadruple the cross-sectional area? In which case the velocity would be 1/4, not 1/2?