# Blood Flow WRT Poiseuille's, Bernouli's, & Contunity

#### joshto

##### Nervous&Neurotic
10+ Year Member
With respect to these laws, which of these does, and which of these do not, apply to blood flow?

#### lorenzomicron

With respect to these laws, which of these does, and which of these do not, apply to blood flow?
Hello,
Well, Poiseuille's Law was actually formulated in an attempt to describe blood flow, because Poiseuille was a physiologist as well as a physicist so this one applies, though it is not as good as current.

The other equations can and do apply, but in their usual forms, they are too simplistic to really model blood flow effectively. However, in certain bloodflow such as that in high-velocity, large-artery blood flow, all of these equations will apply effectively. Also, more specifically, in Poiseuille, we can also describe the blood flow in capillaries.

So, the answer is all of them, though neither is completely accurate, it just depends on how accurate you need an answer and the type of blood flow you are modeling. However, blood has many non-linear effects as it is a casson-like fluid which experiences phenomenon such as rouleax formation.

If asked a question about blood flow, I guess you would need to just calculate based on the parameters which they give you.

Also, just as added info, one reasonable steady flow equation that works in many arteries and veins (neglecting the pulsatile component):
p*pi*r^2 + tau*2*pi*r*deltax - (p + deltap)*pi*r^2 = 0

where p is pressure
tau is the shear force as a function of radial coordinate
delta x is the differential size of the blood elements
delta p is the differential change in pressure over the blood elements

hope this helps.
good luck

#### BerkReviewTeach

##### Company Rep & Bad Singer
Vendor
10+ Year Member
With respect to these laws, which of these does, and which of these do not, apply to blood flow?
Technically, those apply to ideal fluids. But in terms of the MCAT, it would seem that their questions on the circulatory system would have you assuming that blood behaves ideally. There are a few things you might know generally.

• The common circulatory concepts
You should know that a narrowing of an artery (plaque build up for instance) will increase the average blood speed (according to the continuity equation) which in turn reduces the pressure against the insides of the artery walls (according to Bernoulli's principle).

You should know that with branching, the total cross-sectional area of capillaries (when added together) exceeds the cross-sectional area of veins, so the average flow speed through capillaries is slower than other vessels.

The pumping of the heart creates pressure that can be explained by Pouiselle's law. As delta P goes up, Q (the volume flow rate goes up), so an increased heart rate results in increased blood flow. However, as blood viscosity goes up, the delta P must go up proportionally to keep the same volume of blood flowing. This is why blood that has excessive LDLs is associated with higher blood pressure.

Vasoconstriction and vasodilation drastically alter the volume blood flow, because Q depends on r to the 4th power.
There are other facts to know and be able to explain. If you know these four concepts and assume blood to be relatively ideal, then you should be fine on most of the circulatory material.

#### kentavr

10+ Year Member
The most strict equation is continuity. It assumes only the non-compressibility of the liquid. It is not completely true for the blood, but deviations are minor. The next strict is Poiseuille's. It assume laminar flow and many other things. In short distance it may be used, but when arteries start to branch then nodes will create much more friction and viscosity coefficient will not be constant any more. And finally, the most weak is Bernoulli, it assumes mechanical energy conservation, which is not true for blood flow at all: To much friction inside blood and with vessel's wall contact. However, it can be used if you ignore the energy dissipation for small distance and large radius. But capillary system will not fit this model for sure. May be it can be applied to large veins and arteries with caution. (I guess that MCAT will indicate it in the passage)