Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Poiseuille’s Equation

The French physician Poiseuille discovered that the volume V of blood (in cubic centimeters per unit time) flowing through an artery with inner radius R (in centimeters) can be modeled by V(R) = kR^4 where k = π/(8vl) is constant
(here, ν represents the viscosity of blood and l is the length of the artery).

(a) Find the rate of change of the volume V of blood flowing
through the artery with respect to the radius R.

(b) Find the rate of change when R = 0.03 and when R = 0.04.

(c) If the radius of a partially clogged artery is increased from
0.03 cm to 0.04 cm, estimate the effect on the rate of change
of the volume V with respect to R of the blood flowing
through the enlarged artery.

NOTE: I am not seeking the answer but the set up for all three parts only. I will do the math work.

Thank you.

Live long and love math!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Poiseuille’s Equation

Here again dV/dr is your starting point.

B.

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mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Poiseuille’s Equation

Here again dV/dr is your starting point.

B.

This will take some time to do. Bob, the questions posted are the questions for which the author does not provide a sample for.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Poiseuille’s Equation

Here again dV/dr is your starting point.

B.

This will take some time to do. Bob, the questions posted are the questions for which the author does not provide a sample for.

(a). Take the derivative of V(R) with respect to R. I.e use the power rule or the limit definition of the derivative.

(b). Plug in R = 0.03 and R = 0.04 into the derivative of V(R).

(c). Determine V'(0.04) - V'(0.03) to find the increase (or decrease) of the rate at which blood is flowing.

Last edited by Mathegocart (2021-04-19 13:41:57)

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May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Poiseuille’s Equation

Here again dV/dr is your starting point.

B.

This will take some time to do. Bob, the questions posted are the questions for which the author does not provide a sample for.

(a). Take the derivative of V(R) with respect to R. I.e use the power rule or the limit definition of the derivative.

(b). Plug in R = 0.03 and R = 0.04 into the derivative of V(R).

(c). Determine V'(0.04) - V'(0.03) to find the increase (or decrease) of the rate at which blood is flowing.

Thank you. I will do as you said.