Solution Found!
Blood flow The shape of a blood vessel (a vein or artery) can be modeled by a
Chapter 9, Problem 8(choose chapter or problem)
Blood flow The shape of a blood vessel (a vein or artery) can be modeled by a cylindrical tube with radius R and length L. The velocity v of the blood is modeled by Poiseuille’s law of laminar flow, which expresses v as a function of five variables:
\(v=f(P, \eta, L, R, r)=\frac{P}{4 \eta L}\left(R^{2}-r^{2}\right)\)
where \(\eta\) is the viscosity of the blood, P is the pressure difference between the ends of the tube (\(\text { in dynes } / \mathrm{cm}^{2}\)), r is the distance from the central axis of the tube, and r, R, and L are measured in centimeters.
(a) Evaluate f(4000, 0.027, 2, 0.008, 0.002) and interpret it. (These values are typical for some of the smaller human arteries.)
(b) Where in the artery is the flow the greatest? Where is it least?
Questions & Answers
QUESTION:
Blood flow The shape of a blood vessel (a vein or artery) can be modeled by a cylindrical tube with radius R and length L. The velocity v of the blood is modeled by Poiseuille’s law of laminar flow, which expresses v as a function of five variables:
\(v=f(P, \eta, L, R, r)=\frac{P}{4 \eta L}\left(R^{2}-r^{2}\right)\)
where \(\eta\) is the viscosity of the blood, P is the pressure difference between the ends of the tube (\(\text { in dynes } / \mathrm{cm}^{2}\)), r is the distance from the central axis of the tube, and r, R, and L are measured in centimeters.
(a) Evaluate f(4000, 0.027, 2, 0.008, 0.002) and interpret it. (These values are typical for some of the smaller human arteries.)
(b) Where in the artery is the flow the greatest? Where is it least?
ANSWER:Step 1 of 4
The velocity of blood flow is modelled by the following relation.
\(v = f\left( {P,\eta ,L,R,r} \right) = \frac{P}{{4\eta L}}\left( {{R^2} - {r^2}} \right)\)
where \(\eta\) is the viscosity of the blood, P is the pressure difference between the ends of the tube ,r is the distance from the central axis of the tube, R is the radius and L is the length of the tube.