Consider flow of blood in the microvessels of the body, assuming Poiseuille’s law holds and that the viscosity of the blood is constant. Consider a parent vessel that bifurcates into two daughter segments, all within the microcirculation and with blood flow described using Poiseuille’s law (assume that each segment has a different diameter and length). Denoting the pressure at node i by pi (i=1,2,3,4), and the flux in segment j by Qj (j=1,2,3), write down expressions for the segment fluxes in the network, in terms of the nodal pressures. How are the three volume fluxes related, and why? Assuming that the pressures at nodes 1, 3, 4 (the boundary nodes) are known, write down an expression for the pressure at the interior node, p2.
Consider flow of blood in the microvessels of the body, assuming Poiseuille’s law holds and that the viscosity of the blood is constant. Consider a parent vessel that bifurcates into two daughter segments, all within the microcirculation and with blood flow described using Poiseuille’s law (assume that each segment has a different diameter and length). Denoting the pressure at node i by pi (i=1,2,3,4), and the flux in segment j by Qj (j=1,2,3), write down expressions for the segment fluxes in the network, in terms of the nodal pressures. How are the three volume fluxes related, and why? Assuming that the pressures at nodes 1, 3, 4 (the boundary nodes) are known, write down an expression for the pressure at the interior node, p2.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Consider flow of blood in the microvessels of the body, assuming Poiseuille’s law holds and that the viscosity of the blood is constant. Consider a parent vessel that bifurcates into two daughter segments, all within the microcirculation and with blood flow described using Poiseuille’s law (assume that each segment has a different diameter and length).
Denoting the pressure at node i by pi (i=1,2,3,4), and the flux in segment j by Qj (j=1,2,3), write down expressions for the segment fluxes in the network, in terms of the nodal pressures.
How are the three volume fluxes related, and why?
Assuming that the pressures at nodes 1, 3, 4 (the boundary nodes) are known, write down an expression for the pressure at the interior node, p2.
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