15. A mathematical model for blood flow in a large blood vessel predicts that the optimal values of the anglesO and 2, which represent the (positive) angles of the smaller daughter branches (vessels) with respect to theaxis of the parent branch are given byAỗ + A¡ – A}2 A, AjA – A¡ + A}coseandcos0,2 A,A2where A, is the cross-sectional area of the parent branch and A, and A, are thecross-sectional areas of the daughter branches. See FIGURE 4.6.3. Let = 0, + 02be the junction angle, as shown in the figure.Blood flowFIGURE 4.6.3 Branching of a large blood vessel inProblem 74 (b) Show that for the optimal values of 6, and 0, the cross-sectional area of thedaughter branches, A¡ + A, is greater than or equal to that of the parentbranch. Therefore, the blood must slow down in the daughter branches.

Answered: Image /qna-images/answer/c4b61ca3-2b79-441c-ad4d-229dbb6cec7a.jpg

Answered: (b) Show that for the optimal values of…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter14: Fluid Mechanics

Section: Chapter Questions

Problem 62P: A certain hydraulic system is designed to exert a force 100 times as large as the put into it. (a)...

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(b) Show that for the optimal values of 0, and 0, the cross-sectional area of the daughter branches, A, + Az is greater than or equal to that of the parent branch. Therefore, the blood must slow down in the daughter branches.