A simple model of blood flow through the descending aorta is provided at the right. Total flow into the aorta is given by Q. The model includes the effects of vessel taper and outflow through 10 tributary arteries, through which the flow is assumed to be equal and given by q. We will assume that the blood is in-viscid and that the flow is steady and laminar. The effects of gravity are neglected. A₁ P₁ A₂ P₂ Find the pressure (P2) at bottom outlet in terms of Q, P₁, and A₁ for the three cases: a) For a tapered vessel for which A2 = A₁/2; and q = 0. b) For a vessel without a taper, but with q = Q/20. c) For a tapered vessel for which A2 = A₁/2 and q = Q/20.

A simple model of blood flow through the descending aorta is provided at the right. Total flow into the aorta is given by Q. The model includes the effects of vessel taper and outflow through 10 tributary arteries, through which the flow is assumed to be equal and given by q. We will assume that the blood is in-viscid and that the flow is steady and laminar. The effects of gravity are neglected. A₁ P₁ A₂ P₂ Find the pressure (P2) at bottom outlet in terms of Q, P₁, and A₁ for the three cases: a) For a tapered vessel for which A2 = A₁/2; and q = 0. b) For a vessel without a taper, but with q = Q/20. c) For a tapered vessel for which A2 = A₁/2 and q = Q/20.

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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Question

A simple model of blood flow through the descending aorta is provided at the right. Total
flow into the aorta is given by Q. The model includes the effects of vessel taper and outflow
through 10 tributary arteries, through which the flow is assumed to be equal and given by
q. We will assume that the blood is in-viscid and that the flow is steady and laminar. The
effects of gravity are neglected.
A₁
P₁
A₂
P₂
Find the pressure (P2) at bottom outlet in terms of Q, P₁, and A₁ for the three cases:
a) For a tapered vessel for which A2 = A₁/2; and q = 0.
b) For a vessel without a taper, but with q = Q/20.
c) For a tapered vessel for which A2 = A₁/2 and q = Q/20.

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