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# (a) Suppose a blood vessel’s radius is decreased to 90.0%

## Problem 37PE Chapter 12

College Physics | 1st Edition

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Problem 37PE

(a) Suppose a blood vessel’s radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?

Step-by-Step Solution:

a.)

Step 1 of 3</p>

The factor by which the pressure difference must decrease can be calculated by applying Poiseuille's law which states that the flow rate (Q) of a fluid in a pipe is related to the viscosity

() of the fluid, the pressure gradient between the ends (P), the length (l) and diameter(r) of the pipe by

Where, P = Pressure difference between the ends of the artery in N/m2

r = radius of the artery in m

= Viscosity of the blood in Pas

l = length of the artery in m

Step 2 of 3</p>

Let r1and r2 be the radius of the blood vessel before and after the decrease in blood vessel’s  radius to 90% of its original value and P1 and P2 be the pressure difference before and after the decrease in the radius of the blood vessel.

=

The blood flow rate is constant.

Where, Q1and Q2 are the flow rates before and after

the decrease in blood vessel’s radius.

Substituting for Q1 and for Q2

=

==

=

Solving for P2

=

Substituting  for

=

=

= 1.52

= 1.52

Therefore,the pressure difference must increase by a factor of 1.52.

b.)

Step 3 of 3

##### ISBN: 9781938168000

This full solution covers the following key subjects: vessel, rate, pressure, flow, difference. This expansive textbook survival guide covers 34 chapters, and 3125 solutions. The full step-by-step solution to problem: 37PE from chapter: 12 was answered by , our top Physics solution expert on 07/07/17, 04:39PM. Since the solution to 37PE from 12 chapter was answered, more than 567 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: College Physics , edition: 1. The answer to “(a) Suppose a blood vessel’s radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?” is broken down into a number of easy to follow steps, and 61 words. College Physics was written by and is associated to the ISBN: 9781938168000.

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(a) Suppose a blood vessel’s radius is decreased to 90.0%

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