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The velocity $ v $ of blood that flows in a blood vessel with radius $ R $ and length $ l $ at a distance $ r $ from the central axis is$$ v(r) = \frac{P}{4\eta l} (R^2 - r^2) $$where $ P $ is the pressure difference between the ends of the vessel and $ \eta $ is the viscosity of the blood (see Example 3.7.7). Find the average velocity (with respect to $ r $) over the interval $ 0 \le r \le R $. Compare the average velocity with the maximum velocity.

The average velocity is $\frac{P R^{2}}{6 \eta l}$ which is $\frac{2}{3}$ of the maximum velocity

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:53

Blood flow The velocity $v…

03:27

Blood flow The shape of a …

04:10

Refer to the law of lamina…

09:39

Let $v(r)$ be the velocity…

02:32

Relative change in blood v…

01:59

When blood flows through a…

02:13

Blood flow In Example 3.3 …

03:44

Blood Flow As blood moves …

02:11

As blood moves through a v…

04:18

we know that we can use the average value formula and plug in one over R minus zero from zero to our give our d r, which is one over r from zero r. We know now that we end up with p r squared and then we know that we have the degree to therefore the derivative ve promised tea, which is acceleration equals zero indicates when the maximum velocity is reached. They're Farina. The maximum velocity is reached at p r squared for, you know. Therefore, we know the average velocity is this which is 2/3 of the maximum velocity.

Numerade Educator

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