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In Take-Home Experiment: Inhalation, we measured the average flow rate $Q$ of air traveling through the trachea during each inhalation. Now calculate the average air speed in meters per second through your trachea during each inhalation. The radius of the trachea in adult humans is approximately $10^{-2} \mathrm{m} .$ From the data above, calculate the Reynolds number for the air flow in the trachea during inhalation. Do you expect the air flow to be laminar or turbulent?

$v_{\mathrm{avg}}=3.18 \mathrm{ms}^{-1}$$N_{\mathrm{R}}=4216$ and the air flow is turbulent.

Physics 101 Mechanics

Chapter 12

Fluid Dynamics and Its Biological and Medical Applications

Fluid Mechanics

Rutgers, The State University of New Jersey

Simon Fraser University

University of Sheffield

University of Winnipeg

Lectures

03:45

In physics, a fluid is a s…

09:49

A fluid is a substance tha…

01:19

When a person inhales, air…

00:27

During a cough, the veloci…

01:36

FLUID FLOW The veloc…

05:01

Poiseuille's equation…

01:03

Poiseuille’s law remains v…

01:45

(II) Poiseuille's equ…

01:43

05:25

($a$) Show that the flow s…

02:10

When you cough, you expel …

02:42

MIXED REVIEWThe aorta …

03:46

(III) $(a)$ Show that the …

02:59

Experimental data indicate…

02:58

How we cougha. When we…

02:14

Trachea Contraction Coughi…

04:01

(a) Calculate the mass flo…

03:48

Human Cough To increase th…

05:32

(III) (a) Show that the fl…

03:31

Our cycle of normal breath…

02:29

Air whose density is $0.07…

09:39

Let $v(r)$ be the velocity…

So here we know that the volumetric flow rate is equaling the cross sectional area of the trachea multiplied by the velocity of air through the trachea. And so the velocity would be equaling the volumetric low rate divided by the cross sectional area of the trachea pi r squared. And so we inhale at around one leader per second. We're going to multiply this by one cubic meter for every 1000 leaders. This would be divided by pi times. The radius of the trachea tend to a negative second meters. Ah, quantity squared. And so we have a velocity of 3.2 meters per second. And so the speed of flow ah, with which we breathe in air would be 3.2 meters per second. Now we're going to use the formula for the Reynolds number, this would be equaling 22 times pi, the density of air times The velocity times are the radius of the trachea divided by new the viscosity, the coefficient of viscosity for air. So this would be equaling 22 multiplied by 1.2 to 5 kilograms per cubic meter multiplied by 3.2 meters per second, multiplied by the radius of 10 to the negative second meters, divided by ah viscosity of 1.98 times 10 to the negative third Pascal seconds. And so we find that the Reynolds number is equaling 36.6, which in this case is much less than 2000. And so we have a lamp meant we're expecting, rather a laminar flow for the inhalation of air through that her through a human's trachea. So this would be our Reynolds number, our laminar. We have laminar flow and our speed of inhalation. That is the end of the solution. Thank you for watching.

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