   Chapter 12, Problem 58PE

Chapter
Section
Textbook Problem

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 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?

To determine

The average air speed in meters per second through your trachea and the Reynolds number for the air flow in the trachea during each inhalation. State whether the air flow is laminar or turbulent.

Explanation

Given:

Radius of trachea is 102m.

Let's assume flow rate through trachea = 15 L /s = 0.015 m3/s

Formula used:

Q =Avv =QAQ (π10 -2m)2

NR2ρvrη

Q = Flow rate

A = Area

V = velocity

NR = Reynolds Number

ρ= density

η= viscosity

Calculation:

Substituting the values in above equation, we get-

Q =Avv =QAQπ( 10 -2m)2= 0

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