   Chapter 2, Problem 10RQ

Chapter
Section
Textbook Problem

Assuming that pressure remains constant, if the radius of a bronchial airway through which gas glows at a rate of 400 L/min is reduced to one-half of its original size, the flow through the bronchial airway would change toA. 10 L/min.B. 25 L/min.C. 100 L/min.D. 200 L/min.

Summary Introduction

Introduction:

The flow of gas through a tube or an airway is explained by Poiseulli’s law arranged for flow. This law states that the volume of gas or fluid flowing through the tube depends upon the change in the pressure of the tube, the radius and the length of the tube, and the viscosity of the flowing liquid. The volume of fluid flowing through the tube is directly proportional to the change in pressure and the radius raised to a power four and inversely proportional to the length of the tube and viscosity.

V=ΔPr4Π8lη

The volume of gas flowing through the tube is directly proportional to the radius raised to power when the pressure remains constant.

Explanation

Justification/ Explanation for the correct answer:

Option (b) is 25 L/min. The flow through a tube or an airway depends upon many factors and is calculated by using Poiseulli’s equation, which is as follows:

V=ΔPr4Π8lη

From the above equation, it can be seen that when the pressure is constant, then, the volume of gas flowing is directly proportional to the radius raised to power four. If the radius is decreased to half of its original value, then the volume would change from 400 liters to:

V’ is the new volume

V is the original volume

r’ is the changed or new radius

r is the original radius

V'=ΔP(r')4Π8lη=ΔP(r2)4Π8lη =ΔPr4Π16(8l</

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