Breathing is cyclic and a full respiratory cycle from the beginning of inhalatio

Question

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 seconds. The maximum rate of air flow into the lungs is about 0.5 L/s. This explains, in part, why the function f(t) = 1/2 sin(2 pi t/5) has often been used to model the rate of air flow into the lungs. This can then be used to show that the volume of inhaled air in the lungs at time t is given by V(t) = 5/4 pi [1-cos (2/5 pi t)] liters. Use this to compute the average volume (in liters) of inhaled air in the lungs in one respiratory cycle. Average volume = _________ liters

Explanation / Answer

total time from starting of inhalation to end of exalation is given by 5 seconds.

so the total inhalation starts at 0 and ends at 2.5 sec

total volume is given by V (t) = 5pi/4 *(1-cos(2pit/5))

from t = 0 to t= 5/2

V = 5*pi/4*(1-(-1)) = 5/pi/2 L

total volume inhaled = 0.796 liters

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