Question

When you inhale, air flows through the turbinate bones of your nasal passags. Assume that for...

When you inhale, air flows through the turbinate bones of your nasal passags. Assume that for a short length of 15 mm, the flow is passing through parallel plates, the plates having a total mean width of w = 20 mm and spacing of a = 1 mm. If the lungs produce a pressure drop of delta p = 50 Pa, and the air has a temperature of 20 C, determine the POWER needed to inhale air. At 20 C, density of air = 1.202 kg/m^3 and u air = 18.1(10^ -6) N.s/m^2.

Homework Answers

Answer #1

Pressure delta p = 50Pa

cross section A = 20 mm x 1 mm = 20 square mm.

Thus the force is F = delta P x A

F = 50 x 20 x 0.000001 N = 0.001 N = 1 mN.

Now the volume of the nasal passage is V = 20mm x 15mm x 1 mm = 3 x 10^-7 cubic m.

At 20 C the mass of the air in that volume is m = 3 x 10^-7 cubic m x 1.202 kg/m^3 =3.606 10^-7 kg

Thus the acceleration is a = F/m = 10^-3 N / 3.606 10^-7 kg = 2773.15 m/s^2

If the final velocity after crossing the nasal passage v then it can be calculated as

u is given 18.1 x 10^-6 N.s/m^2 ans s is 15 mm.

the average velocity is now (v+u)/2= 41.6 m/s

Thus the power needed is P = F. average velocity = 1 mN x 41.6 m/s = 0.0416 W = 41.6mW

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