Question

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.

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