Question

When a person inhales, air moves down the windpipe at 15 cm/s. Where the windpipe tightens, the average air speed doubles. If the height difference is 1 cm, what is the difference in pressure due to this constriction? The density of air is 1.2 kg/m³.

Answer 1

The difference in pressure due to the constriction in the windpipe is -0.0135 kg/m²/s².

Step-by-step explanation:

The difference in pressure due to the constriction in the windpipe can be calculated using Bernoulli's principle. Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. In this case, the average air speed doubles where the windpipe tightens. We can use the equation:

P1 + 0.5⁡ρ⁡v1² = P2 + 0.5⁡ρ⁡v2²

Where P1 and v1 are the initial pressure and velocity, P2 and v2 are the final pressure and velocity, and ρ is the density of the air.

Given that the height difference is 1 cm, we can calculate the difference in pressure by rearranging the equation:

P2 - P1 = 0.5⁡ρ⁡(v1² - v2²) = 0.5⁡(1.2 kg/m³)⁡(0.15² - 0.3²) = -0.0135 kg/m²/s².

Therefore, the difference in pressure due to the constriction is -0.0135 kg/m²/s².