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Decreasing diameter indeed leads to increasing flow resistance, and that is the dominant factor in lung airway resistance. But branching itself also contributes to airway resistance. When flow is forced to change direction there are energy losses which also cause pressure drop and this adds to the resistance. The trachea is more or less a straight pipe with ...

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I believe the question can be rephrased as asking why is a single big pipe better than two smaller pipes with the same area Since that's really what you are asking. The bronchial tree splits into smaller branches, but tries to carry the same amount of air. Now the answer should be obvious: for the same area A = $2\pi r^2$, where $r$ is the radius of ...

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If you pump gas along a pipe then pressure drop per unit length of the pipe depends on the diameter of the pipe. The smaller the pipe the harder it is to pump the gas through it. The pressure drop is given by the Darcy-Weisbach equation: $$\Delta P = f_D \frac{\rho v^2}{2} \frac{\ell}{d}$$ though with the complication that the density of the gas depends ...

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