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How do we suck air into our lungs, are we generating a vacuum?

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You aren't creating a vacuum, but you are reducing the pressure in your lungs when you inhale.

In effect your lungs are working as a diaphragm pump. When you pull your diaphragm down, and/or expand your chest, this increases the volume inside your lungs. Boyle's law tells us:

$$ P_0V_0 = P_{\rm inhale}V_{\rm inhale} ,$$

where $P_0$ and $V_0$ are ambient pressure and the volume of your lungs when you're not inhaling. Rearranging this we get:

$$ P_{\rm inhale} = P_0\frac{V_0}{V_{\rm inhale}} .$$

When you inhale $V_{\rm inhale} > V_0$ so $P_{\rm inhale} < P_0$. Because the pressure in your lungs is less than the ambient pressure air flows from the outside into the lungs.

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    $\begingroup$ +1 short and concise. @Baconbeastnz for a vacuum to be created, $\Delta P$ has to be so large that the surrounding air molecules won't be able to immediately feel the created vacuum after an inhale (diverging relaxation times). Whereas in reality the relative change in $P$ is usually in the order of $-4mmHg$ to $-6mmHg$. $\endgroup$ – Phonon Aug 2 '14 at 6:49
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    $\begingroup$ To test your pressure drop capability, see how far up a straw or tube you can suck water. Divide height by 13.6 to get Hg pressure... $\endgroup$ – DJohnM Aug 3 '14 at 1:17

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