Consider the astronaut as floating in the middle of the "Kibo" (ISS module) without him having any initial motion. The module has a diameter of 4.2 m (inner), and the goal is to reach any of the module's walls by only blowing air through his mouth. Is it possible for him to reach any wall? If it is, how long would it take him to do it, given that he inhales for about 4-8 seconds and exhales it fully for nearly half a second?
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Just a naive and very approximate calculation:
If you neglect friction, google that human lung capacity is around $6\text{l}$, air density around $1\text{kg m}^{-3}$, take the inhalation time $6\text{s}$ and approximate that the nostrils have area around $1\text{cm}^2$, then the velocity of inhaled air will be $\frac{6\text{l}=6000\text{cm}^3}{6\text{s}\cdot 1\text{cm}^2}=10\text{m s}^{-1}.$ The momentum transferred on inhalation is thus around $10\text{ m s}^{-1}\cdot 0.006\text{m}^3\cdot 1\text{kg m}^{-3}=0.06\text{kg m s}^{-1}.$
The same computation on exhalation with duration $0.5s$ gives $0.72\text{kg m s}^{-1}$. The momentum gained is thus $0.66\text{kg m s}^{-1}$, which for man of weight $66\text{kg}$ gives you velocity $0.01\text{m s}^{-1}$.
So on one breath you would reach the wall (assuming you are in the middle and have a distance around $2\text{m}$ to go) in $200\text{s}=3\text{min}20\text{s}$.
Now, you can make a breath each $7\text{s}$, which adds another $0.01\text{m s}^{-1}$ to your velocity. Thus the distance traveled is $$7\text{s}\Rightarrow 7\text{cm}$$ $$14\text{s}\Rightarrow 7\text{cm}+14\text{cm}$$ $$21\text{s}\Rightarrow 7\text{cm}+14\text{cm}+21\text{cm}$$ And so on. From this the time for traveling distance $2\text{m}$ is around $50\text{s}$.
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