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Say I want to find out how much wind force I would need to lift a tank 10 meters in the air, given I already know its dimensions. Is there a formula for that?

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The volume of air travelling at speed $u$ hitting a perpendicular, flat surface of area $A$ in a time $t$ is $V=Aut$, and its mass is $V=\rho A ut$.

Force is given by change in momentum with respect to time: $F = \frac{dP}{dt}$, or, assuming $u$ is constant: $F=u\frac{dm}{dt} = Au^2\rho$, assuming that all air molecules inelastically collide with the surface. If the collision is perfectly elastic, you pick up an extra factor of $2$.

Thus, setting $F=m_\text{tank}g$, you get: $\sqrt{\frac{m_\text{tank}g}{2A\rho}}<u<\sqrt{\frac{m_\text{tank}g}{A\rho}}$ .

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  • $\begingroup$ I understood up to V = Aut, but after that you lost me. Could you possibly go more in-depth about the variables, as I'm not versed at all in Physics? $\endgroup$ – Dante Jul 7 '17 at 16:01

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