# Force of air lift

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?

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: $\sqrt{\frac{m_\text{tank}g}{2A\rho}}<u<\sqrt{\frac{m_\text{tank}g}{A\rho}}$ .