Professor WL in one of his solution for a Challenge problem mention strange formula for kg of rain that we collect on different parts of our body. He figured it out by the dimensions:
M = p * S * V * T
where p is the density in kg/m^3
S is the area of a part we are interesting in (like head, or body) in m^2
V is the velocity of rain with respect to ours in m/s
and T is the time in s. When we multiple everything above we get kg. And here is the question is this method of getting formula ok? It's just pop out from head and no one knows can we trust it? Or it's true functional method?

Question

Professor WL in one of his solution for a Challenge problem mention strange formula for kg of rain that we collect on different parts of our body. He figured it out by the dimensions:
M = p * S * V * T 
where p is the density in kg/m^3
S is the area of a part we are interesting in (like head, or body) in m^2
V is the velocity of rain with respect to ours in m/s
and T is the time in s. When we multiple everything above we get kg. And here is the question is this method of getting formula ok? It's just pop out from head and no one knows can we trust it? Or it's true functional method?

anonymous · Answer

Well, in the video they said that direction of rain is absolutely vertical, so there is no wind, and body is moving with some velocity, so we can calculated the final velocity of rain with respect to our movements. 
Now, if this staff above is ok then i can say that the mass of the air which go through some screws (like in motor-boats)  is : 
$$M= V *  ( \Pi * D ^{2}) * \rho * T *\tan (\alpha) * \frac{ 1 }{ 4 }$$
Where V is the linear velocity at the end of a screw in $$\frac{ m }{ \sec }$$
$$\Pi * D ^{2} * \frac{ 1 }{ 4 }$$ is the area of my screw rotating in $$m ^{2}$$
$$\rho$$ is density of the air in kg/m^3
T is time 
$$\alpha$$ is angle of attack 
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