Is it possible to lift a bald person with an airstream? (Coanda effect and Bernoulli's principle)

Question

Lately, a high school teacher called Bruce Yeany has been uploading some fluid dynamics demonstrations on his YouTube channel. Here's his first demo video using various objects like vegetables and containers. He's also uploaded a follow-up demo with dolls.

There's a comment thread at the time of writing on that second video about whether or not it would be possible to lift an actual bald person using a rapid airstream.

I wasn't sure how to start, so here are my assumptions:

• the person has average body proportions
• the head of a bald person is roughly three quarters of a sphere (at the back)
• the radius of that sphere is $r_{head}$ of about $8$ cm
• the mass of the person is $m_{person}$ of about $80$ kg
• atmospheric pressure of $1013$ hPa
• airstream velocity $v_{air}$ (variable)

From the Bernoulli's principle wiki page, I'm guessing that this scenario falls under the compressible flow category, but there seem to be three different formulae to get to an answer. Moreover, I'm not sure how to calculate the pressure required to actually lift a human.

Is there a way to model this scenario to get to some kind of answer?

Answer 1

I don't have a complete answer and I'd welcome comments, but here's where I've got to so far.

We need to generate a lift force of at least 80$g$ to lift our person, or about 800 N.

The area available to us for a pressure differential to act on is approximately $3\pi R^2$, 3/4 of the surface area of a sphere. That's about 0.06m$^2$. Therefore, we need a pressure differential of $800/0.06=13,300\,\mathrm{Pa}$.

The pressure differential in the normal direction due to streamline curvature is

$$ \frac{\partial P}{\partial n} = -\frac{\rho V^2}{R}, $$

and this is where I'm a bit unsure. Far above the person's head, the velocity will be at atmospheric pressure. I think we can approximate the pressure differential as $\Delta P/L$, where $L$ is the normal distance which the pressure gradient is acting over. However, I don't know what we should take $L$ to be. If I arbitrarily take $L=1$ m, then with $\rho=1.2$ kg/m$^3$, we get $V\approx30$ m/s, or about 70 mph, which just feels too slow. Taking $L\approx R$ we get $V\approx100$ m/s, or about 30% of the speed of sound.

My gut says that levitating a bald man with an air jet shouldn't be possible, at the very least I think it wouldn't be practical.