Lets play with a ping$-$pong ball and a vacuum cleaner

You're hanging out at your friend's house, and while messing around with his vacuum cleaner,

you notice a ping$-$pong ball lying nearby. Naturally, you get an idea: What happens if you point

the vacuum cleaner outlet upwards and try to balance the ping$-$pong ball on the jet of air? It's a

fun little challenge to see if you can keep the ball floating steadily in the air.

Now, let's figure out exactly what air velocity is required to keep the ball suspended in midair,

given the conditions at sea$-$level air. If the ping$-$pong ball weighs $2\mathrm{.}6$ g and has a diameter of $3\mathrm{.}8$

cm $,$ and the surrounding air is at standard sea$-$level conditions.

So$,$ what air velocity is required to balance the weight of the ping$-$pong ball and keep it floating?

Note: At standard atmospheric conditions, which are commonly referred to as sea$-$level

conditions, the properties of air are as follows: The temperature is typically around $288\mathrm{.}15$ K $.$

The pressure at these conditions is $101\mathrm{.}325$ kPa $.$ The density of air at this temperature and

pressure is approximately $1\mathrm{.}225k\frac{g}{m^3}.$ Additionally, the dynamic viscosity of air at $15C$ is

about $1\mathrm{.}81{10}^{-5}k\frac{g}{m*s}.$