Consider a cooling tower of height $25$ m containing water droplets with diameter equal to $0\mathrm{.}5$

mm and density equal to $1000$ kg m$3.$ The viscosity of air is equal to $0\mathrm{.}018$x$103$ Pa s$.$ Assume

the air is at atmospheric pressure, behaves as an ideal gas at $298$ K$,$ and only contains oxygen

and nitrogen where the mole frac$$on of oxygen is equal to $0\mathrm{.}21.$ The molecular weight of

oxygen is $32$ kg kmol$1$ and of nitrogen is $28$ kg kmol$1.$

i$.$ Estimate the terminal velocity of the water droplet using the Stokes law to calculate

the drag force on the droplet.

ii$.$ How long does it take for a droplet to fall from the top of the cooling tower to the

ground when there is an upward air velocity equal to $3$ m s$1.$ Assume the droplet

diameter remains constant during the fall?

iii. Is the Stokes law assumption valid?