Explore the hypothesis of "desertification" by determining the distances required to evaporate a fully formed spherical raindrop (~2 mm diameter) from typical cumulus cover at 2500m. Let h=height(m) above land at sea level. If P0 and T0 are the pressure (kPa) and temperature (K) at sea level, then the NOAA gives the P and T variation with respect to h as: P=P0-9.23x10^-3(h), T=T0-0.0065(h)
a) Assuming thermal equilibrium, formulate the ODE mass balance (symbols) to give the change in drop diameter (dp) with respect to time (t). You can assume the liquid water density (pw) is constant. The other ODE needed to solve the problem is: dh/dt=-Ut, where Ut is the droplet terminal velocity
b) Derive the relationship (symbols) between y (mol fraction of the water vapor in air) and the %Hum, the humidity at satruation Hsat, and the molecular weights (Mair, Mw).