How can I calculate how fast water will evaporate, if I know its temperature, the relative humidity, temperature, and speed of air flowing over it? Or if that's not enough information, what formulas would I need to use?
First, let me say that you should not use the formula on engineeringtoolbox. Indeed, you can write $$J=K (c-c_s),$$ where $J$ is the evaporation flux, $c$ the concentration of water vapor in the air and $c_s$ the concentration of saturated water vapor at the given temperature.
The problem is that generally, $c$ will not be constant over the position (if you blow dry air into the $x$ direction, then $c=0$ at $x=0$ and $c\rightarrow c_s$ as $x$ increases. Moreover, the coefficient $K$ (the mass transfer coefficient) will generally be position-dependent as well, being larger at the leading edge of your surface than at the trailing edge.
Depending on the size of your system and exactly how you blow, the formula from engineeringtoolbox can be orders of magnitude off. Unfortunately, there is no simple answer; there are thick books with math and empirical formulas for all kinds of common cases. ETB does not tell you what assumptions were made, so do not use it.
The most import parameters are:
- incoming air properties: humidity, temperature, speed (as you already mentioned);
- length (in the flow direction) of the evaporating surface;
- whether the surface is approximately a thin plate parallel to the incoming stream or a wet area on a larger surface. In the latter case, the air speed will depend on the distance to the surface, so you have to define where you measure the air speed.
- whether the gas is flowing through a duct (e.g. between two parallel plates) or whether there is infinite space above the wet surface;
- the temperature of the evaporating surface, which may cool down due to evaporative cooling.