What is the equation that determines evaporation rate for water?

Question

So I'm guessing it has to do with temperature of surface water, temperature of surrounding, surface area, humidity,... I always wondered if there was an equation to describe evaporation, never learned one in high school.

Answer 1

Although there are experimental studies that have led to simple empirical models like the one suggested in the earlier post noted by Ernie, the equations of statistical mechanics provide a model-based, analytical solution that predicts the rate of evaporation/condensation. You need to realize that both condensation and evaporation are both happening at the same time at the interface between a fluid and gas. The relative pressures and temperatures of the fluid and gas just sway the likelihood of one such event happening over the other.

Charles Ward and his students at the University of Toronto have conducted intensive research in the area of the rate of liquid evaporation flux and have derived predictive models based on statistical rate theory (SRT). The derivation includes consideration of a number of first principles including Boltzman's equation and entropy. One of the papers by Ward and Fang that I've personally read, studied, and simulated is offered by ResearchGate here. You'll want to look at equation (54) and (55) as the final result. Furthermore Ward and Fang provide experimental data that supports their theoretical predictions.

Note this paper references an earlier paper authored by Ward & Langmuir. Langmuir's derivation of a theoretical equation and noted in Kyle's comment appears to be earlier work. I'm presuming Ward's 1999 paper may be an improvement on this result.