Thursday, September 11, 2014

experimental physics - Is there an equation to calculate water evaporation taking into account environmental variables?



Is there an equation to calculate rate of water evaporation with following variables: water volume, water flow/speed, ambient air temperature, dew point/humidity, chemical composition of water (e.g. in a pool), temperature of water, wind speed?


Constants and Assumptions: No water leaks and it is contained to a finite amount of gallons. I understand that there may be other environmental variables to control, but this is a good start.



Answer



Engineering ToolBox has a rough empirical formula for predicting evaporation rates in kilograms per hour, $$g_h=\Theta A(x_s-x)$$ where $\Theta=25+19v$ is a dimensionless constant and where $v$ is the air velocity in m/s (but get rid of the units), where $A$ is the exposed water surface area in m$^2$, where $x_s$ is the humidity ratio of fully-saturated air at the water temperature, and $x$ is the humidity ratio of the air which is blowing over the water surface. Just remember to strip off the units of everything before inserting it into the equation (it's one of those annoying equations where the units don't make sense, and you have to make sure you're getting the numerical values using the same units as the designer of the equation did).


I've never used this for anything, so I can't personally vouch for its accuracy, but it should give a rough approximation of water loss rate.



Calculation of water level evaporation with following variables (X): water volume




Water volume is actually not very important, as it's only the water surface area which really matters in determining how fast the water evaporates.



water flow/speed



You might be able to factor that into the velocity term $v$, but if the water is flowing slower than the air is, you can probably ignore the water velocity.



ambient air temperature, dew point/humidity



Accounted for in the dry air humidity ratio.




chemical composition of water (pool)



Pool water is over 99% water, so the chemical composition is not important.



temperature of water



Accounted for in the humid air humidity ratio.



wind speed




Accounted for in the $v$ term.


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