How to find/calculate the yearly evaporation of a given area?
What you are asking is one of the most difficult issues in hydrology. The evaporation from open water is a function of air temperature, water temperature, humidity, wind speed and fetch, water depth, water salinity,  degree of thermal stratification, and boundary effects (as you correctly point out). It is certainly not a trivial calculation!
As a first approximation you can apply an empirical coefficient to class-A pan evaporation data, but don't expect any great accuracy.

But then you progress towards a further aim of calculating a potential irrigation need. For this purpose I would say that calculating open water evaporation is completely the wrong approach. Rather, calculate the potential evapotranspiration ('ET0'), and then apply appropriate crop factors, as explained in the FAO documentation:
http://www.fao.org/docrep/s2022e/s2022e07.htm
Calculating ET0 is best done using the Penmann-Monteith equation, which is horribly complicated, but there are web sites where you can do the calculations on line. You will need monthly or dekad climate data for the crop(s) you envisage growing. This will be max and min temperature, humidity, average wind speed and average daily hours of bright sunshine. You will also need latitude, longitude and altitude to estimate the solar radiation. Even with all this data, it is a fairly lengthy calculation, but it is your best bet at realistic crop water requirements.