I'd first analyse the water to quantify soluble nutrients and soluble detrimental compounds, then use the water to cultivate the plans with the same medium, measure the yield and analyse nutrients content in the whole plant (GC-MS based methods are a possibility). You can express the quantity of nutrients and other compounds in the water treatments as relative change compared to the control with distilled water and check for a correlation with the quantity of the same compound in the water. The choice of the medium is the most difficult part because you need to ensure the growth of the plant while not providing enough nutrients to mask the effect of the water. I'd also keep in mind that the interaction water:plant is different from water:soil:plant. Thus, using hydroponic doesn't necessarily represent the effect of the water on the plant with different media/soils. You could also provide label nutrients in your medium to quantify by measuring the difference between labelled and total (ex. isotopic ratio).
There are a number of works around the subject of factors that affect yield, in your case, irrigation. A direct method is the adjustment of a yield response function to various factors. You can do it experimentally or with cross section information obtained from farmers. If you can read Spanish, a few papers on this topic can be found on my researchgate page. If you can not do it, download the works and with the google translator to pass them to English.