I just bottled a batch of a watermelon beer where the gravities going into and out of primary matched the predictions (OG 1.050, FG 1.012).
I added watermelon chunks in secondary and when it finished I had a gravity of 1.007. Can I use this new number to get a new higher ABV (5.6% rather than 5.0%)? Does this just mean that the water from the fruit diluted the beer that much? What impact do the sugars from the fruit have?
It's not really possible to answer this question without knowing how sweet the watermelon was. That is, we need to the watermelon's brix.
When you added the watermelon, you added some water and some sugar. The sugar will ferment, increasing the alcohol content and the water will dilute, decreasing the alcohol content.
According to this page, watermelons average around 10 brix, which corresponds to a specific gravity of 1.040. Given that the sugars in watermelon juice are 100% fermentable, unlike beer wort, which is around 75% fermentable, I would expect the watermelon to contribute roughly the same amount of water and sugar to the beer as the wort. That is, after all is said and done, the beer will have the same alcohol percentage, while the volume will have increased.
So it's a bit surprising that the gravity dropped after the watermelon had fermented. There are two possibilities. 1) the watermelon was sweeter than 10 brix, and the extra alcohol it contributed is lowering the specific gravity, or 2) it was less than 10 bris, and the added water is diluting the beer and lowering the specific gravity.
Not much of an answer, I'm sorry to say.
One thing you can do, if you have access to a refractometer, is estimate the beer's overall starting gravity by plugging the refractometer and hydrometer reading into a calculator like the third one on this page. You can enter the estimated original gravity and measured final gravity into an ABV calculator to get an estimated alcohol percentage for the beer.
You've sussed out the two changes from the addition of the fruit: you'll dilute the original beer, and also change its gravity, which after more fermentation will result in a new FG.
Ideally you'd measure the pre-addition specific gravity, the post-addition SG, and the post-ferment FG. The difference between the OG and the pre-add SG, plus the difference between the post-add SG and FG would be summed to arrive at your true ABV.
I agree with other commenters that it is not possible to determine the effect of the watermelon on the beer given the current data. You don't know the weight of the watermelon, its water or sugar content, how much of it made it into the beer so it was accessible to yeast (and how much is unfermentables like cellulose).
In fact, it is possible that at least some of the change in gravity was due to measurement error, or is within the margin of error for resolution on the refractometer. (And we are assuming that temperature correction was done).
I suppose in the future, you could take an average sweetness sample of the watermelon (based on appearance or tasting corners of chunks), pulp the sample, and take its Brix. Then you could figure out the weight of the watermelon, and make an assumption about its water weight, thereby estimating the volume and OG of the watermelon addition. Then you could use the parti-gyle method to calculate the combined OGs of the wort plus watermelon, and finally use the FG to get an ABV and apparent attenuation figure.
