Do you have a bottle? If you give milk feeds in a bottle then try offering a bottle of water at a couple of points during the meal. You will be able to judge then how much he really wants to take when he has a comfortable way of taking it. If you've never used a botle then this isn't going to be a helpful suggestion.
In my experience some LOs just don't need to drink much, a few sips, they can also get a lot of fluid from the solids depending what you are feeding. If you are giving puree then each mouthful has fluid in it, if you give fruit as finger food then he can be getting a lot of his fluid from the fruit. I think the key really is the number of wet nappies.
WRT constipation it isn't necessarily due to not drinking enough. Some foods can constipate very quickly. It will all depend on the individual LO but there are foods which can be quite common. Have you seen the laxitive food thread? I found it really useful when we started solids, discovering that carrots firm my LO up, and prunes loosen him up. Using just those two foods I could balance up his poos and offer a varied diet because I knew how to manage the poops in a natural way if they went one way or the other. It was a revelation to me that carrots would do this, I didn't stop giving him carrots, I just made sure he had a prune too. Under ripe bananas can cause constipation (over ripe can cause diarrhoea) ...who ever knew poo could be so interesting a subject??
