If that's just one vine/plant? and you've watered it well then it could be a Squash Vine Borer. They suck the life out of the main stem near the root which causes the whole plant to wilt, then die. Check for borer damage at that point and remove them if possible (they look like fat maggots). Best guess.

will they be on the exterior of the stem?

Dale

While I can't rule out SVB, to my eyes your pumpkins look normal if it is a really hot day out (90F+, maybe lower). All that is happening is the plant can't take up water as fast as all those large leaves are losing it so they get wilty.

check back in the evening to see if the plant perks up. If it does it is just normal water stress and nothing to worry about. If the cool of the evening doesn't see a perk up then it is soil too dry or damage to the stem.

I have to agree with "justaguy".

Go check them out after the sun goes down or tomorrow morning, they may just perk back up.

My squash plants and cucumber plants do this all the time if it's unbearingly hot out (90+).

That huge pumpkin plant consists of several long radial vines. Those vines want to drop roots at each leaf node, thereby allowing it to forage for more water and nutrients. But it looks like you have plastic mulch down everywhere preventing that, so all of the feeding is done at the main stem. I think that's going to be a problem for any such large, sprawling curcubit. The same thing happens to my Hubbard squashes that wander into dry, hard ground and only get watered at the main hill. If they perk up on cool days and at night, then I'd guess it's having trouble getting enough water. But as long as the leaves don't start turning crispy, and they recover OK from wilting, I think the plant can deal with it. If it were me, I'd try giving it some extra water. Maybe fill a 5-gallon water bucket with a small hole in the bottom and park it close to the main stem, and see what happens.
Although, I would think it's not so much a problem that there's not enough water available, but that it can't draw it fast enough on warm days to keep up with evapotranspiration. Wilting is the plant's way of dealing with that problem.

What quantity of water should my watermelons and this pumpkin vine be getting every day?

Dale

I don't think it is possible to say how much water they need given that soils drain differently, local conditions dictate evaporation and transpiration rates etc.

Water in the morning and if plants wilt dig down 6 or so inches well away from the roots and look at the soil. If it isn't dry, it is OK. You kind of just have to look and learn and get a feel for what is needed.

False alarm!!! I just got home from work and went out back and the vines are fine. I will eliminate the black plastic around the pumkin vine so that it can get more water. Thanks for the replies.

Dale

If you remove plastic to allow more roots to grow, you should probably water those areas too, to encourage root formation.
I kinda wonder about this too, how necessary is it to provide "rootable" conditions at the leaf nodes for rooting there. I know that if you want to grow the most massive pumpkin possible, you cultivate, fertilize and water the *entire* area the pumpkin covers. So that it can send down as many roots as possible and draw the most water and nutrients. So I would gather that any winter squash would benefit similarly.
Personally, I figure it's good enough to provide a couple feet of moist fertile soil for the wandering vines to root in. After that, they are on their own.

I have just removed the plastic and gave the vine a considerable amount of water, I hope it continues to grow as it was up until yesterday. It was wilted again today when I went out to remove the plastic. I am going to go and check again now.

Dale