minecraft-buildcraftminecraft-java-edition
7.10 with buildcraft and my combustion engines are giving me problems.
They will use all the water when they turn green but then they'll stop accepting more because they heat up quickly to orange or red afterwards. I'm not sure why that is but I'm pretty sure I've set it up correctly with more than enough water.
Picture of the setup: 
Instead of attaching the engines directly to the quarry, use conductive pipes to pipe engine energy into the quarry. I have a VERY nice setup using plain steam engines powered by coal from a self feeding glowstone dust generating system using equivalent exchange.
You put a wooden conductive pipe above the steam engine with the engine pointed up, then use stone conductive (or gold) pipes to pipe the energy into the quarry. By piping the energy off the engines, you will never run the risk of them overheating if you're using steam engines, and if your combustion engines have water then they'll be fine too.
Wooden pipes extract items from chests (and perhaps automatic crafting tables; I haven't tried). Engines can then be attached to the wooden pipe.
I recommend watching the videos on the official YouTube channel to gain a basic, working knowledge of the mod.
Best Answer
Stone pipes, in my experience, don't provide enough water that the thirsty combustion engines require. This is also easy to tell in your picture as the pipes are not filled... meaning they are only just able to feed the engine.
Use gold pipes as they are able to transfer much more water per pipe.
If that still isn't enough, then use emerald pipes as well as the gold pipes. Emerald pipes pull out 4 times as much as a wooden pipe can do.
Look here for more info on piping