My car has the exact same thing, only with gas in stead of liquid, and it works a treat; it's called: turbo....my concept is to develop a valvy/pump type thing which uses the flow from the cold mains to turn an impellor which "sucks" water from the hot supply so that the output flow rate/pressure from the hot and cold is equalised by this governor effect. ...
Don't see why it wouldn't work with water, go for it; if you can produce it for under 50 quid, you are in business.