My Mercury 50 hp outboard engine with a new water pump will not pump water?

The first check would be to ensure that the tell tale hose is open. Dirt daubers are notorious for crawling up in the hose to build their nest. If you have access to an air compressor, try shooting a short blast of air through the hose. Another method that works is to slide a short length of wire up the hose, in an attempt to unplug it. If the hose is not clogged, the lower unit should be removed for further diagnosis. Make sure that the water tube seal, located in the pump housing, is serviceable. Sometimes when the foot is installed, the tube is not properly inserted, or missed altogether. While the foot is off, blow air, or run water through the water tube to insure that there are no other blockages.