My water pump chirped, until I replaced the fan clutch, no excessive load on pump no chirp.

 

A worn belt will chirp at the water pump. The pump rides on the back of the belt and will chirp where the logo is embossed on the belt. My a/c compressor bearings were going bad internally, putting excess strain on the belt, causing a chirp at the water pump. New belt and pump and it still chirped. The pump was horrible and needed to be swapped anyway. Point is, check everything. The noise doesn't always indicate the problem...