How does a water pump in a desert cooler work??
Are you talking about an evaporation cooler? These are also called swamp coolers in the USA. Below are some links on evaporative coolers.
There are a variety of different types of evaporative coolers some have pumps to bring up the liquid to the evaporative plates or fabric others do not. Some rely on wicking to bring water to the plates.
There are also coolers that create a high press liquid stream that when force though special nozzles will form very small droplets which evaporate very quickly and cool the air.
I am not sure I have answered you question. If it is still open could you be a little more explicit in what you are looking for?