Can a car run without a water pump?

The water pump circulates the water though the cooling system of the engine, the radiator and associated pipes. Without the pump to circulate the water through the system temperature control will be staled and the engine will overheat.

Some water cooled engines were designed to run without the use of a water pump. An example of one would be a 1958 Massey Harris Pony tractor. It has a 20 hp water cooled engine with a radiator that relies on convection cooling.