How to new when my water pump is not movihg water.

A stuck thermostat is the likely cause of that. If you remove the radiator cap and start the engine you should see water movement.

Could be the water pump leaking.

ck your water pump, sounds like no water movement,

I presume you have a pressure gauge installed on the radiator. and the engine is running. If you have no pressure after running the engine until the water temperature is hot, you should check the instrument of your vehicle to see if the engine is not over heating. The water pump is circulating the water so the water is in constant motion and is cooled by the air flowing thru the radiator. The air is drawn thru the radiator by the fan, either engine driven or electric powered. When the cap is off you should see movement of the collant in the radiator. also chech if you see any oil residue mixed with the water. in that case the water level should drop because the water is draining into the oil tank.. If you see no water movement the water pump is not moving the coolant thru the engine and the engine will over heat.The water pump is bad in that case.

SOUND LIKE COOLANT FANS HAS A FAULTY THERMO SWITCH LOCATED AT THE BOTTOM OF THE RADIATOR ON LEFT HAND SIDE.CHECK THE FUSES 8 IN THE ENGINE COMPARTMENT AND CHECK FUSE 16 IN THE PASSENGER COMPARTMENT FUSE BOX.WHEN ENGINE OVERHEATING IF BOTH COOLING FANS WORKING.OVERHEATING PROBLEM COULD BE BLOWN HEAD GASKET.CHECK ENGINE OIL LOOKS LIKE MILK HEAD GASKET LEAKING.SEE WHEN YOU DRIVING LOW AND HIGH SPEEDS THE COOLING FANS SUPPOSE TO BE RUNNING.IF THEY NOT RUNNING THAT IS YOUR OVER HEATING PROBLEM.

After the car is cool and has been sitting for a while, remove the radiator cap, have someone start the car, the coolant in the radiator should drop a little, and there should be movement, if there is no movement, let the car run for a while, with some systems it won't cycle enough to notice until the engine warms up. If there is still no movement, you likely have a bad water pump and/or thermostat.
Another method as a "just to be sure", drain the coolant overflow tank, and fill it with clean distilled water. Drive the car for a few days (carefully not to overheat it obviously, if the engine is getting too hot to drive normally don't do this test). If after a few days of driving the fluid in the overflow tank is still clear (water), then there is no circulation in the system.
It's usually best to start by replacing the thermostat, and then re-check. If that doesn't fix the problem it is most likely a water pump, or in very rare cases a plugged radiator or coolant passage.

FILL RAD AND BOTTLE, LEAVE CAP OF AND WATCH WHEN ENGINE IT RUNNING , IF LEVEL DROPS WHEN MOTOR REVS PUMP OK, IF NO CLEAR MOVEMENT PUMP FAULTY, IF BLOWS WATER OUT, POSSIBLE HEAD GASKET OR CRACKED BLOCK/HEAD, YOU CAN DO THIS WHEN COLD,
ALSO CHECK THERMOSTAT IS NOT UPSIDE DOWN AND ALL HOSES CONNECTED ON REBUILD ON CORRECTLY

try the water pump - first - make sure the radiator is really full - take the cap off cold and fill - if it looks full - start and run 8 minutes or so - then fill it up - look at ur fan belt - is it tight - tight is about how much pressure u use to make a firm hand shake with little movement - any movement over about an inch is loose - when the jeep warms up the belt can slip and not even make a noise - - new materials don't always squeal. - then be sure ur water pump is ok - they go slowing - the fins wear down - one more thing is the radiator - u don't say how many miles or what maintenance schedules you have or not so that's it for now

Did you install a new thermostat and make sure to bleed all the air out of the system when you replaced the radiator? If you didn't, or installed a Stant thermostat, replace it with a FACTORY OEM thermostat. Make sure the cooling system is bled by opening your radiator cap (WHILE THE CAR IS OFF AND COLD), starting the car and running the heater. Add coolant to the radiator as the engine heats up, until is at normal operating temperature AND starts spitting coolant back out.

Hope this helps,
matt
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Do the fan(s) come on when hot? Blow out the radiator core with compressed air (from the engine side) to clear it of bugs and other debris. Make sure the radiator is full to the top (when cold) and check the radiator cap seal rubber and the over-flow tank and tubing for leakage. It's possible that the water pump impeller is slipping on it's shaft and not pumping water properly. Remove the thermostat temporarily and remove the radiator cap. Remove some of the water so that the level is somewhat below the cap bottom, then start the engine and watch for rapidly moving water. That will show that the pump is moving water well. Allow the engine to heat up and keep track of the water movement. Shut the engine off at low end of 'normal' on the temp gauge and replace the cap so that it doesn't blow out boiling water into your face. Replace the thermostat and top up the water when cold again.