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It is a very bad idea to drive a car without coolant. You will overheat your motor and risk warping or cracking your head(s) and blowing your head gasket. It's also not good for water pumps to operate without coolant in the system. If it's an old Volkswagen, as long as you like (VW bugs had air-cooled engines).
I assume you want to change out the water pump and would like to know if you can do it without draining the radiator. You will lose approximately all the coolant in the radiator reservoir when you remove the radiator hose from the water pump. If the coolant is in good, clean condition, it might be wise to drain the radiator into a container and re-use the coolant.
Possibly a blown head gasket, allowing coolant water into the engine cylinders. Check the tail pipe exhaust for water vapor (be careful! it is hot!).
sounds like you have a blown head gasket
it will say low coolant and it means you need to add a mix of 50/50 coolant and water to the overflow.
If an engine has no water or antifreeze in it, it is better off than an engine without the proper anitfreeze to water ratio. You can buy a tester to determine the actual low temperature the water/coolant is safe down to. If the vehicle is not running and it only has water in it, cut the lower hose and let the water drain out and this will prevent the engine from freezing up and possibly busting the block or popping out the freeze plugs. If it has coolant in it you can drain the coolant and recycle or dispose of it properly according to local regulations.
mars is a planet like earth without water
Very few cars have a low coolant light but will have a overheating light. You can be sure it will look like water or a thermometer. Why not just raise the hood and check the coolant level.
Perhaps "check your coolant water"
sounds like the water pump is gone. that may be where the leak is coming from. could also be the cap for the coolant res. or thermostat
You should look under your vehicle while its running. If you haven't noticed a puddle of coolant on the drive way, you may have a bad head/gasket. Does the car smoke? If it does, your head gasket is gone. Check your engine oil. If it looks like muddy water on the dipstick, you've got coolant mixed with the engine oil. If you see coolant on the ground, you may have a bad water pump. First, check your radiator hoses. Remember to check the hoses going into the heater core as well.
You need coolant. This happened when my water pump went bad and I needed to refill the coolant.