Fuel pump runs for a while then it will stop

the operation of most fuel pumps is controlled by the fuel pressure regulator
when the fuel pump gets to set pressure , the pump is switched of by the ECM at the relay level
maybe nothing wrong with your system just the system working as designed
if you have pressure in the fuel manifold when you turn the ignition on then the pump will not run but will if there is a fuel leak somewhere and the pressure drops off

check your fuel pump relay. if not that, then it's your fuel pump. the gas gauge is in the fuel pump, so if your fuel pump stopped working, your gas gauge won't work

When you turn the key the pump runs till it pressurises the system you then crank over the engine fuel gets used pump starts again to keep up fuel pressure and stops when fuel is not being used

Hi all happy new year 2016 i have exactly same problem with Audi a3 8p 2.0l fsi 2005 fuel pump running all the Time ( with and without ignition)non stop . For stop it i need to remove fuel pump fuse.
I think this part is defective

I want to have helps before buy it

Thanks in advance.

test computer sounds like internal problem

Does the pump stop running when you turn off the key? With electric fuel pump, the fuel pump relay sends voltage to the pump. The control side of fuel pump relay needs voltage and ground.
Engine cranking do you have spark at the plugs and fuel injector pulse? Use a gage and check proper fuel pressure, my info says 35--45 psi. Usually, if pressure is too high you check for a problem on the return side. If pressure is too low, you check the supply side of the fuel system.
Usually with initial prime the computer grounds the control side of fuel pump relay, for a couple of seconds, then w/o rpm signal, it shuts off. Maybe the ground wire is shorted to ground or problem with computer?

The fuel pump will run long anough to buid up pressure then shuts off,if the pressure goes down the pump comes back on.Once it is started the pump will run to maintain the pressure as the gas is used up.

If the crankshaft sensor is bad, ECM will give no voltage to the pump. It is design to stop the pump running in a case the engine stop during an accident. Check it out. Good luck.

check fuel filter and fuel pump

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check the fuel pressure before and after its running i asume its fuel injected