My 2003 model L322 ( petrol BMW V8 ) began indicating low coolant level on cold starts. After refilling some litre of fluid things looked normal. But low level reappeared after a few days. I noticed fluid dripping in front of the engine bay and with a hand lamp I got enough illumination to track down the source of leak. Turned out the expansion tank have developed a crack on the side and fluid sips out when pressurized (mileage some 140000 kilometres). Remedy is getting a new tank, some GBP 50, and I will be good to go again. Some history is the vehicle has had radiators swapped for new ones at two times since 100000 kms and a top radiator hose blew off at one time due to a cracked plastic mount. Since then all new hoses were installed. Here´s a video showing the tank leak: