The flowrate of a fluid in a pipe is the mean velocity of the fluid multiplied by the cross sectional area of the pipe. If you are pumping fluid through a 50 mm pipe which is then connected to a 25 mm pipe then the flowrate actually remains the same... All that happens is that the velocity of the fluid increases when it flows through the smaller pipe. Logical really, you're trying to squeeze the same quantity of water through a smaller area, so it has to pass through quicker.