I'm designing a testing unit where I need to estimate the smallest diameter of a short complex pipe (around 1 meter, three bends and some diameter viariations). Since the pipe is being cooled down in a water bath after production, my idea is to force water with a known pressure in one end of the tube (other end is at pressure of the water bath) and measure the flow rate. I'm assuming that when the smalles diameter of the pipe is much smaller than normal due a construction fault, the flow rate will be lower due to higher pressure buildup in the smallest section of the pipe (like what happens if you almost close the end of your garden hose). However, I'm having troubles proving this. Are my assumptions correct and can someone get me started to prove this?