I have a question about the flow rate in a pipe. If a fluid is incompressible and enters a pipe at a certain rate, shouldn't the rate at which it exits be the same? Otherwise, the pipe would be filled with more water than it can hold and have to either expand or compress the fluid within it.
From this textbook that I found, it agrees with this idea in that the velocity profile in a pipe changes - the no slip condition causes fluid molecules in contact with the pipe to stop and slow adjacent fluid layers down, causing the flow in the centre of the pipe to increase in velocity so as to maintain flow rate.
However, some videos that I watched say that as the length of a pipe increases, the flow rate within that pipe would decrease such as in Poiseuille's Formula:
This doesn't make sense to me as that would be like saying if I had an almost infinitely long length of pipe, no water would come out of the end of it even if I pumped a lot of water through it.
So does the flow rate of fluid in a pipe change with its length? I also considered the possibility that fluid flow may be different in laminar and turbulent flows when looking at Poiseuille's Formula and the Darcy-Weisbach Equation.