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I have a question regarding the flow rate in a pipe. According to the general rule the flow rate is:

Q = v * A

where Q [m3/s]

v [m/s]

A [m2]

So according to this formula the flow rate depends only on the inner area of the pipe and the velocity of the fluid and does not matter what the pressure loss is until a certain point. So I had this argument this other day with someone and he said that the flow rate depends on the friction losses in the pipe. But I don't see where that happens according to this formula. If I have a pump that provides 2 [m3/h] and there is only one pipe, no matter how long or how many curves it makes the water flow at the end of the pipe will still be 2 [m3/h] because no mass is lost anywhere if there is no ramification.

The only doubt that I have is that the pump might not be able to provide 2 [m3/h] because it has limited power therefore it will soon succumb to the accumulating friction losses in the pipe therefore the declining flow rate. But if the pump would have unlimited power then the flow rate would remain the same right ? Anyway I could not find the relation between the friction losses, power and flow rate and how this all comes together in an elegant explanaition and if someone could provide one it would be much appreciated. Thanks!