Why is fluid velocity unaffected by a change of pipe roughness here?

[cdux]

I had no luck in the coursework forums though I guess the question becomes simpler if I state it the way I did here.

Assuming no complex network, or just a single pipe first feeding the network, why do the speeds in the pipe and even the rest of the network pipes remain unaffected if I change the roughness of that first pipe? The pressures do change.

I guess I need the basic answer which I'm sure is simple so I can then expand to a very rational explanation that will make me remember it because the way I think of it now, it's a bit unclear how roughness can keep velocities unaffected (in a non-part-of-a-branch, single pipe scenario).

 

[cdux]

OK I got an answer from somewhere, but I still can't get it to hold still in my head.

The answer is basically that since Q = V * A then V remains the same since Q is the same (and A).

Now, how can I make that make sense when also thinking of roughness as irrelevant?

edit: Basically how can Q remain the same? hrm.. I'm probably trapped in a circular logic that is totally wrong but I'm not sure exactly how.

 

[cdux]

Now I'm thinking of Darcy–Weisbach et al. complex equations and I can't figure out how while they do include coefficients for friction/roughness, they just take velocity for granted as stable (if the above is true).

 

[cdux]

Ah, I think I got somewhere. In the simulations I was running, I guess whatever output is entered, "it must be supplied", hence Q is taken as a hard-constant no matter what hence V is satisfied to a constant based on that, provided same cross section.

Or at least that's how far I got.