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.

 

[PJC01]

The roughness of a pipe refers to the surface texture or irregularities on the inner walls of the pipe. These roughness elements can cause frictional resistance to the flow of fluid, which can affect the pressure within the pipe. However, the velocity of the fluid is not directly affected by the roughness of the pipe.

This is because the velocity of a fluid is determined by the pressure gradient within the pipe, which is the difference in pressure between two points. In a single pipe scenario, the pressure gradient is determined by the difference in pressure between the inlet and outlet of the pipe. The roughness of the pipe does not change this pressure gradient, so the velocity of the fluid remains the same.

In other words, the roughness of the pipe may cause a change in pressure, but it does not change the overall pressure difference that drives the flow of fluid. Therefore, the velocity of the fluid remains unaffected by the change in pipe roughness.

Additionally, the roughness of a pipe can only have a significant impact on the velocity of the fluid if the pipe is very long or if the fluid is highly viscous. In most practical scenarios, the length of the pipe and the viscosity of the fluid are not significant enough to cause a noticeable change in velocity due to roughness.