# Pipe protuberance's effect on flow

1. Nov 6, 2017

### Mangoes

Hi,

I've been reading over Transport Phenomena by Bird, Stewart, and Lightfoot and I've been going over the friction factor $f$. I've gone through the whole development leading to the observation that, for time-averaged turbulent flow, when we neglect entry effects, $f = f(Re; k/D)$, where $k$ is the (average?) height of pipe protuberances for rough pipes.

I'm assuming that the reason why rough pipes introduce additional losses is because of the introduction of some minor form drag along the pipe wall whereas smooth pipes only have frictional drag. I'm not really understanding why this doesn't seem to be an issue for laminar flow though. Why is pipe roughness seemingly not a factor in frictional losses for laminar flow? The Moody diagram only has one curve for the laminar region corresponding to the Hagen-Poiseuille equation.

2. Nov 6, 2017

### DoItForYourself

In case of turbulent flow and when you have rough pipeline (big sized protuberances), the collisions between the molecules of the fluid and the molecules of the piping material are more (in number) and more violent than in laminar flow (low velocity). In addition, as we increase the Reynolds number (turbulent flow) the molecules of inner layers can collide with the pipe protuberances. The number of collisions depends on the velocity, density, viscosity, diameter of tube (Reynolds number) and on the size of the protuberances comparing to the diameter of the tube (k/D).

When the collisions are more, the loss in the kinetic energy will be more, because the collisions are not completely elastic.

3. Nov 6, 2017

### Mangoes

That makes sense, thank you. I'm guessing then that since only a relatively minor fraction of fluid molecules are impacted by protuberances and their impacts are at lower velocity, the effects are negligible for laminar flow.

4. Nov 6, 2017

### DoItForYourself

Yes, and thus f depends only on Reynolds number in laminar flow. In turbulent flow you need also the protuberances' effect on f.