Does Average Fluid Velocity Increase Along an Inclined Pipe?

MEC516/BME516 Fluid Mechanics, Chapter 3: This short problem concerns the variation in the average velocity for incompressible flow in a pipe. Does the average flow velocity increase in an inclined pipe? The answer is NO! This problem is from a past Chapter 3 quiz. It demonstrates (and hopefully corrects) a very common misconception. This is an important concept for solving pipe flow problems in engineering fluid mechanics.
All the videos in this course and copies (pdf) the presentations can be downloaded at: www.drdavidnayl...
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics #fluid dynamics #continuityequation

[@FluidMatters]

All the videos for this introductory Fluid Mechanics course are now available at: www.drdavidnaylor.net/

[@science_engineering]

It's pretty counterintuitive I would say :)

[@FluidMatters]

Yes. That is what I find so interesting, as an instructor. If I had given a flow rate Q and pipe diameter D in say, a Bernoulli problem, 99%+ would get the same mean velocity at the top and bottom, without thinking twice.

[@rhinobridge]

@@FluidMatters I never thought about this before but I'd also think the velocity increases. If we think about the fluid as particles, they should increase their velocity due to the gravitational force as they travel downwards. Why would they go against physics?

[@FluidMatters]

@@rhinobridge You are thinking the water is like a ball rolling down a hill, which gains kinetic energy (only). (This would be true for a film of water sliding down a hill at constant pressure). The water film would get thinner as the flow speeds up due to gravity. But the physics in a pipe is more complicated. Conservation of mass requires that the velocity is constant -- so you have energy changes due to changes pressure. I hope that helps.

[@birbahadurthokarcrn0494]

If we apply Bernoulli equation at the discharge point and somewhere upstream of the pipe it seems that the velocity at discharge point should increase as the loss of potential energy of the fluid should be converted into kinetic energy as the pressure at the discharge point is constant at atmospheric pressure, but continuity says it should remain constant. Please clear this one

[@FluidMatters]

Conservation of mass rules supreme, of course. So, the velocity MUST remain constant, since water is incompressible. So, if you apply the Bernoulli equation between two points In a constant diameter pipe you only have the conversion of potential energy into pressure (flow work) because the kinetic energy terms are constant a both points. A constant discharge pressure to atmosphere does not change that fact. I hope this helps.

[@islamdk4844]

Thank you for your videos professor, but it is fair to say you must mention that the flow rate is constant ...

[@FluidMatters]

No. It is liquid water, hence an incompressible flow. So the flow rate at each cross section is constant, even for unsteady flow.

[@islamdk4844]

@@FluidMatters thank you for the clarification sir have a nice day .

[@9wyn]

There's no right, there's no wrong, there's only popular opinion.😁

[@FluidMatters]

"Alternative Physics" ha ha!