The Bernoulli Equation and its Limitations

MEC516/BME516 Fluid Mechanics, Chapter 3 Control Volume Analysis, Part 7: A derivation of the Bernoulli equation for frictionless fluid flow. The limitations of the Bernoulli equation are discussed. The video ends with a sample calculation of the discharge rate from an open tank, using the Bernoulli equation.
A copy (pdf) of this presentation can be downloaded at www.drdavidnayl...
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmatters #fluidmechanics #fluiddynamics

[@hanaalqam7228]

amazing presentation, explanation, and demonstration. Thanks

[@FluidMatters]

Glad it was helpful!

[@Ensign_Cthulhu]

3:50 - Chain rule, or implicit differentiation? Sometimes I think the lines are blurred on this one.
Also, in the tank example, what about the pressure of the water at a depth of 3.9 metres? Doesn't that count for something? Or is the only relevant pressure the one the short pipe is discharging against?

[@samkeloinnocent8316]

Thank you so much sir.

[@aliVimtaj]

I've got a question: in the example of discharge flow from a tank, if I put my finger at the discharge point, I see the speed of the discharging fluid is increasing, but Bernulli equation shows the discharge speed is not function of discharge diameter. Is there any explanation for that?

[@FluidMatters]

Interesting question. I haven't tried it, but I suspect your intuition is not correct. Try drilling a small hole and a larger hole at the same depth near the bottom of large plastic water bottle. My bet is that both water streams follow the same arc and extend the same distance from the bottle i.e., they have the same exit velocity. It would make a nice short video. I'm completely open to be proven wrong! Thanks for the question.

[@guanchucheng]

Amazing presentation! 05:50: it seems to be dv/dt of material derivative rather than del (v)/del (t)?

[@FluidMatters]

Correct. This is a material derivative. However, there is no time variation, because it is a steady flow. So, acceleration is only caused by spatial gradients in velocity.

[@naf2016]

The description has, "Chapter 3 Control Volume Analysis..." What is the title of the book please?

[@FluidMatters]

Fluid Mechanics by Frank White (McGraw-Hill)

[@naf2016]

@@FluidMatters Thank you sir

[@FluidMatters]

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