Solved Problem: Conservation of Linear Momentum, Forces Generated in Nozzle

MEC516/BME516 Fluid Mechanics, Chapter 3 Control Volume Analysis, Part 6: This fluid mechanics video describes the application of the conservation of linear momentum equation to the calculation the forces generated by flow through a nozzle. The issue of calculating the net pressure force is discussed, followed by a detailed sample calculation.
A copy (pdf) of this fluid mechanics presentation can be downloaded at www.drdavidnaylor.net
Course Textbook: F.M. White and H. Xue, Fluid Mechanics, 9th Edition, McGraw-Hill, New York, 2021.
#fluidmechanics #fluiddynamics #linearmomentum

[@sonofaspine]

If you’re somebody studying fluid mechanics and you are contemplating not watching this video in full, take my word, this is worth every minute. I’ve seen a lot of videos on KZbin regarding this topic, and no other video builds upon theoretical fundamentals and challenges adaptation of real life phenomena quite like this video. Just finished watching this video and I am very very pleased. I considered switching to a new video at about 4/5 mins in. I am very glad I stuck it through. Excellent work here. Thank you.

[@FluidMatters]

Thanks for the very nice comment. Glad to hear the video was helpful.

[@sonofaspine]

Great video!

[@indrarahyang]

Hi Mr Fluid, how to factor different nozzle type in one flowing at time, let says 1 same direction as inlet another is 30degree off the axis, would that reate some vorttex force?

[@FluidMatters]

I'm not entirely sure what you are asking. Here is another solved example where the nozzle outlet is "off the axis", which may be what you are looking for: kzbin.info/www/bejne/Z6XTaGCbZsurnsU

[@nikan4now]

That was great. Am I correct in assuming that when we do a cut thru a solid even if there is no ATM pressure in that section we still imagine ATM pressure is there to use the trick and work with gauge pressure? For instance in the horizontal nozzles at the left end there is no air acting on the solid and liquid but we still assume its there and instead work with gauge.

[@FluidMatters]

I not 100% sure of your question. The absolute pressure inside a pipe will be affected by local atmospheric pressure even though "there is no air acting on the solid and liquid" inside the pipe. It will be the pressure provided by, say a pump, plus to local atmospheric pressure. So, yes, the atmospheric pressure "is there" and you need to work with gauge pressure. I hope that helps.

[@bcyalcin]

so can you say that if the diameter of the nozzle decreases (so that it is not a nozzle anymore, it is a basic circle), we obtain more thrust force ?

[@FluidMatters]

A change in the outlet diameter will change the inlet pressure. You could work out p_1 using Bernoulli (plus some estimated head losses, if you want more accuracy). I haven't done the analysis. But my intuition is that the thrust due to the change in moment of the water might go up or down. Although the outlet velocity (V_2) will increase as D_2 decreases, but the the mass flow rate will decrease. Not sure if that answers your question.

[@FluidMatters]

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