Fluid Mechanics: Topic 10.5 - Kinematics of fluid elements (shear strain, rotation, and vorticity)
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- เผยแพร่เมื่อ 25 ก.ค. 2024
- Note: Some fluid mechanics textbooks omit the 1/2 in the shear strain rate expression. That is, the shear strain rate is defined simply as [ d(alpha)/dt + d(beta)/dt ]. We keep the 1/2, as in Dr. Frank White's textbook, "Viscous Fluid Flow".
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Why do professors not teach like this? Everything is visual and it gives you an intuitive sense where the derivations are coming from. As a result it makes you ten times more invested in what you're learning.
Glad you enjoyed the video.
I have a question. Can we devise a strain rate matrix (3x3) for the strain rates? Where the linear strain is along the diagonal and the shear strain rates are along the non-diagonals. Is it safe to assume that E_xy is equal to E_yx? If so, the matrix will be symmetric. This is interesting to think about.
@@CPPMechEngTutorials Back again, but this time taking graduate level fluid mechanics. We are talking about tensors now. We are discussing symmetric and Symmetirc Velocity gradient tensors...help lol
@@carbon273 hey dud! I have same doubt about it.. i can get the displacement tensor and split it into a symmetric tensor by (e+eT)/2, which gives me the strain tensor and the ant-symmetric one, by (e-eT/2), which is the solid rotation tensor.. thats what gives the 1/2 on expressions.. not sure why he talks about average values.. have any clue? And shear strain is the sume of both angles (du/dy + dv/dx) so.. again not sure why should we take the average.. regards.
Absolutely great!!! In a regular class, teachers do not tend to explain like this, I mean, in a detailed way. Thank you much for your time and effort and sharing knowledge worldwide. Greetings from Perú 🇵🇪
Very well illustrated and neatly explained. This is the way to teach! Looking forward to more videos from you
They are coming along... slowly.
Thanks a lot for this video it's very easy to understand the derivation here rather than in direct text books
Whenever I find your your video on any topic i feel glad and rest assured that i will surely get it from this.
More are being developed... stay tuned.
Hey thank you so much, We watched this video in transport phenomena class. We really appreciate all your explanations.
Neat! Hopefully it was helpful.
Well explained. Thank you!
Thanks a lot! I finally understood what I've questioned for at least two years :0
Please explain more that how did you apply the Taylor series approximation as you said ?..
Another question: when doing this derivation we are reliant on the fact that the clockwise direction gives us -dB/dt. Wouldn't this make the (later in the video) full body rotation become Omega = - (dv/dx+du/dy)/2, i.e. giving two minus signs?
The best 👍💯!! Thanks a lot!
REALLY HELPFUL
I cannot thank you enough for this video. I had a lot of trouble understanding this, but know I got it!
Glad it helped!
Awesome explanation, thanks
No problem.
Is it a control mass or control volume analysis?
Great video. Thank you
Our pleasure.
Just one question. Why in the shear strain rate is the mean sum of velocity gradients while in the angular velocity is the mean difference?
Thank You
Man this also explained elasticity for me. Two birds with one shoot. Thank you
There is a lot of overlap between solid mechanics and fluid mechanics. One of the main differences is that fluid keeps deforming if there is a shear stress while solids will stop at some point (assuming the shear stress is not too large).
thank you so much for the video man
No problem man
Nice and simple
Thanks.
Amazing videos
Thanks!
it's awesome video!!
but i have a question!!
when explain angular velocity
why do a and b rotate different way?
i think that picture means shear strain, not rotation
전하성 Same doubt bro , this is rather a case of angular deformation in which both the sides oppose each other's motion. I have no idea why it is used to explain rotation. Morover even in books the same technique has been used
Yeah, you're right.. in that picture both angles are positive since both displacement are positive as well.. so, hes explaining pure rotation with a pure shear sketch. And i still dont see why shoud we talk about average values.. looks like we need it to fit the expressions given by splitting the displacement tensor into the sume of the symmetric tensor (pure strain) and the anti-symmetric tensor (solid rotation).. which give the 1/2 in ecuations.. but really need that? Cant see the meaning of doin it
excellent
Superb
Thanks sir
Thanks.
Very nice video, but the most tricky part to me is not explained: why are the distances moved by A and B respectively given by (dv/dx)dxdt and (du/dy)dydt?
Erik Nilsson tan (alpha) is given by perpendicular upon base
In 2:21 you have to explain how the taylor series gives you the parcial derivative. This is critical. Other than that is a very nice video.
It's difficult to balance the length of the video with the depth of explanation. In other videos the first order Taylor series approximation is discussed in a little more depth.
Its just a way to approximate a future state position. At least that is what my gut tells me from this video alone. I'm pretty sure there is a deeper explanation. I would recommend BlueBrown1 for that explanation. I haven't seen the video yet so let me know how good it is if you view it.
last tutorial you said incompressible flow doesn't undergo expansion or contraction , but you say opposite in this video
i love you
No prove of how we derived omega x and y
shouldn't the shear strain rate be the change in the angle between two sides that were originally perpendicular? Why is there a 1/2 term in front of the shear strain rate?
It's the average contribution from both sides moving.
Same question. The expression for shear stress tau (xy)=(mu)(du/dy+dv/dx). This is the viscous coefficient multiplied by strain rate right? So where is the 1/2 term gone? Note that the derivatives are partial, I can't type them here.
Apart from that, amazing video.
Yeah, i have the same doubt.. shear strain is how many grades decrease or increase the original 90º angle because deformation.. so.. is the sume of both angles (du/dy + dv/dx).. so.. why talking about average here.. why there is 1/2 here?.. i know that 1/2 came fron splitting the displacement tensor into the sum of a symmetric and an antisymmetric tensor (fisrt is pure strain and second is pure rotation), which gives me the 1/2 expressions.. but cant see it cleary on the sketch.. neither its meaning
@@flavioluisginobertolini6144 My understanding like this, the deformation in xy plan comes from two shear stresses, i.e. Taux,y and Tau,yx. Taux,y give the angle of dAlpha and Taux,y give the angle of dBeta. since Taux,y and Tau,yx and qual, the strain rate come from Taux,y is half the total angular velocity.
Why are we interested in the average angular rotation and not the instantaneous rotation?
It is instantaneous average.
@@CPPMechEngTutorials and what is the point of the average rotation if at the end we use vorticity, which scales average rotation by a factor of 2 (asking as a curious student)
Thanks.
You're welcome :)