Fluid Mechanics: Topic 10.5 - Kinematics of fluid elements (shear strain, rotation, and vorticity)

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".

[carbon]

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.

[jdtaramona]

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 🇵🇪

[ashutoshkumar]

Whenever I find your your video on any topic i feel glad and rest assured that i will surely get it from this.

[KJ-oqxr]

Very well illustrated and neatly explained. This is the way to teach! Looking forward to more videos from you

[luiscarlospradanino]

Hey thank you so much, We watched this video in transport phenomena class. We really appreciate all your explanations.

[shwethakc]

Thanks a lot for this video it's very easy to understand the derivation here rather than in direct text books

[azadalmasov]

Man this also explained elasticity for me. Two birds with one shoot. Thank you

[hwlzruk]

Thanks a lot! I finally understood what I've questioned for at least two years :0

[christianvalencianarva]

I cannot thank you enough for this video. I had a lot of trouble understanding this, but know I got it!

[Yoyimbo]

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?

[jdtaramona]

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?

[xiangchamling]

Please explain more that how did you apply the Taylor series approximation as you said ?..

[Yoyimbo]

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?

[uponxbo]

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

[rockhopper]

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?

[truedhonifan]

Is it a control mass or control volume analysis?

[hp-hnzo]

last tutorial you said incompressible flow doesn't undergo expansion or contraction, but you say opposite in this video

[jrsa]

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.

[lq_]

Why are we interested in the average angular rotation and not the instantaneous rotation?

[desmondselasi]

No prove of how we derived omega x and y