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

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.

They are coming along... slowly.

More are being developed... stay tuned.

Neat! Hopefully it was helpful.

Glad it helped!

No problem.

Our pleasure.

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).

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

Thanks.

Erik Nilsson tan (alpha) is given by perpendicular upon base

No problem man

Thanks!

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.

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.

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)

You're welcome :)