Fluid Mechanics Viscous Dissipation

AI Thread Summary
The discussion centers on finding the correct expression for viscous dissipation in the context of Burgers' vortex, specifically in cylindrical coordinates with a velocity component in the V theta direction. There is confusion regarding the appropriate equations, with references to different forms such as τ:S and τ:∇V. Clarification is provided that the rate of deformation tensor S is defined as (∇V + ∇VT)/2, leading to the conclusion that τ equals 2μS. Ultimately, all mentioned relations are consistent and should yield the same results for viscous dissipation. Understanding these equations is crucial for accurate analysis in fluid mechanics.
Jade Sola
Messages
2
Reaction score
0
I am trying to find an expression for viscous dissipation for burger's vortex Velocity field which only has velocity component in the V theta direction. I'm confused as to which equation for viscosity dissipation is correct. I am seeing a lot of different things tau:S, tau:delV..which one is correct?

Thanks!
 
Engineering news on Phys.org
Um.. I think you need to be a bit more specific. What form are you working with?
 
a_potato said:
Um.. I think you need to be a bit more specific. What form are you working with?
cylindrical coordintates...so this is what the velocity field is
upload_2014-11-26_18-20-1.png

what I am confused about is what exactly is the equation for viscous dissipation ... My professor said in class that it is 2muS:S (from Navierstokes eq.3) but I am seeing differen things online and I also heard from another classmate of mine that it has something to do with Sxtau components. I am just confused ...sorry if I am confusing the matter here.
 
Jade Sola said:
cylindrical coordintates...so this is what the velocity field is
View attachment 75868
what I am confused about is what exactly is the equation for viscous dissipation ... My professor said in class that it is 2muS:S (from Navierstokes eq.3) but I am seeing differen things online and I also heard from another classmate of mine that it has something to do with Sxtau components. I am just confused ...sorry if I am confusing the matter here.
If S is the rate of deformation tensor (which it certainly appears to be), then:
S = (∇V+∇VT)/2
and
τ = 2μS
So, the rate of viscous dissipation is τ:∇V = τ:S = 2μS:S. All the relations you wrote are the same, and should give the same results.

Chet
 

Thread '2:1 Pulley Question'

I have Mass A being pulled vertically. I have Mass B on an incline that is pulling Mass A. There is a 2:1 pulley between them. The math I'm using is: FA = MA / 2 = ? t-force MB * SIN(of the incline degree) = ? If MB is greater then FA, it pulls FA up as MB moves down the incline. BUT... If I reverse the 2:1 pulley. Then the math changes to... FA = MA * 2 = ? t-force MB * SIN(of the incline degree) = ? If FA is greater then MB, it pulls MB up the incline as FA moves down. It's confusing...
View full post »

Thread 'Why do all my clocks run slow?'

Hi. I noticed that all electronic devices in my household that also tell time eventually lag behind, except the ones that get synchronized by radio signal or internet. Most of them are battery-powered, except my alarm clock (which runs slow as well). Why does none of them run too fast? Deliberate design (why)? Wrong temperature for quartz crystal? Decreasing battery voltage? Or just a coincidence?
View full post »

Similar threads

Computational Fluid Dynamics: Dissipation Function Density Based Solver
Replies
9
Views
3K
How Do Viscous Interactions Differ in Vertical and Horizontal Geometries?
Replies
31
Views
3K
[Fluid Mechanics] Negative sign on the viscous work term
Replies
1
Views
3K
I How is the Reynolds number derived (is my derivation wrong)?
Replies
6
Views
3K
Where Does Viscous Pressure Enter the Pressure Balance?
Replies
19
Views
2K
Brownian Ratchet (exercise framed by Feynman's Lectures, l. 46)
Replies
32
Views
2K
How does the viscosity of a fluid change with temperature in a rotating system?
Replies
7
Views
2K
A Why are the Navier-Stokes equations inconsistent in this case?
Replies
18
Views
2K
A Stressing Over Stress Tensor Symmetry in Navier-Stokes
Replies
2
Views
2K
Fluid Flow Equations With Real Values
Replies
20
Views
3K

Hot Threads

Recent Insights

Back
Top