Re: [Vo]:Calculate the torque from the stress tensor
Hi and thanks Actually I need the per area or per volume value. I intend to multiply this with the vorticity to get the power losses in the fluid. This is a stationary fluid. Does anyone know if this kind of power loss, or gain, has been calculated by anyone else before? I intend to calculate this theoretically and analytically on a retarded potential flow. The problem is to determine the retardation. I realize I have to do that in the velocity domain. But I am still not convinced about how to calculate the retarded velocity. One one hand I realize that I could just retard the potential but taking the gradient of that will include no vorticity. So I currently think I have to set the retardation in the velocity field. The calculus and algebra will likely be enormous. I also don't know from where to calculate the retardation. But the problem should be very similar to retardation in electrodynamics. David David Jonsson, Sweden, phone callto:+46703000370 On Wed, May 13, 2009 at 11:25 PM, Stephen A. Lawrence sa...@pobox.comwrote: I think, for a stationary shaft... Assume you're given a stationary shaft lying along the x axis. Assume further that it's under torsion. To find the applied torque, I think you would want to integrate R x (Txy, Txz) over the surface of a cut through the shaft, where R is the radius vector from the center of the shaft to each point on the cut surface, and x is the cross product. But I'm not sure; these comments of mine are pretty half-baked. Of course, if the shaft is stationary (or rotating at constant velocity) then the applied torque must be the same no matter where you look along the shaft. Stephen A. Lawrence wrote: What you just said sounds right, but what you've actually got looks to me like the torque per unit volume. I think you need to integrate that over a volume to get the actual torque acting on that volume. OTOH if that value is nonzero then your object is spinning up -- it's not just sitting there. If you're looking at something like a steel shaft which is under torsion but stationary then T12 = T21 and you need to look at something more complicated to figure out what the torque on the shaft is -- maybe the gradient of the stress tensor? David Jonsson wrote: On Wed, May 13, 2009 at 9:36 PM, David Jonsson davidjonssonswe...@gmail.com mailto:davidjonssonswe...@gmail.com wrote: Hi Can someone explain to me how to calculate the torque from the stress tensor? It seems to be this simple Torque = T12 - T21 For a two dimensional tensor T= T11 T12 Â Â Â Â T21 T22 Right? Now I will do some nice calculations, but first I would like to have this confirmed. David
Re: [Vo]:Calculate the torque from the stress tensor
On Wed, May 13, 2009 at 9:36 PM, David Jonsson davidjonssonswe...@gmail.com wrote: Hi Can someone explain to me how to calculate the torque from the stress tensor? It seems to be this simple Torque = T12 - T21 For a two dimensional tensor T= T11 T12 T21 T22 Right? Now I will do some nice calculations, but first I would like to have this confirmed. David
Re: [Vo]:Calculate the torque from the stress tensor
What you just said sounds right, but what you've actually got looks to me like the torque per unit volume. I think you need to integrate that over a volume to get the actual torque acting on that volume. OTOH if that value is nonzero then your object is spinning up -- it's not just sitting there. If you're looking at something like a steel shaft which is under torsion but stationary then T12 = T21 and you need to look at something more complicated to figure out what the torque on the shaft is -- maybe the gradient of the stress tensor? David Jonsson wrote: On Wed, May 13, 2009 at 9:36 PM, David Jonsson davidjonssonswe...@gmail.com mailto:davidjonssonswe...@gmail.com wrote: Hi Can someone explain to me how to calculate the torque from the stress tensor? It seems to be this simple Torque = T12 - T21 For a two dimensional tensor T= T11 T12 Â Â Â Â T21 T22 Right? Now I will do some nice calculations, but first I would like to have this confirmed. David
Re: [Vo]:Calculate the torque from the stress tensor
I think, for a stationary shaft... Assume you're given a stationary shaft lying along the x axis. Assume further that it's under torsion. To find the applied torque, I think you would want to integrate R x (Txy, Txz) over the surface of a cut through the shaft, where R is the radius vector from the center of the shaft to each point on the cut surface, and x is the cross product. But I'm not sure; these comments of mine are pretty half-baked. Of course, if the shaft is stationary (or rotating at constant velocity) then the applied torque must be the same no matter where you look along the shaft. Stephen A. Lawrence wrote: What you just said sounds right, but what you've actually got looks to me like the torque per unit volume. I think you need to integrate that over a volume to get the actual torque acting on that volume. OTOH if that value is nonzero then your object is spinning up -- it's not just sitting there. If you're looking at something like a steel shaft which is under torsion but stationary then T12 = T21 and you need to look at something more complicated to figure out what the torque on the shaft is -- maybe the gradient of the stress tensor? David Jonsson wrote: On Wed, May 13, 2009 at 9:36 PM, David Jonsson davidjonssonswe...@gmail.com mailto:davidjonssonswe...@gmail.com wrote: Hi Can someone explain to me how to calculate the torque from the stress tensor? It seems to be this simple Torque = T12 - T21 For a two dimensional tensor T= T11 T12 Â Â Â Â T21 T22 Right? Now I will do some nice calculations, but first I would like to have this confirmed. David
