The rate of deformation tensor is frame invariant. Please provide the velocity distribution, and we can discuss further.vin300 said:A fluid with forced vortex flow and constant angular velocity is given. Newton's shearing says there must be strain due to differential linear velocity. The problem is, the difference of linear velocity is only visible to the external observer, the fluid particles themselves do not observe relative difference, thus accounting to only centrifuging and nothing else. So is there shear or not?
If you are on a boat, floating on a lake, and spin around, the water also has differential linear velocity in your rotating frame. Is there strain in the water because of this?vin300 said:A fluid with forced vortex flow and constant angular velocity is given. Newton's shearing says there must be strain due to differential linear velocity. The problem is, the difference of linear velocity is only visible to the external observer, the fluid particles themselves do not observe relative difference, thus accounting to only centrifuging and nothing else. So is there shear or not?
. There is nothing extraordinary to provide. I am taking the simplest case of bounded fluid like in a bucket (not a boat in the unending sea), which anybody can imagine to rotate in a similar fashion as a moment arm, and every particle rotates around the same axis making constant angular advances at constant times, with linear variation of linear velocity. I can imagine even though it is frankly speculation, that derivative of (r w) with respect to r would not provide any meaningful "strain" (w is ang. vel.)because there is no tangential strain in a rotating rod either. Clearly there has to be a differential of "angular velocity" in this case for fluid particles to be rubbing past each other and causing distortions.Chestermiller said:The rate of deformation tensor is frame invariant. Please provide the velocity distribution, and we can discuss further.
Chet
Yes, you are correct. The fluid is rotating as a rigid body here, and there is no deformation occurring. To get rates of deformation in a fluid, we need to subtract out the rigid body rotations of the fluid elements. We do this by resolving the velocity gradient tensor into an antisymmetric part (the vorticity tensor, which accounts for rotation) and the symmetric part (the rate of deformation tensor), which accounts for rates of strain. In Newtonian fluid mechanics, it is only the symmetric part of the velocity gradient tensor that determines the stress tensor.vin300 said:. There is nothing extraordinary to provide. I am taking the simplest case of bounded fluid like in a bucket (not a boat in the unending sea), which anybody can imagine to rotate in a similar fashion as a moment arm, and every particle rotates around the same axis making constant angular advances at constant times, with linear variation of linear velocity. I can imagine even though it is frankly speculation, that derivative of (r w) with respect to r would not provide any meaningful "strain" (w is ang. vel.)because there is no tangential strain in a rotating rod either. Clearly there has to be a differential of "angular velocity" in this case for fluid particles to be rubbing past each other and causing distortions.
The fluid shear paradox is a phenomenon observed in fluid mechanics, where the shear stress at the wall of a fluid flow decreases as the flow rate increases, even though one would expect the shear stress to increase with increasing flow rate.
The fluid shear paradox is caused by the presence of a boundary layer, a thin layer of fluid near the wall of a flow where the velocity of the fluid is significantly lower than the bulk flow. This boundary layer is responsible for the decrease in shear stress as the flow rate increases.
While there is no definitive solution to the fluid shear paradox, there have been various theories proposed to explain the phenomenon. Some suggest that the paradox can be resolved by taking into account the effects of viscosity and turbulence in the boundary layer, while others propose that the paradox is a result of incorrect assumptions made in traditional fluid mechanics models.
The fluid shear paradox is a topic of interest in many practical applications, such as in the design of pipelines, pumps, and other fluid systems. Understanding the paradox can help engineers optimize their designs and ensure that the fluid flow operates efficiently and safely.
Current research on the fluid shear paradox focuses on developing more accurate models and theories to explain the phenomenon. Some areas of interest include the effects of surface roughness, non-Newtonian fluids, and turbulent flows on the fluid shear paradox. Additionally, there is ongoing research on practical applications, such as the development of new flow control techniques to mitigate the effects of the paradox.