viscous flows are always rotational because of shear stress that is exerted on the fluid element due to viscosity.
what about the inviscid flows? can they be rotational ? if yes then what are the factors which makes the inviscid flows rotational?
minger
Oct8-08, 10:08 AM
By rotational do you mean have vorticity? If so then yes, in fact the fundamental equations can be written in terms of vorticity rather than velocity by taking the curl of the equations.
For any flow, you can write the equations of the flow in terms of vorticity rather than velocity by simply taking the curl of the flow equations that are framed in terms of velocity (may have to apply the 2nd Fundamental Theorem of Calculus to do this rigorously). In such a case you get the vorticity transport equation which is as follows in the case of incompressible (i.e. low mach number) fluids, with conservative body forces
\frac{D\omega}{Dt} = \omega \cdot \nabla u + \nu \nabla^2 \omega
jason.bourne
Oct8-08, 10:28 AM
okay fine but what is it that is making it to rotate?
like in viscous flows its the shear stress that causes the rotation of the fluid element.
minger
Oct8-08, 11:38 AM
Anything. Don't think of vorticity as a whirlpool in your bathtub; any time the flow turns even a little bit, it has vorticity.
jason.bourne
Oct9-08, 02:59 AM
viscous flows are always rotational because of the shear stress exerts a rotational moment about the center of the element .
what about the inviscid flows? what causes rotation in an inviscid flows?
shear stress is absent. The only forces acting on the fluid element are pressure force and weight. Weight acts through COG, pressure acts normal to the element surface, neither can cause rotation , then what is causing rotation in inviscid flows?
i dont think it can just rotate at its own wish. There has to be something right?