Recent content by spin2he2

It looks like the method of control volumes can be used to generate additional physical equations from the Navier-Stokes equation (in conservation form). If you take the cross product of both sides with the radial vector and pull the cross product through the divergence operators, additional...

How do we know that the stress tensor must be symmetric in the Navier-Stokes equation? Here are some papers that discuss this issue beyond the usual derivations: Behavior of a Vorticity Influenced Asymmetric Stress Tensor In Fluid Flow http://www.dtic.mil/dtic/tr/fulltext/u2/a181244.pdf...

Thank you Chestermiller for the cool variant of Euler's equation - I haven't seen that one before. I tried to paste a word file reply to this post here but couldn't get the equations to print out. In short - it looks like I was not remembering Euler's equation correctly and so the results I was...

Calculations are correct! But I think there is also a (convective derivative of the density)xV on the left hand side of the bottom equation.

I think for Euler's equation, you want to take the convective derivative of the product of the density and the velocity. The convective derivative of the velocity is indeed zero - as there are no accelerations in the (unfiltered) flow. The convective derivative of the density, on the other hand...

I have two ways to set up this flow: If you set up a continuum filter in the flow with a differential cross section of dx/x, the calculated pressure is felt on the filter - though technically not every particle in the flow obeys x=(1+ct)x0 nor is the mass conserved globally IN the flow...

If you think of this fluid as a continuum limit of a bunch of point masses evenly spread out at time t=0, they would each continue to move according to x = (1+ct)x0 only if there are no forces acting on them - so, physically, the pressure should be zero. Literally imagine setting up a flow of...

Consider the following flow: x = (1+ct)x0. Let the density rho(t) = rho0/(1+ct) so that the flow conserves mass. Physically, this is just a bunch of fluid elements on the positive x0-axis each given initial velocities that are proportional to their initial positions. Each fluid element should...