Hmm, lost the OP somehow.
Here it is:
GonzoGal’s doing an independent study in modeling fluid flow, and her Professor gave her the following equation:
Where vbar is apparently the velocity of a particle, omegabar is the angular velocity of the particle, and x is the distance from the particle. a is the radius of the particle, cross() is the cross product, and v is the velocity of the fluid.
I’ll try my best to make it look nice:
v= 3a(vbar+x(x.vbar)+a[sup]2[/sup]*(vbar-3x(x.vbar))))+a[sup]3[/sup]*(x X omegabar) 4 |x| |x|[sup]3[/sup] 3 |x|[sup]3[/sup] |x|[sup]5[/sup] |x|[sup]3[/sup]
We’ve been scouring the textbooks and the net for this equation, but can’t find it anywhere. We don’t know where he got it from, and we’ve got suspicions that it’s not the right formula, or he wrote it wrong. (when vbar and omegabar are 0 or when x is large, v goes to 0, but we expect it to go to some v[sub]infinity[/sub] which doesn’t even appear in the equation.)
I know this is obscure, but maybe there’s a fluid mechanics expert in the house… if so:
a) where does this equation come from, and does it have a name?
b) does it have any typos or errors in it?
c) Is there a way to express it in terms of the force on the particle?
Thanks in advance…