Physics HW help plz

On October 28 2008 22:25 jgad wrote:
Strange to write the divergence as V•∇ - it's usually written with the gradient first, but dot product is commutative so it should be zero in any case. That makes the whole first term zero, so you essentially have to solve

∂V/∂t = v∇V - 1/ρ∇P + ƒ

The second term is independent of V (so it seems), so you just have to solve the basic form

∂V/∂t = v∇V - C

Which should be pretty straightforward.

dot product is commutative for normal vectors, which contain (commutative) scalars and not derivatives, which are of course not commutative.

On October 28 2008 23:12 jgad wrote:


Yeah, I thought of this too, but it would seem that the first term would end up being

-(Vx∂/∂x + Vy∂/∂x + Vz∂/∂z)V

anyway, which would come out as :

-V(∇•V)

so I think -(V•∇)V = -V(∇•V) = 0 (given the second equation)

I could be wrong.

On October 28 2008 23:18 Maenander wrote:

You are wrong, it is

-(Vx∂/∂x + Vy∂/∂x + Vz∂/∂z)Vx,
-(Vx∂/∂x + Vy∂/∂x + Vz∂/∂z)Vy,
-(Vx∂/∂x + Vy∂/∂x + Vz∂/∂z)Vz,

which is a vector in itself and that vector does not equal (0,0,0), atleast not because ∇•V=0 (scalar!)

On October 28 2008 23:24 Chill wrote:
lol i got owned

On October 28 2008 23:50 Maenander wrote:
∆ is the Laplace-Operator, I guess in the US you would write ∇ ^2.

And I don´t see why
-Vx∂/∂x(Vx) - Vy∂/∂y(Vx) - Vz∂/∂z(Vx) = -Vx(1) - Vy(0)- Vz(0)
should be correct.

On October 29 2008 00:10 jgad wrote:
looks like ~third year electrodynamics. Incompressible vector fields (∇•V=0) define the magnetic field or the electric field in regions of no space charge, for example.

On October 28 2008 23:24 Chill wrote:
lol i got owned