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You need to prove this?

yes sir

and i dont think it's hard...just long...and i think i'm missing steps

Yes. Calculate both sides separately and show they are equal. Just work through it patiently.

when do i use the (1/2)?

what do you mean when? It's attached to the ∇(V∙V) term.

right...do i calculate the ∇(V∙V) first then take 1/2...or distribute the 1/2 first

whatever you like. I would calculate ∇(V∙V) first. You'll see every term has a 2.

alright you gonna be on for a while?

i'll post if i get stuck here

hint: there will be a product rule somewhere in there!

and by the way, if you have been torturing yourself over this, there's a very good reason.

I will have to put you out of your misery...

It's not
\[(V\cdot \nabla )V = \frac{1}{2}\nabla(V\cdot V) - (\nabla \times V)\times V.\]

i'm still working on breaking down the left side of the equation as much as i can

ohh yeah! lol thanks. Yeah that's a cross product rule isn't it.

okay...so just for the section of 1/2∇(V dot V)

i get 1/2( du^2/dx + du^2/dy+du^2/dz + dv^2/dx+dv^2/dy+dv^2/dz+dw^2/dx+dw^2/dy+dw^2/dz)

what happens with the 1/2 now?

agreed?

i'm trying to figure out if we have the same thing here

same as what i wrote or not

use any of the above notations?

I don't understand what you're asking.

I should have included the components.

yes?

okay...uux can be rewritten as just du/dx correct where d is the partial

is that correct?

yes, it's notation that's faster the write and in many ways easier to read.

i'm just trying to make sure i understand the notation your using

\[ u_x = \frac{\partial u}{\partial x} \]
hence
\[ uu_x = u\frac{\partial u}{\partial x} \]

alright

just a quick question....is that the entire equation - v cross del cross v

nevermind

\[ \nabla \times V = (w_y - v_z) \hat{i} + ... \]

then i cross product that answer with V or negative V?

exactly as you have written it at the top of the question.

minus sign is killing me

i think i've shortcircuited

i'm getting nowhere

I shall now shoot myself because entering all that has been a very annoying experience...

so we all seem to be getting to the point of vxdelxv and going mad lol

The challenge wasn't to dream up the math, but to enter the damn stuff! :D