question

dont know so heres a bump
also when do u use equivalent instead of equals

>>8213844
I treat it more like a stylistic difference, or when distinguishing between stating an equation and stating something being the same as something else (equivalent, if you like)

also bump

>>8213832
you have to take the gradient of that expression which is kinda its derivative if you think about it (the first term from the left in eq 9, there you have a vectorial derivative which is equivalent with taking the gradient of the square of v )
so when you differentiate v^2 you would get 2v but that's a no-no as you only need v so that 1/2 comes in and saves the day

>>8213894
ok i see what you mean, i stupidly assumed a wrong identity and carried on. thanks for the help

also note that i misquoted the ax(bxc) identity as im tired, enough of this for today.

>>8213894
no idea what this guys talking about you just want to use
https://en.wikipedia.org/wiki/Vector_calculus_identities#Vector_dot_product

>>8213963
yeah i was about to also post that (OP here), for anyone interested. didnt realise it was a special case if A=A...

>>8213957
it's okay nigga, I've never bothered learning it, mechanics prof busted my balls about it but I ain't no nerd lol xxxDD

integrating v

>>8213963
that's cause you stupid, try to understand your math
okay so I'll explain it (I sit here with a desk full of physics books but instead of learning something or solving some problems I play MOBAs and listen hip hop and shitpost on sci):
eq 11 is eq 9 combined with eq 10 where he moved the terms to the right side and he divided by rho. in eq 9 we have dv/dt which is the derivative of a vector and as you can guess it produces a vector (the acceleration). how can we rewrite that using the GRADIENT operator??! shit nigga that's tough, you can only take the gradient of a SCALAR quantity and we got a vector there, what we gonna do??!! whooa, what if we like square that vector? #yolo shieee, that gives as what we need, a scalar, and it has the bonus of having physical meaning (it's THE MAGNITUDE of the vector, i.e. how fast that liquid is moving), we some sort of mathy Indiana Jones. b-b-ut then we would get a vector twice as big, nigga that wrong!!!! lol no just add a 1/2 all good now, see? xD

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>>8214001
are we shitposting now?

>>8214030
shitposting and teaching 1st year physics to anons, yes

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>>8214034
well in my defense i forgot a lot of babby physics :(