The discussion revolves around the term $$\hat{\jmath} \times r$$ in the context of fluid motion and its role in computing vorticity. Participants seek clarification on the meaning and implications of this term within the framework of fluid dynamics.
Participants express varying levels of understanding regarding the term $$\hat{\jmath} \times r$$, and there is no consensus on its specific implications or how to compute it.
There are unresolved aspects regarding the definitions of $$r$$ and the specific physical context in which $$\hat{\jmath} \times r$$ is applied, which may affect interpretations.
shen07 said:Hi guys, i am solving a problem but I am unable to figure out what is $$\hat{\jmath} \times r$$? Please help me
Sudharaka said:Hi shen07, :)
Obviously what is meant by $\hat{\jmath} \times r$ depends on the context. Can you post the full question please?
shen07 said:I just edited it
$\hat{\jmath} \times r$ is the cross product of $\hat{\jmath}$ and $r$, but you already know this. Are you asking how to compute it? Then see here. Are you asking what $\hat{\jmath}$ and $r$ are? It looks like $\hat{\imath}$, $\hat{\jmath}$ and $\hat{k}$ are unit coordinate vectors. I don't know what $r$ is. Or are you asking what the physical meaning of the term $\hat{\jmath} \times r$ is?shen07 said:A fluid motion has velocity $$\underline{u}=\sin{(at)}\hat{\imath}+\hat{\jmath} \times r +\cos{(at)}\hat{k}$$
I need to know what is $$\hat{\jmath} \times r$$ to find Vorticity and other things.