Looking for the rate of flow outward through a sphere from a given velocity field and fluid density using the divergence theorem. (Image of problem and my work attached below).

Question

anonymous · Answer

attachment

ganeshie8 · Answer

question is not readable 
can u take a screenshot of question only and attach ?

anonymous · Answer

Yup, here you go:

ganeshie8 · Answer

why are you parameterizing the sphere ?

ganeshie8 · Answer

you're supposed to use divergence thm right ?

anonymous · Answer

Ugh. 

Yes, I thought I was, but I must have had my notes mixed up. I'll try again after I finish lunch with my kid.

ganeshie8 · Answer

div(5v) = 5(0+0+5) = 25

ganeshie8 · Answer

$$\begin{align}\iiint_S \mathrm{div}(F) ~dV &=  \iiint_S 25dV \~\ &= 25 \iiint_S 1 dV \~\&= 25\times(\text{volume of sphere}) \~\&= 25\times \frac{4}{3}\pi 4^3\end{align}$$

anonymous · Answer

Ok, I finally get it, thank you. I'm not sure why, but the end-of-semester panic is really messing with me this time around. Even if I score well on this final, I don't think I'll have anything approaching mastery. Time for more practice, I guess. :)