A fluid having density $f(x, y, z) = x^{2} + 2y^{2} + z^{2}$ flows with velocity $v(x, y, z) = x^{2}i + xy^{2}j + zk$. Determine the rate of mass flow through the sphere $ρ = 1$ in the outward direction

I am unsure of where to start on this problem. I see outward direction, which makes me think use divergence formula but $f(x, y, z)$ is a scalar function, not a vector field.


1 Answer 1


Hint: What is the definition of rate of mass flow?

  • $\begingroup$ What is the rate of mass flow? line integral of functions? $\endgroup$
    – Kracie
    Dec 9, 2014 at 13:53
  • $\begingroup$ @Kracie Check your notes. You probably defined what mass flow is and what the rate of mass flow is. $\endgroup$
    – 5xum
    Dec 9, 2014 at 14:03

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