Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have a 3d closed surface. This closed surface lies in a 3d vector field. I know the value of the vector at discrete points along the surface and the surface normal at these points. Essentially, say vector U and vector n at these points. This is the only information that I have. I need the *volume* mean of U in this closed surface. I also know that the divergence of U = 0. Seems trivial, but I can't seem to get through the calculation. Here is what I did:

mean(U) = 1/V ∫ U dV

where V is the volume enclosed by the closed surface.

Lets take the divergence on both sides, assuming mean U and U are continuously differentiable and the divergence and integration operators can be interchanged.

∇. mean(U) = 1/V ∫ ∇. U dV

= 1/V ∫_A U . n dA

So I can connect the divergence of mean of U with the information along the surface. However, I need the mean(U).

Any thoughts?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mean of vector field using info at surface

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**