- #1

- 26

- 3

(DU

_{j}/Dt) = v [(∂

^{2}U

_{i}/∂x

_{j}∂x

_{i}) + (∂

^{2}U

_{j}/∂x

_{i}∂x

_{i})] – 1/ρ (∇p)

where D/Dt is the material (substantial) derivative, v is the kinematic viscosity and ∇p is the modified pressure gradient (taking into account gravity and pressure). Note that the velocity field is non-solenoidal (∇⋅U ≠ 0).

How, then, can we take the divergence of this equation and get the following result?:

I can follow all of the terms other than the one underlined in blue. I know that it comes from the blue section of the Navier-Stokes written above, since I can easily get all the other terms.

Thanks in advance