The divergence of the velocity vector in spherical coordinates can be written as:
⃗∇
· ⃗V = 1 r2 ∂

r2Vr 
∂r +
1 r sin (θ)
∂
∂θ
(Vθ sin (θ)) +
1 r sin (θ)
∂Vϕ
∂ϕ
where Vr, Vθ, and Vϕ are the velocity coordinates in the r−, θ−, and ϕ−
direction, respectively. Determine if a flow with the following flow field velocity is incompressible:
Vr = −U cos (θ)

1 −
3R 2r +
R3 2r3 !
Vθ = U sin (θ)

1 −
3R 4r −
R3 4r3 !
Vϕ = 0 where R and U are constants (note, R is not the gas constant in this problem).