Problem 8: Given a velocity field V = v,e, + v,e,e + v,e,z in cylindrical coordinates, the curl operator is:
∇ × V = (1/r) (∂(rVz)/∂r - ∂Vr/∂z) e,r + (1/r) (∂Vr/∂z - ∂Vz/∂r) e,z + (1/r) (∂(rVr)/∂r - ∂Vr/∂r) e,θ
In cylindrical coordinates, a pressure-driven flow inside a pipe of radius R can be expressed as:
Vr = U(1 - (r/R)^2)
As: Vr = Vθ = 0.
Calculate and plot the vorticity. Find the radial position where the vorticity is maximum and calculate it.