Texts: A two-dimensional planar incompressible flow is described by the y-component of velocity given as u = x + 2xy. It is known that:
(1) Derive an expression for the x-component of the velocity u.
(2) Derive an expression for the stream function Ψ (z, y) with the boundary conditions Ψ(0, 0) = 0; Ψy <= 0, Ψz = 0, Ψv = 0.
(3) Draw the velocity field using Python or MATLAB following the code provided in the Handout.
(4) Derive the acceleration fields a = Du/Dt for this flow, where Du/Dt = 0, y = 0.
A two-dimensional planar incompressible flow is described by the y-component of velocity given as uy = x + 2ry.
1. Derive an expression for the x-component of the velocity u.
2. Derive an expression for the stream function Ψ with the boundary conditions Ψ(0, 0) = 0 and Ψy = 0, Ψz = 0.
3. Draw the velocity field using Python or MATLAB following the code provided in the Handout.
4. Derive the acceleration fields a = Du/Dt for this flow.