The velocity potential, phi(x), of irrotational and incompressible flows satisfies Laplace's equation, \nabla^{2} \phi=0 Consider the incompressible and irrotational 2D flows v₁ = (V₁,x, V₁,y)(1, 1) and №₂=(V2,x, V2,y) = (x, —y). (a) Calculate the velocity potential $₁(x, y) of the flow ₁, defined by№₁ = V0₁, and sketch some potential lines. Take $1(0, 0) = 0. (b) Calculate the velocity potential $2(x, y) of the flow №2, defined by√2 = V02, and sketch some potential lines. Take $2(0,0) = 0. (c) Assume that ₁ and 2 are solutions to Laplace's equation. State thesuperposition theorem for linear equations and apply it to show thatthe velocity potential ¢ = (x+1)² − (y− 1)² is a solution to Laplace’sequation. Hence derive an expression for the corresponding flowvelocity in terms of 7₁ and 7₂.