Working from first principles show that the condition for irrotationality of a two-dimensional ideal fluid flow is given by:
Δu/Δy = Δv/Δx
Hence, define in mathematical terms the velocity potential Φ, and show that potential lines of constant Φ are perpendicular to streamlines of constant streamfunction ψ. You may assume that the gradient of the tangent to a streamline is given by dy/dx = v/u.
By deriving the condition for continuity for the flow,
Δu/Δx = Δv/Δy = 0,
Show that the velocity potential Φ satisfies Laplace's equation.
Show that the flow given by Φ = x^2 - y^2 satisfies Laplace's equation.