Assignment:
Working from first principles show that the condition for irrotationality of a two-dimensional ideal fluid flow is given by:
delta(u)/delta(y) = delta(v)/delta(x)
Hence, define in mathematical terms the velocity potential psi, and show that potential lines of constant psi are perpendicular to streamlines of constant streamfunction phi. 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,
delta(u)/delta(x) + delta(v)/delta(y) = 0,
Show that the velocity potential psi satisfies Laplace's equation.
Show that the flow given by psi = x^2 - y^2 satisfies Laplace's equation.