An irrotational fluid can be equivalently expressed as a fluid characterized by one of these functions defined from the velocity field. For 10 points each:
[10m] Name these scalar functions. Generically, they are defined from a vector field such that their negative gradient equals the vector field.
ANSWER: potentials [accept scalar potentials or velocity potential; reject “vector potential”; reject “potential energy”]
[10h] A fluid’s velocity potential and stream function together satisfies these equations. A handy mathematical trick in physics relies on the fact that the pairs of functions that satisfy these equations also individually satisfy Laplace’s equation.
ANSWER: Cauchy–Riemann equations [prompt on CR equations]
[10e] The Joukowsky transform is a conformal map from the unit circle into the cross-section of an idealized one of these structures. The motion of these structures through air generates lift.
ANSWER: wings [or airfoils or aerofoils]
<GC, Physics>