Question

A steady, two-dimensional, incompressible, irrotational flow field in the rθ-plane has a stream function ψ and a velocity potential function φ. (a) Write down the Cauchy-Riemann equations, in polar (cylindrical) coordinates, satisfied by the potential functions ψ and φ. [02] (b) Let ψ be given as ψ(r, θ) = Aθ, where A is an arbitrary constant. (i) Use (a) to determine φ. [06] (ii) Find the equations for streamlines and equipotential lines.

Name: a steady two dimensional incompressible irrotational flow field in the r plane has a stream function and a velocity potential function a write down the cauchyriemann equations in polar cylin 82565
Uploaded: 2023-01-28T05:08:18-08:00
Duration: 2 min 18 s
Channel: Sri K
Description: a steady two dimensional incompressible irrotational flow field in the r plane has a stream function and a velocity potential function a write down the cauchyriemann equations in polar cylin 82565

          A steady, two-dimensional, incompressible, irrotational flow field in the rθ-plane has a stream function ψ and a velocity potential function φ.

(a) Write down the Cauchy-Riemann equations, in polar (cylindrical) coordinates, satisfied by the potential functions ψ and φ. [02]

(b) Let ψ be given as ψ(r, θ) = Aθ, where A is an arbitrary constant.
(i) Use (a) to determine φ. [06]
(ii) Find the equations for streamlines and equipotential lines.

Added by Gary M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Thanks for your feedback!

A steady, two-dimensional, incompressible, irrotational flow field in the rθ-plane has a stream function ψ and a velocity potential function φ. (a) Write down the Cauchy-Riemann equations, in polar (cylindrical) coordinates, satisfied by the potential functions ψ and φ. [02] (b) Let ψ be given as ψ(r, θ) = Aθ, where A is an arbitrary constant. (i) Use (a) to determine φ. [06] (ii) Find the equations for streamlines and equipotential lines.