Steamlines and Equipotentials for Ideal Flow Near a Stagnation Point
Author's Data: Housam BINOUS
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Acknowledgement :
Expressions of stream and potential functions are taken from Bird et al. (Transport Phenomena, 1st Edition, Wiley 1960).

Notation:
Φ: potential function
Ψ: stream function

Ideal Flow Near a Stagnation Point

Φ = y^2 - x^2; Ψ = -2 x y;

Streamlines

plt1 = 
      ContourPlot[Ψ, {x, -10, 10}, {y, 0, 10}, 
        ContourShading -> False, Contours -> 20, 
        ContourStyle -> {{RGBColor[1, 0, 0]}, {RGBColor[0.7, 0, 
                0]}}]

Equipotentials

plt2 = 
      ContourPlot[Φ, {x, -10, 10}, {y, 0, 10}, 
        ContourShading -> False, Contours -> 20, 
        ContourStyle -> {{RGBColor[0, 1, 0]}, {RGBColor[0, 0.7, 
                0]}}]

Equipotentials and Streamlines in the same plot

Show[plt1, plt2]