Problem 5.56[Difficulty: 3]Given:Steady, two-dimensional velocity field represented aboveFind:(When C = 0 the streamline is onthe x- and y-axes.)Solution:We will apply the acceleration definition, and determine the streamline slope.tVzVwyVvxVuDtVDapGoverningEquations:(Particle acceleration)Assumptions:(1) Two-dimensional flow (velocity is not a function of z)(2) Incompressible flowStreamlines along the x-y plane are defined bydydxvuAyAxThus:dxxdyy0After integrating:ln x( )ln y()ln Cwhich yields:xyC(Q.E.D.)yVvxVuapBased on the above assumptions the particle acceleration reduces to:Substituting in the field: jyi
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