Fluid Mechanics: streamlines for a flow

  • Thread starter yrael
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  • #1
yrael
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Homework Statement


Show that the streamlines for a flow whose velocity components are u=c(x^2-y^2) and v=-2cxy, where c is a constant, are given by the equation x^2*y-y^3/3=constant. At which point (points) is the flow parallel to the y axis? At which point (points is the fluid stationary?


Homework Equations


dy/dx=v/u
u=c(x^2-y^2)
x^2*y-y^3/3=constant
v=-2cxy


The Attempt at a Solution


dy/dx=v/u=(-2cxy)/(c(x^2-y^2))=-2xy/(x^2-y^2)

intergral dy(x^2-y^2)=intergral -2xy dx
x^2y-1/3*y^3=-x^2y
ans y=sqrt(6)x?

How do i show what point is parallel to y axis and what point is fluid stationary?
 

Answers and Replies

  • #2
22,148
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It is parallel to the y axis when dx/dy = 0, or, from the equations, when x = y. The fluid is stationary when u = v = 0.
 

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