(Fluid Mechanics) stream function graph

[DoctorCasa]

Hello, I got this stream function
ψ(r,θ)=sqrt(r)*sin(θ/2)

I have to draw the streamlines of this fuction, however, I'm not sure how to afford this, should I consider this just like a normal function that depends on tetha and rho, or it's more like a polar plot?

When i drew the streamlines using polars, I got a family of cardioids(heart-like graph). When I plotted this on matlab, keeping r constant, I got a sin, which it's pretty obvious, but I don't think that's correct.

What do you guys think?

 

[eys_physics]

Hello, I got this stream function
ψ(r,θ)=sqrt(r)*sin(θ/2)

I have to draw the streamlines of this fuction, however, I'm not sure how to afford this, should I consider this just like a normal function that depends on tetha and rho, or it's more like a polar plot?

When i drew the streamlines using polars, I got a family of cardioids(heart-like graph). When I plotted this on matlab, keeping r constant, I got a sin, which it's pretty obvious, but I don't think that's correct.

What do you guys think?

I think you are supposed to plot $\Psi(r,\theta)=C=\mathrm{constant}$ for different values of C. For each value you will get a curve in the x-y plane.