# How to plot a stream function

This question relates to fluid mechanics and I have the components in polar coordinates. The components of the velocity field are; $$v_r= \frac{-kr}{z}$$ $$v_z= kz$$ $$v_\theta= 0$$ and I have solved for the streamline function and got;

$$\psi=-kzr^2$$

but I have no idea how to plot this so we can see the direction of the fluid flow. Any help would be greatly appreciated.

• Could you please specify $\psi$? Is $v$ a vector field with components $v_r$ etc...or a function with partial derivatives $v_r$...etc? – Avitus Nov 3 '13 at 9:58
• Hi @Avitus, yes $v$ is a vector field, namely a velocity field and $\psi$ is the streamline function for the fluid. After plotting the streamline function, we should be able to see direction of the flow of the fluid. The streamline function is in polar coordinates – Andrew Smith Nov 3 '13 at 10:39
• Did you see this ? – Tony Piccolo Nov 3 '13 at 11:30
• Hi @TonyPiccolo, Yes I did but I am still unsure. Since there is no theta term, will the axis be r and theta still or will it be r and z? I still wouldn't know how to plot – Andrew Smith Nov 3 '13 at 14:00