Fluid Dynamics: Determining Velocity Coefficients

[nicorette]

Homework Statement

I have an incompressible, irrotational fluid with velocity v in the form:

v_x = c_xx x + c_xy y + c_xz z
v_y = c_yx x + c_yy y + c_yz z
v_z = c_zx x + c_zy y + c_zz z

The coefficients c_xx, c_xy, etc. are constants.

How can I determine how many independent coefficients I need to specify the velocity uniquely?

Homework Equations

The Attempt at a Solution

 

[nicorette]

I've used div(v)=0 and curl(v)=0 to come up with a few relationships between the various coefficients. What other conditions can I use to find relationships?