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Hi, I am having a lot of trouble on the parameterization part of this problem:

Suppose there is a cylindrical container of liquid with circular flow velocity given in cylindrical coordinates by v(r,[tex]\theta[/tex],z) = <-f(r,z)sin[tex]\theta[/tex], f(r,z)cos[tex]\theta[/tex],0> for some function f(r,z) which we will determine. The vector field is divergence free.

Find a curve, x(t), that represents the path followed by a particle of liquid at radius r. So, x’(t) = v(x(t)) and x(0) = (r,0,z). Use this to find[tex]\theta[/tex](t), v(t) and a(t) = v’(t). Then write a in therms of r,[tex]\theta[/tex], z.

This is a long problem and I understand how to do the rest of it but this section is really confusing to me and I can't think of anything that would work. Thanks for any help.

Suppose there is a cylindrical container of liquid with circular flow velocity given in cylindrical coordinates by v(r,[tex]\theta[/tex],z) = <-f(r,z)sin[tex]\theta[/tex], f(r,z)cos[tex]\theta[/tex],0> for some function f(r,z) which we will determine. The vector field is divergence free.

Find a curve, x(t), that represents the path followed by a particle of liquid at radius r. So, x’(t) = v(x(t)) and x(0) = (r,0,z). Use this to find[tex]\theta[/tex](t), v(t) and a(t) = v’(t). Then write a in therms of r,[tex]\theta[/tex], z.

This is a long problem and I understand how to do the rest of it but this section is really confusing to me and I can't think of anything that would work. Thanks for any help.

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