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- Homework Statement
- If liquid contained within a finite closed circular cylinder rotates about the axis k of the cylinder prove that the equation of continuity and boundary conditions are satisfied by u = ΩxR where Ω = Ωk is the constant angular velocity of the cylinder. What is the vorticity of the flow? Here R=xi+yj+zk.

- Relevant Equations
- Can someone check if my answer is correct please?

Can someone check if my answer is correct please?

If liquid contained within a finite closed circular cylinder rotates about the axis k of the cylinder prove that the equation of continuity and boundary conditions are satisfied by

Therefore:

vorticity:

**Question**:If liquid contained within a finite closed circular cylinder rotates about the axis k of the cylinder prove that the equation of continuity and boundary conditions are satisfied by

**u**=**Ω**x**R**where**Ω**= Ω**k**is the constant angular velocity of the cylinder. What is the vorticity of the flow? Here R=x**i**+y**j**+z**k**.**My answer**:**u**= (-Ωy)**i**-(-Ωx)**j**Therefore:

**∇****·u**= 0vorticity:

**ω**=**∇**x**u**= (0)**i**+ (0)**j**+ (-Ω + Ω)**k**= 0