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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?
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 = ΩxR where Ω = Ωk is the constant angular velocity of the cylinder. What is the vorticity of the flow? Here R=xi+yj+zk.
My answer:
u = (-Ωy) i -(-Ωx) j
Therefore: ∇ ·u = 0
vorticity: ω = ∇ x u = (0) i + (0) j + (-Ω + Ω) k = 0
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 = ΩxR where Ω = Ωk is the constant angular velocity of the cylinder. What is the vorticity of the flow? Here R=xi+yj+zk.
My answer:
u = (-Ωy) i -(-Ωx) j
Therefore: ∇ ·u = 0
vorticity: ω = ∇ x u = (0) i + (0) j + (-Ω + Ω) k = 0