Recent content by Raees

If it is a cylinder, then the perpendicular vector to the curved surface is (rcosθ,rsinθ,0) and to the top/bottom surfaces is (0,0,±1). Thus, we both these vectors we get 0.

Thanks, that helps a lot!

Thanks you! So, for u·n = 0, we have: u = (-Ωy) i -(-Ωx) j and n = (1,1,0) which gives: u·n = Ω(x-y) This is not equal to zero. Did I do something wrong here?

Thanks, would the boundary condition be u·n = 0, where n is the vector perpendicular to the cylinder? Therefore, n = (1,1,0)?

Not yet

Hi, how would I go about drawing these two graphs? and The first one would be concentric circles with the centre at (0,0). The second one would be straight lines through (0,0). Is this correct? Also, what happens at ln(0) = constant for the first graph and x = 0 for the second graph...

Thanks for the reply. Are you required to show that ∇ ·u = 0 implies that ∇·(ρu) + ∂ρ/∂t = 0 for this problem? No we are not, I can't find that equation in the notes nor has it been taught to us. Check this. I don't think the vorticity is zero. I recalculated the vorticity to be 2Ω. What...

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...