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Taylor-Couette flow

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Old   April 17, 2016, 16:39
Default Taylor-Couette flow
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Jack Alderson Taggart Penny
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I am trying to solve a problem where there is a rod within a cylinder and the rod moves at a certain velocity with the help of a fluid that fills the gap between the rod and the cylinder. I believe that this is a Taylor Couette problem. I worked out the velocity of the fluid field, which is dependent on the radius of the rod and the radius of the cylinder. The velocity of the fluid field is:
u(R) = U ln(R/Ra)/ln(Ra*Rb).
U is the velocity of the fluid at radius Rb. Ra is the radius of the cylinder, and Rb the radius of the rod, and the velocity of fluid at Ra equals to zero because of the no-slip condition. u(R) is the axial velocity, i.e. the fluid only moves axially, and not radially or tangentially (azimuthally). My question is quite simply this: what is the force needed to move the rod at a constant speed V. I am guessing that the answer could be as simple as F=ma?
The formula above is the velocity, so I differentiate the velocity once to get acceleration and then just stick the "m" to get F=ma? Or am I missing something?

Last edited by Big Kahuna; April 17, 2016 at 16:43. Reason: Wanted to make details clearer.
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Old   April 17, 2016, 16:56
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Filippo Maria Denaro
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what do you mean for constant V as then it implies a=0 ??
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Old   April 17, 2016, 17:26
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Quote:
Originally Posted by FMDenaro View Post
what do you mean for constant V as then it implies a=0 ??
Yes, you're right. I overlooked that. But all I have been told in order to solve this problem is "What force is required to pull the rod with a constant speed U0? Neglect the end effects." It's clear that F = ma won't work here.
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couette flow, laplacian operator

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