Question

(30 pts) Consider fully developed Couette flow (flow between two infinite plates with the top plate moving and the bottom plate stationary. We know the velocity profile equation from previous lessons, $u = Vy/h$. Suppose, however, that you do not know this. Instead, you approach the problem using dimensional analysis and the method of repeating variables. You set up the problem as $u = u(h, V, \mu, y)$. For consistency, choose your repeating variables in the same order as in the list of variables above. In other words, if you need two repeating variables, choose $h$ and $V$. If three, choose $h$, $V$, and $\mu$, etc. (a) Go through the step-by-step procedure, showing all your work, to generate an expression with one or more nondimensional II parameters in the usual fashion, namely, $\Pi_1 = \text{function}(\Pi_2, \Pi_3,...)$. (b) Show that your result (if done correctly) is consistent with the known velocity profile equation.

          (30 pts) Consider fully developed Couette flow (flow between two infinite plates with the top plate moving and the bottom plate stationary. We know the velocity profile equation from previous lessons, $u = Vy/h$. Suppose, however, that you do not know this. Instead, you approach the problem using dimensional analysis and the method of repeating variables. You set up the problem as $u = u(h, V, \mu, y)$. For consistency, choose your repeating variables in the same order as in the list of variables above. In other words, if you need two repeating variables, choose $h$ and $V$. If three, choose $h$, $V$, and $\mu$, etc.
(a) Go through the step-by-step procedure, showing all your work, to generate an expression with one or more nondimensional II parameters in the usual fashion, namely, $\Pi_1 = \text{function}(\Pi_2, \Pi_3,...)$.
(b) Show that your result (if done correctly) is consistent with the known velocity profile equation.

Added by Christopher T.

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