# Computational Fluid Dynamics - Couette flow & Reynolds Number

1. Aug 26, 2011

### HRufus

1. The problem statement, all variables and given/known data

This is a part of an assignment for a computational modelling paper requiring the modelling of couette flow between two (infinite) parallel plates in MATLAB. The lower plate is stationary while the upper plate moves at 0.1m/s, the plates are 0.01m apart and the no slip condition is applied to find the fluid velocity at the upper and lower edge. In the model the distance between the plates is broken down into 10 (equally sized) cells and fluid velocity at each point is established numerically over time until stability is reached. Essentially this gives a (near) linear velocity profile between the plates.

I have no problems with the numerical analysis, but a later section requires calculation of the maximum Reynolds number and a statement as to whether the flow is laminar or turbulent.

2. Relevant equations

Re = UL/v (v is given as 1E-6m2/s)

3. The attempt at a solution

The maximum speed occurs at the upper boundary (~0.1m/s) but what would be the appropriate length scale?

Thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 26, 2011

### RandomGuy88

The length scale should be the height of the channel. 0.01m in your case. Sometimes the length scale could be defined as half of the channel height as well. It doesn't really matter as long as you are clear on which one you are using and you know how to determine if the flow is laminar or turbulent. For example if the flow is assumed to be turbulent for a Reynolds number greater than about 2300 (pipe flow) you need to know what length scale is used to determine that Reynolds number.