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RobWilk

Drag Force Ratio for Flat Plate

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I did a Civil Engineering course some years ago and this is a question from my textbook that I haven't been able to solve.

A flat plate 1m wide and 4m long moves with a velocity of 4m/s parallel to its longer sides through still air of kinematic viscosity 1.5 * 10^-5 m^2/s and density 1.21 kg/m^3. On one side of the plate an initially laminar boundary layer is formed. On the other side the leading edge is roughened and the boundary layer may be considered to be entirely turbulent. Assuming a critical Reynolds number of 5 * 10^5 determine the ratio of drag forces on the two sides.

For laminar flow CD = 1.46/ (Rex)^1/2 and for turbulent flow CD = 0.074/ (Rex)^1/5


How do you work out Rex ?

and where does critical Reynolds number come into it ?

I really would like to get an understanding on this,
If someone knows about this, it will be much appreciated that you could please reply to.

Also On one side of the plate it says that an initially laminar boundary layer is formed".
Does this mean that this side of the plate has laminar and turbulent flow ?

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From what I see, Re_x is the Reynolds number using the distance from the leading edge as the length scale in the calculation - along with free-stream velocity and viscosity.

It does seem it refers to laminar-to-turbulent transition - which you can also model in AcuSolve with either a one-equation or two-equation transition model.
I would suggest running two different models - one assuming standard turbulence model assuming fully turbulent flow, and the other using the transition model.  Then you can compare the two overall drag results.

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