The terminal speed V shipping boxes sliding down an inclined air table with the

Question

The terminal speed V shipping boxes sliding down an inclined air table with the air injected though a dense array of pinholes depend on the box mass m, base area A, gravitational acceleration g, the angle of the air table (degree), the viscosity of the air u, and the thickness of the layer of air . determine the dimenionless parameter characterizsing this flow. two boxes have the same mass, but different base areas are sliding down the incline at the same time. Which box (large area or small area has a higher terminal velocity?

I am have a very hard time starting this problem. A little guides would greatly be helpful

Explanation / Answer

The dimensionless ratio I believe you want is the Reynolds Number. This ratio is dimensionless, and is a ratio of Inertia Forces/Viscous Forces. How the mass moves compared to the Forces stopping motion, (Viscous effects).

The larger surface area will have more airflow raising it, thus making it stay above the surface of the table better.

The other dimensionless ratio I considered was the Froude Number, which has gravity in the equation and relates Inertia forces/Gravity forces.
This ratio is used for things like settling tanks to determine how long of a tank is required to let heavier particles fall out of a fluid and thus clean the system.

I hope this helps you get started :)

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