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The following nondimensional equations govern conservation of mass and momentum.

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These equations can be combined in order to create a governing equation that will dictate the flow in our lid-driven box. Below is the equation which was created when combining the above.

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The terms on the left govern the net convection flow in the volume while the terms on the right govern net diffusion, with the exception of S which represents source generation of the flow.

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Using the equation below, the Reynolds number can be calculated for the problem. This will allow us to predict how the flow will behave inside the box before running the simulation. It is specified in the problem that the inside length of the box is 0.1 m and the speed of the lid is 1 m/s. Since the fluid inside of the box is water, the density is 997.05 kg/m^3 and the viscosity is 0.00089002 N*s/m^2. These values can be found online or later on in the Material properties section of the Physics template.

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The resulting value from the Reynolds number calculation indicates that the flow will be turbulent and will produce multiple eddies.

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