IIRC dimensional analysis lets you put constraints on the form of the equation, by requiring that the variables form dimensionless groups. But you still have t

IIRC dimensional analysis lets you put constraints on the form of the equation, by requiring that the variables form dimensionless groups. But you still have to include the right variables, and then measure the values of those dimensionless quantities under different conditions (for instance the Reynolds number for different velocities or length scales) to figure out how the groups scale relative to one another. But I'm sure that data already exists for the situation in question. It would just be a matter of estimating the values from the video and dropping them into the equation.