It all goes back to the initial experiments with lift. They were able to measure the lift, and were trying to devise a formula that gave them the answer they already had.
All related to Kinetic Energy, which is 1/2 x mass x V squared (obtained by integration from momentum, mV)
To find mass, you need air density (rho) x surface area
Thus for airflow, you got 1/2 x (rho x s) x V squared
Plus the variable with angle of attack, the coefficient of lift.
Or near enuf .....