While considering the pressure balance to the air inside and outside the open window; the increased air pressure caused by the temperature difference between the inside and the outside ― which can be estimated after the ideal gas law ―, depressed by the pressure drop caused by the open window frame ― which can be estimated based on Fanning friction factor ―; should, for a weak enough window-crossing stream of air, equilibrate the dynamic pressure due to that air flux ― a function of air velocity. From that we should be able to estimate the air velocity and mass flow.

However, for a stronger stream of (hot) air crossing the window to the outside, the outside rising plume of warm air might play a stack/chimney effect, which should positively contribute to further enhance the air flow, but not to such an extent as if a stack/chimney actually was there, conducting the air flux between the window and the top of the building.

Besides the temperature difference, also the relative humidity and composition difference between the inside and outside air should influence the air density, and hence, the estimated figure.