Simplified engineering models are essential to design and control natural ventilation, yet there are not many theories that can predict cross ventilation with reasonable accuracy. Models based on the orifice equation are known to be inadequate for large openings, but there is no precise definition of the large opening. In this paper, we show that it is not just the opening size but also the wind angles that affect the prediction accuracy of the orifice based equations. The mass flow rate predicted by CFD simulations is within 10% of the flow rate predicted by the orifice equations with sealed body pressure coefficients as long as the total pressure drop in the presence of openings is nearly equal to the static pressure drop in cases with no openings. The total pressure drop in the presence of openings when the openings are aligned to the wind, i.e. when wind can pass directly through two openings, is smaller than the static pressure drop in cases with no openings. If the wind is angled, and the entering wind cannot pass undisturbed through the outlet because of the building walls, the total pressure drop will not be much smaller than the static pressure drop of the sealed building. In this condition, the orifice equation can still be used, even for porosities of up to 50%. However, when the wind can pass undisturbed between two opposite openings, the orifice based equations are not adequate, even for a porosity as small as 6%.