Evaluating the risk of inundation flooding and its deleterious effects in urban environments is key, considering that such natural disasters are poorly predictable, costly, and are expected to increase with global warming. To insight and evaluate flooding impact in cities and the role played by city textures, we propose a statistical physics computational approach called on-lattice density functional theory. Originally developed in Materials Science, the model is applied to the city scale, considered here as a porous media. We thus show that the strength of such an equilibrium-based approach stems from the combination of three aspects: i. the model has a minimum of inputs and an efficient computational time, ii. the model comes with an ease of modeling a variety of city elements that are critical for inundation flooding (e.g., buildings, pavements, permeable soils, and drainage systems), iii. the model has physically meaningful output parameters, such as adsorption and desorption isotherms, which can be linked to a city's drainage capacity and steady-state gage heights. We found that isotherms exhibit a pronounced hysteresis, indicating that flooding and draining properties can be blocked in metastable microstates. Such behavior is key since it provides a fundamental means to qualitatively identify the risk of inundation flooding.