Fig. 3: Considering mass and momentum conservation laws to develop a non-dimensionalized relation between flood height, driving forces, and urban form attributes.

a A schematic of the control volume through which water, shown in blue, flows between gray square obstacles. In dense urban environments, the floor shear is negligible compared to the other forces, and the gravitational force balances the form drag at the steady state. A limited number of one-factor-at-a-time flow simulations corroborate with the proposed dimensionless relationship, showing the flood height (b) scales linearly with flow rate per width (q), and (c) is proportional to the inverse square root of the bottom slope (α^−1/2).