For more reading on Manning's Formula and storm drain system design, see "Storm Drain System Design (4) - Horizontal Pipe Sizing".
The popular empirical equation for calculating gravity flow is Manning Formula.
For open channels and conduits other than circular, use hydraulic radius, R, directly in Manning Formula:
Flow in partial full pipes can be calculated with the following tables by entering n, D, h/D and S directly, where n is Manning roughness coefficient, h/D is the ratio of wate depth to pipe diameter, D is pipe diameter in ft and S is slope. Other hydraulic elements are also listed for reference.