Drainage
Manning's Equation / Pipe Flow
Manning's equation calculator for full-pipe capacity and velocity using Manning's n — solve for discharge or back-solve for slope.
Manning's Equation / Pipe Flow
Manning's equation relates flow rate to channel geometry, slope, and roughness. For circular pipes flowing full, hydraulic radius equals D/4 and cross-sectional area equals πD²/4, producing a direct formula for full-pipe capacity and velocity.
The Manning's roughness coefficient (n) depends on pipe material and condition. Common values: PVC 0.009–0.011, concrete 0.011–0.013, corrugated HDPE 0.011–0.013, corrugated metal 0.021–0.025. This calculator also back-solves for the slope required to convey a target design flow.
Q = (1.486/n) · A · R^(2/3) · S^(1/2)
Full circular pipe: A = πD²/4, R = D/4
Velocity: V = Q / A
A 24-inch concrete pipe (n = 0.013) laid at a 0.5% slope, flowing full, has a cross-sectional area of 3.14 ft² and hydraulic radius of 0.50 ft. Plugging into Manning's equation gives a full-pipe capacity of 16.0 cfs (7,180 gpm) at a velocity of 5.09 fps — comfortably inside the 2–10 fps range that avoids both sedimentation and scour in a typical storm drain.
Manning's Equation Calculator
Circular pipe, full-flow — imperial units