Manning's Equation Calculator

What is Manning's Equation?

Manning's equation is the standard formula for calculating flow in open channels and partially-full pipes (culverts, drains, sewers). Developed by Robert Manning in 1891, it relates flow velocity to channel geometry and roughness.

Manning's Equation

v = (1/n) × R^(2/3) × S^(1/2)

Q = A × v = (1/n) × A × R^(2/3) × S^(1/2)

Where:

• n = Manning's roughness coefficient
• R = hydraulic radius = A / P (wetted perimeter)
• S = channel slope (m/m)
• A = cross-sectional area of flow (m²)

Manning's n Values

| Surface | n | |---------|---| | Concrete channel | 0.012 | | Smooth asphalt | 0.013 | | Earth channel, clean | 0.022 | | Natural stream | 0.030–0.050 | | Mountain stream (boulders) | 0.040–0.070 | | PVC pipe | 0.009 |

Practical Examples

Example: Rectangular concrete channel, 2m wide, 1m deep (full), slope 0.001, n=0.012. A = 2m², P = 4m, R = 0.5m. v = (1/0.012) × 0.5^0.667 × 0.001^0.5 = 83.3 × 0.63 × 0.0316 = 1.66 m/s. Q = 2 × 1.66 = 3.32 m³/s = 3,320 L/s.

Applications

Sewer design, stormwater drainage, culvert sizing, irrigation canals, and open channel flood modelling.