Engineering
Manning's Open-Channel Flow formula: hydraulic radius, velocity & discharge Q
Estimate velocity and discharge for a rectangular SI open channel under steady uniform-flow assumptions.
Estimate rectangular open-channel flow under uniform-flow assumptions
Manning’s empirical equation estimates mean velocity in steady uniform open-channel flow. The rectangular section has area width*depth and wetted perimeter width+2*depth, excluding the free surface. Hydraulic radius is area/perimeter.
S is the energy/friction slope, approximated by bed slope for uniform flow. Use consistent SI units, positive width and roughness, and nonnegative depth and slope. The chosen n=0.013 is illustrative, not a universal concrete value. Backwater, inlet control, rapidly varied flow and flood capacity require additional analysis; this is not a complete culvert design.
| Channel Parameter | Cell / Formula | Rectangular Concrete Canal | Hydraulic Meaning |
|---|---|---|---|
| Bottom Width b & Depth y | B2 = 2.0 m, B3 = 1.0 m | Area B6 = 2.0 m^2 | Wetted P = b + 2*y = 4.0 m |
| Hydraulic Radius R_h | B7 = B6 / (B2 + 2*B3) | 0.50 m | Efficiency of channel shape |
| Roughness n & Slope S | B4 = 0.013, B5 = 0.004 | Smooth concrete, 0.4% grade | Lower n = faster flow |
| Velocity V & Discharge Q | Manning SI Equation | V = 3.06 m/s | Q = 6.13 m^3/s | 6,130 liters per second! |
Manning flow velocity V = (1 / n) * Rh^(2/3) * SQRT(S) (m/s)
For US customary units (ft and ft^3/s), replace numerator 1 with 1.486; in SI meters, the numerator is 1.
=IF(OR(COUNT(B2:B5)<>4,B2<=0,B3<0,B4<=0,B5<0),"Invalid inputs",ROUND((1 / B4) * (B7 ^ (2 / 3)) * SQRT(B5), 2))Volumetric channel discharge Q = Area * Velocity (m^3/s)
Multiplying cross-sectional area B6 by unrounded Manning velocity prevents intermediate rounding drift.
=IF(OR(COUNT(B2:B5)<>4,B2<=0,B3<0,B4<=0,B5<0),"Invalid inputs",ROUND(B6 * (1 / B4) * (B7 ^ (2 / 3)) * SQRT(B5), 2))Try the example
Use the original values or change them to test your understanding.