Manning's Equation Open Channel Calculator
Compute flow velocity and discharge in open channels — rivers, canals, and drains — using Manning's equation. Essential for flood modelling, irrigation design, and stormwater drainage sizing.
About this calculator
Manning's equation is the most widely used formula for uniform open-channel flow. It relates discharge Q to channel geometry and roughness: Q = (1/n) × R^(2/3) × S^(1/2) × A, where n is Manning's roughness coefficient (dimensionless), R is the hydraulic radius (cross-sectional area divided by wetted perimeter) in metres, S is the longitudinal slope (m/m, dimensionless), and A is the cross-sectional flow area in m². The hydraulic radius R captures how efficiently the channel shape conveys flow — circular or trapezoidal sections with less wetted perimeter relative to area are more efficient. Lower n values (smooth concrete) yield higher velocities; higher n values (natural streams) slow flow. The formula assumes steady, uniform flow with a constant water surface slope equal to the bed slope.
How to use
Consider a concrete-lined rectangular channel (n = 0.013) that is 3.0 m wide with a flow depth of 1.2 m and a slope S = 0.001. Cross-sectional area A = 3.0 × 1.2 = 3.6 m². Wetted perimeter P = 3.0 + 2 × 1.2 = 5.4 m. Hydraulic radius R = 3.6 / 5.4 = 0.667 m. Now apply Manning's: Q = (1/0.013) × 0.667^(2/3) × √0.001 × 3.6. R^(2/3) = 0.667^0.667 ≈ 0.748. √0.001 ≈ 0.03162. Q = 76.92 × 0.748 × 0.03162 × 3.6 ≈ 6.55 m³/s.
Frequently asked questions
What is Manning's roughness coefficient n and what values are typical?
Manning's n is a dimensionless empirical coefficient that quantifies the resistance to flow caused by the channel boundary. Lower values indicate smoother surfaces that offer little resistance; higher values indicate rough, irregular boundaries. Typical values include 0.010–0.013 for smooth concrete, 0.020–0.025 for clean earthen channels, 0.030–0.040 for natural streams with some vegetation, and 0.060–0.100 or higher for densely vegetated floodplains. Selecting an appropriate n value is often the largest source of uncertainty in open-channel calculations, and published tables (e.g., Chow, 1959) provide guidance based on channel type and condition.
How is hydraulic radius different from the flow depth in a channel?
Hydraulic radius R is defined as the cross-sectional flow area A divided by the wetted perimeter P — the length of channel boundary in contact with the water. It is not the same as depth. For a wide, shallow channel, R approaches the flow depth because the wetted perimeter is dominated by the wide base. For a narrow or deep channel, R is significantly smaller than depth because the side walls add substantial wetted perimeter relative to area. R is the key geometric parameter in Manning's equation because it measures how efficiently the channel shape conveys flow with minimal boundary friction.
When does Manning's equation give inaccurate results for open channel flow?
Manning's equation assumes steady, uniform flow — meaning the water surface slope equals the bed slope and velocity is constant along the channel. It becomes inaccurate in rapidly varied flow situations such as near hydraulic jumps, weirs, bridge contractions, channel bends, or where the flow is changing depth rapidly. It also assumes fully turbulent flow, so it can be unreliable at very low velocities. In natural rivers with compound cross-sections (main channel plus floodplain), Manning's equation must be applied separately to each subsection with appropriate n values for each, then flows are summed.