Manningformule

Manningformule, commonly known as Manning's equation, is an empirical relation used in open-channel hydraulics to estimate the discharge or velocity of water in channels with a specified cross-section and roughness. It is widely used in civil engineering and hydrology for design and analysis of rivers, channels, and drainage conduits.

The most common form expresses discharge as Q = (1/n) A R^(2/3) S^(1/2), where Q is the volumetric flow rate, n is Manning's roughness coefficient, A is the cross-sectional area of flow, R is the hydraulic radius (R = A/P, with P the wetted perimeter), and S is the energy slope (approximately the bed slope for uniform flow). Velocity can be written as v = (1/n) R^(2/3) S^(1/2). The equation assumes steady, uniform, turbulent flow in non-pressurized open channels.

Applicability and limitations: Manning's equation applies to open-channel flow with relatively smooth channels and known roughness, for channels of regular cross-section where flow depth is constant along the reach. It is not suitable for laminar flow, highly irregular conditions, rapidly varied flow, or flows with significant sediment transport unless calibrated. The coefficient n encapsulates roughness from surface texture, vegetation, and obstructions and varies with material, surface condition, and flow regime. The formula is named after the Irish engineer Robert Manning, who introduced it in the late 19th century, and remains a foundational tool for hydraulic design and flood-hazard assessment.