gen-define-the-manning-equation-and-give-one-short-worked-exampl-bc86

Define the Manning equation and give one short worked example.

# Manning Equation The **Manning equation** is an empirical formula used in open channel flow hydraulics to relate the flow velocity to the channel characteristics and slope. ## Formula **V = (1/n) × R^(2/3) × S^(1/2)** Or in SI units: **V = (1/n) × R^(2/3) × S^(1/2)** Where: - **V** = mean flow velocity (m/s or ft/s) - **n** = Manning's roughness coefficient (dimensionless) - **R** = hydraulic radius = A/P (m or ft) - A = cross-sectional area of flow - P = wetted perimeter - **S** = slope of the energy grade line (m/m or ft/ft), approximately equal to channel bed slope ## Worked Example **Problem:** A rectangular channel is 3 m wide with water depth of 1.5 m. The channel slope is 0.001 and Manning's n = 0.015. Find the flow velocity. **Solution:** - Width (b) = 3 m - Depth (y) = 1.5 m - Area (A) = b × y = 3 × 1.5 = 4.5 m² - Wetted perimeter (P) = b + 2y = 3 + 2(1.5) = 6 m - Hydraulic radius (R) = A/P = 4.5/6 = 0.75 m **V = (1/0.015) × (0.75)^(2/3) × (0.001)^(1/2)** **V = 66.67 × 0.826 × 0.0316** **V = 1.74 m/s**