Manning Equation

V = \frac{1}{n} R^{2/3} S^{1/2}

Open channel flow velocity depends on hydraulic radius, slope, and roughness.

By Robert Manning

Earth System Sciences

Manning Equation

1890 · Robert Manning

Why it matters: Standard tool for river engineering, flood modeling, and drainage design.

Discoverers: Robert Manning (1890)

What does it mean?

Open channel flow velocity depends on hydraulic radius, slope, and roughness.

Standard tool for river engineering, flood modeling, and drainage design.

Symbol	Name	Unit	Meaning
$V$	Velocity	m/s	Mean flow velocity
$n$	Roughness	—	Manning roughness coefficient
$R$	Hydraulic radius	m	A/P wetted perimeter
$S$	Slope	—	Energy grade line slope

Steep slope and smooth channel → higher velocity.

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V = \frac{1}{n} R^{2/3} S^{1/2}

Real-world impact

Precision agriculture

Equations optimize food production for billions.

Photo: Unsplash — precision farming

Open channel flow velocity depends on hydraulic radius, slope, and roughness.

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