In Manning's equation, what does the symbol n represent?

• A. The Manning roughness coefficient.
• B. The Reynolds number.
• C. The channel slope.
• D. The cross-sectional area.

Answer: (A)

In open-channel flow, Manning's equation links discharge to the channel’s shape, slope, and roughness. The symbol n is the Manning roughness coefficient, an empirical factor that represents how rough the channel bed and walls are, including texture, vegetation, and other irregularities. It governs energy losses due to friction: the rougher the surface (larger n), the more resistance to flow, so the discharge for the same cross-section and slope is smaller. You can see this directly in the equation through the inverse relationship with n: doubling the roughness halves the discharge when A, R, and S stay the same. Examples: smooth, paved channels have small n; natural rivers with rocks and vegetation have larger n. The other terms in the equation—cross-sectional area, hydraulic radius, and slope—are independent factors that define the flow geometry and grade; they aren’t what n represents.