Question

If Manning&#x27;s roughness coefficient increases in an open channel while the slope and hydraulic radius remain constant, does the flow velocity increase, decrease, or stay the same?

Accepted Answer

If Manning&#x27;s roughness coefficient increases while the slope and hydraulic radius remain constant, the flow velocity decreases. This relationship is defined by the Manning formula, which states that velocity is equal to the product of the hydraulic radius to the power of two-thirds and the square root of the slope, all divided by the Manning roughness coefficient. The Manning roughness coefficient represents the friction or resistance to flow created by the channel&#x27;s boundaries, such as the material of the bed and banks or the presence of vegetation. Because the coefficient appears in the denominator of the velocity equation, any increase in resistance directly forces the velocity to drop to maintain equilibrium. Think of it like a marble rolling down a ramp; if you cover the ramp in sandpaper instead of glass, the increased friction slows the marble down even though the steepness of the ramp remains identical. In an open channel, a higher roughness coefficient indicates a rougher surface that extracts more energy from the water, resulting in a lower flow velocity.

Home → All Courses → Engineering and Technology Courses → Environmental Systems Engineering → Flashcard

If Manning's roughness coefficient increases in an open channel while the slope and hydraulic radius remain constant, does the flow velocity increase, decrease, or stay the same?