Manning Roughness Coefficient Analysis

This solution evaluates two statements concerning the Manning roughness coefficient ($n$) and its relationship with flow conditions.

Analysis of Statement A

Incorrectness of Statement A

Statement A claims that the Manning roughness coefficient ($n$) increases as flow depth increases up to bankfull discharge. This is generally incorrect.

• The Manning coefficient ($n$) is primarily a function of the channel's boundary material (e.g., soil, gravel, vegetation) and geometry.
• It does not typically increase directly with flow depth within the channel. While hydraulic radius and flow velocity change with depth, $n$ is often treated as constant for a given channel section unless conditions like significant sediment transport or vegetation growth occur.

Analysis of Statement B

Incorrectness of Statement B

Statement B states that when channel capacity is exceeded, flow spreads over a larger area, causing the Manning roughness coefficient ($n$) to decrease. This is also incorrect.

• Overbank flow occurs when discharge exceeds the channel's capacity, spreading onto the floodplain.
• Floodplains often have much higher roughness due to vegetation, buildings, and uneven terrain compared to the main channel bed.
• While the flow area increases, the resistance offered by the floodplain surface typically does not lead to a decrease in the *effective* Manning roughness. It might remain similar or even increase, depending on the floodplain's characteristics. The assertion of a definite decrease is inaccurate.

Conclusion

Both Statement A and Statement B present inaccurate descriptions of how the Manning roughness coefficient behaves under different flow conditions. Therefore, the correct conclusion is that both statements are incorrect.