QuestionJuly 25, 2025

True or false, all else being equal, water flows with a higher velocity thorough a semi- circular channel than a wide, shallow channel. True False

True or false, all else being equal, water flows with a higher velocity thorough a semi- circular channel than a wide, shallow channel. True False
True or false, all else being equal, water flows with a higher velocity thorough a semi- circular channel than a wide, shallow channel. True False

Solution
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Answer

True Explanation 1. Compare Channel Shapes A semi-circular channel has a smaller wetted perimeter compared to a wide, shallow channel for the same cross-sectional area. 2. Apply Manning's Equation **Manning's equation**: v = \frac{1}{n} R^{2/3} S^{1/2}, where v is velocity, R is hydraulic radius (area/perimeter), S is slope, and n is roughness coefficient. A smaller perimeter increases R, increasing v. 3. Conclusion Higher hydraulic radius in a semi-circular channel leads to higher velocity.

Explanation

1. Compare Channel Shapes<br /> A semi-circular channel has a smaller wetted perimeter compared to a wide, shallow channel for the same cross-sectional area.<br />2. Apply Manning's Equation<br /> **Manning's equation**: $v = \frac{1}{n} R^{2/3} S^{1/2}$, where $v$ is velocity, $R$ is hydraulic radius (area/perimeter), $S$ is slope, and $n$ is roughness coefficient. A smaller perimeter increases $R$, increasing $v$.<br />3. Conclusion<br /> Higher hydraulic radius in a semi-circular channel leads to higher velocity.
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