CSIR NET June 2016 Q109: Hydrology
The Manning equation for open-channel flow velocity is V = (1/n) R^(2/3) S^(1/2), where R is hydraulic radius, S is channel slope, and n is Manning's roughness coefficient.
In V = (1/n) R^(2/3) S^(1/2), the hydraulic radius R is raised to the power 2/3 while the channel slope S is raised to the power 1/2. Since 2/3 (~0.67) is greater than 1/2 (0.5), velocity is more sensitive to (carries higher power from) hydraulic radius than from channel slope. Option 3 is correct.
1) Incorrect -- channel slope is directly (not inversely) related to velocity; higher slope increases velocity. 2) Incorrect -- reverses the power comparison; slope's exponent (1/2) is smaller than hydraulic radius's (2/3). 3) Correct -- hydraulic radius's 2/3 power exceeds slope's 1/2 power. 4) Incorrect -- Manning's roughness n is inversely related to velocity (higher roughness reduces velocity), not positively related.