Open Channel Flow MCQ with answer and solution

Concept

From Manning's formula, n = R^2/3 S^1/2 / V. S has no dimension, so we can find the dimension of n.

Formula

V = (1/n) R^2/3 S^1/2

Step-by-step solution

1. Manning's formula: V = (1/n) R^2/3 S^1/2. 2. So n = R^2/3 S^1/2 / V. 3. S (bed slope) has no dimension. R = L. V = L T^-1. 4. n = L^2/3 / (L T^-1) = L^{2/3 - 1} T = L^-1/3 T. 5. Answer is option (D).

Explanation

Manning's n is not a pure number. When we take n from the formula and put in dimensions, we get L^-1/3 T. So its value depends on the unit system (SI or FPS).

Why the other options are wrong

(A) L^-1/2 T^-2 does not come from the formula. (B) L^-2/3 T uses the power of R wrongly. (C) L^-1/6 T^-1 is not correct. The power 1/6 appears in Strickler's relation n ∝ d^1/6, not in the dimension of n.