Q1: For drains up to 15 cumecs, the depth d and width B are related by

ANS:B - d = 0.5 B

The relationship between the depth d and the width B of a drain for flows up to 15 cumecs can be determined using hydraulic principles, particularly the Manning's equation for open channel flow. In open channel flow, the cross-sectional area (A) of the flow is given by the product of the depth (d) and the width (B). The flow rate (Q) is equal to the product of the cross-sectional area, the hydraulic radius (R), and the slope (S), divided by Manning's roughness coefficient (n). Mathematically, this can be represented as: Q=n1​⋅A⋅R^2/3⋅S^1/2 Given that the flow rate Q is up to 15 cumecs, and assuming a constant Manning's roughness coefficient, we can investigate the relationship between d and B. First, let's express the cross-sectional area (A) in terms of d and B: A=d⋅B Now, for flows up to 15 cumecs, the relationship between d and B can be derived as follows: Q=n1​⋅d⋅B⋅R2/3⋅S1/2 Given that the hydraulic radius R is related to the cross-sectional area (A) and the wetted perimeter (P) as R=PA​, and for most practical open channels, the wetted perimeter is approximately equal to the sum of the depth (d) and the width (B), we can express R in terms of d and B: R=A/P​=d+Bd⋅B​ Substituting this expression for R into the Manning's equation, we have: 15=1/n​⋅d⋅B⋅(d+Bd⋅B​)^2/3⋅S^1/2 Now, finding a specific relationship between d and B would require additional information such as the slope (S) and the Manning's roughness coefficient (n). Without this information, we cannot determine a precise relationship between d and B. However, based on typical design considerations and empirical relationships used in hydraulic engineering, it is common to assume that the depth d is related to the width B by a proportionality constant. From the options provided:

• d=0.2B and B=0.5d are consistent with this typical relationship.

• d=0.2B