What is hydraulic radius equal to?

• A. Wetted area divided by wetted perimeter
• B. Wetted perimeter divided by area
• C. Area divided by the square of wetted perimeter
• D. Square root of the area

Answer: (A)

The hydraulic radius is a crucial concept in fluid mechanics, particularly in open channel flow and hydraulic engineering. It is defined as the ratio of the cross-sectional area of flow to the wetted perimeter. This definition is articulated mathematically as the area of the flow divided by the wetted perimeter, which is precisely what the choice identifies.

The significance of the hydraulic radius lies in its relationship to flow characteristics and efficiency. It plays a vital role in determining flow velocity and is utilized in calculations involving the Manning equation, which helps to estimate flow rates in open channels. The larger the hydraulic radius, the more efficient the flow generally becomes, as a greater area compared to the wetted perimeter minimizes the friction impact on flow.

In contrast, the other options do not accurately represent the definition of hydraulic radius. For instance, dividing the wetted perimeter by the area or involving the square of the wetted perimeter contradicts the established definition and would yield results that do not align with practical applications in hydrodynamics.