Question

In Chezy's equation, ‘R' stands for

• A. Hydraulic radius
• B. Reynolds number
• C. Radius of curvature
• D. Coefficient of roughness

Hint:

In Chezy's equation \(V=C\sqrt{RS}\), \(R\) means hydraulic radius.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Chezy's equation is one of the earliest empirical formulas used to calculate the mean flow velocity in an open channel under uniform flow conditions. The question asks for the meaning of the term 'R' in this equation.
Step 2: Key Formula or Approach:
Chezy's equation is given by: \[ V = C \sqrt{R S} \] where: - $V$ is the mean velocity of flow. - $C$ is Chezy's coefficient, which depends on the channel roughness and flow conditions. - $R$ is the hydraulic radius of the flow cross-section. - $S$ is the channel bed slope (or the slope of the energy line).
Step 3: Detailed Explanation:
Based on the standard form of Chezy's equation, the variable 'R' represents the hydraulic radius. The hydraulic radius is a crucial geometric parameter for open channel flow (and non-circular pipe flow). It is defined as the ratio of the cross-sectional area of the flow (A) to the wetted perimeter (P). \[ R = \frac{A}{P} \] It provides a measure of the flow's hydraulic efficiency; a larger hydraulic radius for a given area means less frictional resistance from the channel boundary. The other options are incorrect: - (B) Reynolds number (Re) is a dimensionless number used to characterize the flow regime (laminar or turbulent). - (C) Radius of curvature refers to the radius of a bend in a channel or pipe. - (D) Coefficient of roughness is a parameter that accounts for the frictional resistance of the channel boundary. In the Manning equation (a more common formula that evolved from Chezy's), this is represented by 'n'. Chezy's coefficient 'C' is related to this roughness. Step 4: Final Answer:
In Chezy's equation, 'R' stands for the hydraulic radius. Therefore, option (A) is the correct answer.