Chezy's Constant

Chezy's constant is a dimensionless coefficient used in open channel flow to relate the velocity of the flow to the hydraulic radius and the slope of the channel. It is denoted by the symbol "C" and is named after the French engineer Antoine de Chezy.

Dimensions of Chezy's Constant

The dimensions of Chezy's constant can be determined by analyzing the equation in which it appears. The equation relating the velocity (V) to the hydraulic radius (R) and slope (S) is given by:

V = C * sqrt(R * S)

Where:
- V is the velocity of the flow
- R is the hydraulic radius (the ratio of the cross-sectional area of flow to the wetted perimeter)
- S is the slope of the channel

By rearranging the equation, we can express Chezy's constant (C) in terms of the dimensions of V, R, and S:

C = V / sqrt(R * S)

Analyzing the Dimensions

To determine the dimensions of Chezy's constant, we need to analyze the dimensions of the variables in the equation.

- Velocity (V): The dimensions of velocity are [L/T] (length per unit time).
- Hydraulic radius (R): The dimensions of hydraulic radius are [L] (length).
- Slope (S): The dimensions of slope are [L/L] (length per length), which simplifies to [1] (dimensionless).

By substituting the dimensions into the equation, we get:

C = [L/T] / sqrt([L] * [1])

Simplifying further:

C = [L/T] / sqrt([L])

C = [L/T] / [L^1/2]

C = [L^1/2 T^-1]

Conclusion

From the analysis, we can conclude that the dimensions of Chezy's constant are [L^1/2 T^-1]. Therefore, the correct answer is option 'B' which states that Chezy's constant has dimensions [L^1/2 T^-1].