Question

The dimensions of Chezy’s coefficient \( C \) in [MLT] notation system are:

• A. \( L^{1/2} T^{1/2} \)
• B. \( L^{-1} T^{1/2} \)
• C. \( L^{-1} T^{-1} \)
• D. \( L^{1/2} T^{-1} \)

Hint:

Chezy’s coefficient has dimensions of \( L^{1/2} T^{-1} \), which helps in open channel flow calculations.

Answer 1

The Correct Option is D

Step 1: The Chezy’s equation for velocity \( V \) in an open channel is: \[ V = C \sqrt{RS} \] where: - \( R \) is the hydraulic radius (\( L \)), - \( S \) is the slope (dimensionless), - \( C \) is Chezy’s coefficient.
Step 2: Solving for \( C \): \[ C = V \div \sqrt{R} \] Using \( V = LT^{-1} \) and \( R = L \), we get: \[ C = \frac{LT^{-1}}{L^{1/2}} = L^{1/2} T^{-1} \] Thus, the correct answer is (D) \( L^{1/2} T^{-1} \).