Chezy’s formula in open-channel hydraulics In steady uniform open-channel flow, Chezy’s equation V = C * sqrt(R * S) is primarily used to determine which quantity?

Introduction / Context:
Chezy’s formula is one of the earliest empirical relations in open-channel hydraulics. It relates mean velocity to channel resistance and slope, and remains foundational for understanding modern equations such as Manning’s formula.

Given Data / Assumptions:

• Prismatic open channel with steady, uniform flow.
• Hydraulic radius R = A / P (area over wetted perimeter).
• Energy slope S ≈ bed slope for uniform flow.

Concept / Approach:

Chezy’s equation is written as V = C * sqrt(R * S), where V is mean velocity, C is Chezy’s resistance coefficient (depends on roughness and Reynolds number), R is hydraulic radius, and S is energy grade line slope. It is explicitly a velocity formula for open channels, not closed full-flow pipes (though an analogous form can be used with care).

Step-by-Step Solution:

Verification / Alternative check:

Compare with Manning’s formula V = (1/n) R^(2/3) S^(1/2). For a given channel, C can be related to n and R, showing consistency between the two approaches.

Why Other Options Are Wrong:

(a) and (b) pertain to pipe flow; Chezy’s relation is standard for open channels. (d) is incorrect since the formula clearly provides velocity, and (e) is unrelated.

Common Pitfalls:

Confusing hydraulic radius with hydraulic depth; assuming C is constant across regimes; applying pipe friction concepts directly to free-surface flow without adjustments.

Final Answer:

velocity of flow in open channels