Identify the correct Lacey-type velocity relationship for regime channels (metric form): V as a function of hydraulic mean depth R and bed slope S.

Introduction / Context:
Regime theory (Lacey) provides empirical relations for stable alluvial channels carrying their sediment load. A frequently used form expresses mean velocity V as a function of hydraulic mean depth R and bed slope S, with a metric coefficient.

Given Data / Assumptions:

• Alluvial channel in regime conditions.
• V in m/s, R in m, S dimensionless bed slope.
• Use standard metric adaptation.

Concept / Approach:

The velocity formula analogous to Chezy/Manning forms but calibrated for regime channels is V = 10.8 R^{2/3} S^{1/2}. The exponents reflect hydraulic similarity; the coefficient 10.8 is the empirical metric constant used in many design examples.

Step-by-Step Solution:

Verification / Alternative check:

Comparisons with Chezy or Manning yield similar exponent structure; design charts reproduce the 10.8 coefficient for metric units.

Why Other Options Are Wrong:

(a), (c), and (d) use incorrect exponents; (e) uses a nonstandard coefficient.

Common Pitfalls:

Mixing unit systems; confusing Lacey with Manning where coefficients differ and depend on roughness rather than regime conditions.

Final Answer:

V = 10.8 R^{2/3} S^{1/2}