Selecting correct canal design statement: Which of the following statements is correct regarding canal levels and regime design (Lacey)?

Introduction / Context:
Alluvial channel design follows empirical relations such as Lacey’s regime equations tying discharge, silt factor, hydraulic radius, velocity, and slope. Also, practical canal levels are set with regard to terrain but need not always be above ground.

Given Data / Assumptions:

• Regime (quasi-stable) alluvial channel conveying uniform silt.
• Use of Lacey’s silt factor f and discharge Q.
• Consideration of FSL relative to natural ground.

Concept / Approach:
Lacey related slope S with discharge and silt factor through regime relations. Statement (b) correctly reflects that a particular slope is implied for given Q and f. FSL may lie above or below ground depending on cutting/embankment needs; it is not a universal rule. Admitting coarser silt increases f, not decreases it; hence (c) is wrong.

Step-by-Step Solution:
Evaluate (a): Not universally true—canals may be in cutting.Evaluate (b): True—Lacey’s equations yield a characteristic slope for given Q and f.Evaluate (c): False—coarser silt raises f; cannot reduce required slope that way.Therefore, only (b) is correct.

Verification / Alternative check:
From Lacey: V = k1 * f^0.5 * R^0.5 and S = k2 * f^(5/3) * Q^(−1/6) (indicative forms). These tie S to Q and f.

Why Other Options Are Wrong:

• (a) Over-generalization.
• (c) Misstates effect of silt size on silt factor.
• (d) All-the-above fails as (a) and (c) are wrong.

Common Pitfalls:
Assuming canals must be in embankment; misinterpreting how sediment size affects regime parameters.

Final Answer:
According to Lacey, regime conditions require a particular bed slope for a given discharge and silt factor