Sarda fall discharge formula: For a trapezoidal crest operating under free over-fall, which discharge expression is appropriate (symbols: L crest length, H head over crest, B canal bed width, g gravity)?

Introduction / Context:

Sarda type falls are canal falls designed to measure and dissipate energy while passing discharge. The empirical rating for their crests (rectangular or trapezoidal) modifies the standard sharp-crested weir relation Q ∝ L * H^(3/2) with a width-ratio correction to account for approach conditions.

Given Data / Assumptions:

• Free over-fall (modular flow) with negligible submergence.
• Trapezoidal crest used on distributaries as per standard layouts.
• Correction term involves the relative head H to bed width B.

Concept / Approach:

The base weir equation Q = C * L * H^(3/2) is adapted with C ≈ 0.45 * sqrt(2g) for Sarda fall geometry and an additional factor (H/B)^(1/6) that captures approach contraction effects. Thus the formula becomes Q = 0.45 * sqrt(2g) * L * H^(3/2) * (H/B)^(1/6).

Step-by-Step Solution:

Verification / Alternative check:

Comparisons with standard rating tables for Sarda falls confirm the 1/6 exponent trend for trapezoidal crests under free fall conditions.

Why Other Options Are Wrong:

• Different exponents on H or (H/B) distort the empirical calibration.
• Expressions with H^(2/3), H^(1/6), or inverted ratios do not match established Sarda ratings.

Common Pitfalls:

• Using the rectangular crest coefficient for trapezoidal crests without correction.
• Applying the formula under submergence without submergence corrections.

Final Answer:

0.45 * sqrt(2g) * L * H^(3/2) * (H/B)^(1/6)