Irrigation Water Conveyance and Application Methods
Subtopic: Design of irrigation channels and underground pipelines
Question Statement:
According to Lacey's regime theory for alluvium channels, the regime scour depth $R$ is given by:
Options:
(A) $R = 0.47 \left(\frac{Q}{f}\right)^{1/3}$
(B) $R = 1.35 \left(\frac{q^2}{f}\right)^{1/3}$
(C) $R = 0.47 \left(\frac{f}{Q}\right)^{1/3}$
(D) $R = 0.75 \left(\frac{Q}{f}\right)^{1/2}$
Answer Key:
A
Step-by-Step Solution & Explanation
Lacey's regime formulas state:
1. In terms of total discharge $Q$: $R = 0.473 \left(\frac{Q}{f}\right)^{1/3}$.
2. In terms of discharge per unit width $q$: $R = 1.35 \left(\frac{q^2}{f}\right)^{1/3}$.
Hence, Option A correctly matches the total discharge equation.