A channel designed by Lacey’s theory has a mean velocity of 1 m/sec. If silt factor is unity, then the hydraulic mean radius will be
- A2.5 mCorrect
- B2 m
- C1 m
- D0.5 m
Solution
Concept
Lacey's regime velocity–radius relation
Formula
R = 5 V² / (2 f)
Step-by-step solution
1. Lacey's regime relation: V = √(2fR/5), i.e. R = 5V²/(2f). 2. V = 1 m/s, f = 1. 3. R = 5 × 1² / (2 × 1) = 2.5 m.
Explanation
In Lacey's regime theory the hydraulic mean radius R of a stable channel is 5V²/2f, where f is the silt factor. With V = 1 m/s and f = 1 we get R = 2.5 m.
Shortcut
Lacey: R = 5V²/2f, V = (Q f²/140)1/6, P = 4.75√Q, f = 1.76√d(mm).
Common mistake
Forgetting the factor 5 or writing R = V²/f.
Correct answer: A) 2.5 m