Question

According to Lacey’s regime theory, what will be the regime scour depth for a channel in soil having silt factor of unity and carrying a discharge of 96 m³/s? The base width of the channel is 12 m:-
1. 2.7 m
2. 10.8 m
3. 8.0 m
4. 5.4 m

Answer 1

Correct Answer - Option 4 : 5.4 m

Concept:

Lacey's Regime Width and Depth of Alluvial River:

• According to lacey's, for the alluvial river, the regime width = wetted perimeter = 4.75 √Q
• For such rivers lacey's normal scoured depth, R = 0.473 (Q/f)^1/3

This equation of scoured depth will be applicable only when the river width = regime width of 4.75 √Q

• For any other value of actual river width, the normal scoured depth is given by,

R' = 1.35 (q²/f)^1/3

Where, q = Q/B

B = Base width of the channel

f = Sil factor

Calculation:

Given,

f = 1, Q = 96 m³/s, B = 12 m

q = Q/B = 96/12 = 8 m²/sec

Normal scoured depth is given by,

R' = 1.35 (q2/f)1/3

R' = 1.35 (8²/1)^1/3 =5.4 m