Question

Arrange the following design steps for the design of channel section on the basis of Lacey's Theory in the correct sequence :
A. Finding out the perimeter
B. Finding out the velocity
C. Calculation of the silt factor
D. Finding out the area
Choose the correct answer from the options given below:

• A. D, A, C, B
• B. C, B, D, A
• C. D, B, C, A
• D. C, A, D, B

Hint:

Lacey's Theory is unique because the wetted perimeter ($P$) depends solely on the discharge ($Q$), regardless of the silt factor or soil type!

Answer 1

The Correct Option is B

Concept: Lacey's Theory for the design of stable alluvial channels is based on the concept of regime conditions. It provides empirical equations to determine the dimensions of a channel that will neither silt nor scour for a given discharge and silt grade.

Step 1: Initial Step - Silt Factor.
The first step in Lacey's design procedure is always to identify the characteristics of the sediment. The silt factor ($f$) must be calculated using the average particle size ($d$ in mm): \[ f = 1.76 \sqrt{d} \] Therefore, C is the first step.

Step 2: Determining Velocity.
Once the silt factor and design discharge ($Q$) are known, the regime velocity ($V$) is calculated using: \[ V = \left( \frac{Q f^2}{140} \right)^{1/6} \] Therefore, B follows C.

Step 3: Determining Hydraulic Parameters.
After finding the velocity, the required cross-sectional area ($A$) is determined from the continuity equation ($A = Q/V$): \[ A = \frac{Q}{V} \] Therefore, D follows B.

Step 4: Determining Wetted Perimeter.
Finally, the wetted perimeter ($P$) is calculated directly from the discharge: \[ P = 4.75 \sqrt{Q} \] Therefore, A is the final step in this sequence. The correct order is C-B-D-A.