This is an improved version of Kennedy’s theory. Lacey proposed that there were 3 types of regimes - True, Initial and final regimes.

As per Lacey’s theory a true regime channel can be achieved only if the below conditions are satisfied (Ideal conditions)-

Channel has a constant discharge

The channel is on coherent alluvial soil which is a loose soil that can be easily scoured as it is deposited.

The 2 other regimes are described below-

Initial regime: it is the type of regime that appears having ideal conditions but not so because the width of the canal keeps on varying.

Final Regime: As water keeps flowing, depth, perimeter, slope keeps varying which forms a final stable regime.

Lacey’s theory would be applicable to the final regime/true regime only. Similar to Kennedy, Lacey also introduced another term called silt factor.

### Silt factor

The silt supporting power depends upon the wetted perimeter which implies the eddies from the sides are also considered. Thus, Lacey introduced a term called silt factor, f that depends upon the size of the grains.

Silt factor f = 1.76 x d^0.5, where d - the average size of particles in mm.

Now, let's see how to design a channel using Lacey's theory.

### Design procedure

**Step1: **Calculate the velocity v using the equation, v = (Qf²/140)^(1/6).

Here Q - discharge, f - silt factor and v - velocity

**Step 2: **Calculate the Hydraulic depth (R) using the equation, R = 5/2(v²/f)

**Step 3:** Calculate the area (A) and wetted perimeter (P) from the equations, A = Q/v and P = 4.75 x Q^(0.5)

Based on the Area (A) and Perimeter (P) assume a side slope.

**Step 4:** Calculate the bed slope (S) from the equation below

S = f^(5/3)/(3340 x Q^(1/6))

Even though it was an improved version of Kennedy's theory, there were some drawbacks to this theory.

### Drawbacks of Lacey's theory

Equations are empirical.

A single factor, f is not adequate to define the silt characteristics.

Silt grade and silt charge are not differentiated.

The concentration of silt is not included.

**Now, Try this question out! **

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