# Lacey’s regime Silt theory of Canal Design

According to ** Lacey** Natural streams have a tendency to assume a

**, the**

*semi-elliptical shape***, while the finer the material carried, the more the section approaches a semi-circle.**

*coarser the silt, the flatter and wider the semi-ellipse*A channel flowing in its own silt will, if continued interfered with, reach final stability, and where the conditions of discharge and silt remain constant final regime will be obtained in time.

If a canal is designed with a section too small for a discharge and its slope is kept steeper than required, scour will occur till the final regime is obtained.

** Related Article: **Kennedy’s Silt Theory: concept, formula, Drawbacks

According to Lacey, the ratio of bed width to depth affects the silt-bearing capacity of the channel or in other words, the shape of the channel for a given discharge is a function of the silt grade. Channel in finer material being narrower and deeper.

There is only one section of a channel and only one slope at which the canal carrying a given discharge will carry a particular grade of silt. For constant silt grades, the ratio of the bed width to depth steadily diminishes with a reduction in discharge.

**Requirement of a regime channel**

A channel will be in regime if it flows incoherent unlimited alluvium of the same character as that transported and the silt grade and silt charge are all constant.

** Regime conditions:**– For a regime channel following conditions should be satisfied :

i) The channel is flowing in unlimited incoherent alluvium of the same character as that transported.

ii) Silt charge and silt grade are constant.

iii) Discharge is constant.

iv) Sediment characteristics-constant.

v) Flow-uniform

*Assumptions in lacey’s theory*

*Assumptions in lacey’s theory*

- The silt-supporting eddies are generated from the bottom as well as from the die sides of channel. Kennedy neglected the eddies from the sides but Lacey did not.

2. Grain-size of the silt is an important factor. Silt factor (f) is produced in Lacey’s equation which depends upon the particles size, *f=176√d*

Which *d=av. particle size in ‘mm’*

- Kennedy said that the channel will be under the regime channel if there is neither silting nor scouring in the channel.
- But Lacey states that even a channel showing no silting is no Scouring may actually not be in the regime.
- Here are three regime conditions.

(1) True regime

(2) Initial regime

(3) Final regime

- Lacey’s theory is applicable only to the true regime & final regime.
- Lacey stated that the dimensions, depth, width & stripe of the regime channel to carry a given discharge, loaded with a given sediment concentration are fixed by nature.

*Lacey’s design Procedure*

*Lacey’s design Procedure*

1. Calculate the sift factor, f=1.76√mr

2. Calculate velocity of flow, **V= {Qf ^{2}/140}^{(1/6)}**

3. Find c/s area, A= Q/V

4. Find wetted perimeter, P=4.75√Q

5. A=BD+( D^{2})/2

P=B+D√5

6. Work out the hydraulics radius

R= 5/2 (v^{2}/f)

7. knowing these values, the channel section is known and the slope is obtained:

Calculate,** S= f ^{(5/3)}/ 3340Q^{(1/6) }**

*Defects of Lacey’s Theory*

(1) Lacey did not properly define the silt & silt charge.

(2) Lacey introduced semi-ellipse as ideal shape of a regime channel which is not correct.

(3) Strikingly speaking an artificial channel is not a regime channel & regime theory can not be applicable to it.

(4) Alluvium (erodible channels carrying clear water)

- Alluvium channels carrying clear water should be designed in such a way that the erodible materials of the boundary are not scouring.
- The design of such a channel is therefore based on the tractive force theory.
- The scour on the channel bed occurs when the tractive force on the bed exerted by the flow is adequate to cause the movement of the particles.
- A sediment particle resting on a side slope of the channel will be more due to the resultant tractive force in the component of gravitational force, which makes the particle roll or slide down the side slope.

*Comparison of Kennedy and Lacey’s theory*

*Comparison of Kennedy and Lacey’s theory*

Following table shows difference between Kennedy and Lacey silt theory of canal design:

Kennedy theory | Lacey theory |

1) Kennedy introduced the term m(C.V.R) in his equations for different grades of channels but did not give any idea to measure its value. V=0.55 m D^{0.64} | 1) Lacey introduced a concept of silt factor ‘f in his equation and suggested a method to determine V V=√(2/5)fR, f=1.76√mr |

2) Lacey assumed that the silt is in suspension due to the vertical eddies raised from the bottom and side of channels. | 2) Kennedy assumed that the silt is in suspension due to the vertical eddies raised from the bottom of the bed of the channel only. |

3) Kennedy used Kutter’s formula to find the mean of the canal. | 3) Lacey give own formula, V= {Qf^{2}/140}^{(1/6)} |

4. Kennedy gave no formula for the longitudinal slope of the canal. | 4)Lacey gave the formula S= f^{(5/3)}/ 3340Q^{(1/6)} |

5. Kennedy simply gave the idea that a non-silting, non-scouring velocity channel will be a regime channel. | 5) Shape gave regime channel will be semi-elliptical. |

### Use of Lacey regime diagram

These diagrams have been prepared by Lacey to provide a graphical procedure for channel design. There are two separate diagrams. One is used for determining bed width, and depth, and the other to determine the regime slope.

The diagrams have been plotted for the channel section having side slopes of (1/2):1. The procedure of channel design with the depth help of these diagrams is given below:

i) Find the intersection of discharge, Q, and silt factor, (Plate-viic)

ii) Find the bed width from the abscissa and the value of depth from the ordinate corresponding discharge.

iii) Determine the regime slope, s. Use plate vii (c), Find again the intersection and discharge, Q with silt factor f.

iv) Read the value of the ordinate corresponding to this point of intersection and determine slope, S.

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