Design of Canal/Basic Design Parameters/Design Theories for Unlined Canals/Kennedy’s Theory/Lacey’s Theory

Design of Canal

Designing an irrigation canal is a balancing act. The goal is to create a channel that carries the required amount of water without silting (mud settling and blocking the flow) or scouring (water flowing so fast it erodes the canal bed).

Basic Design Parameters

Before drawing any shapes, engineers must determine:

• Discharge (Q): The volume of water required per second (measured in m^3/s or Cusecs). This depends on the area to be irrigated and the "Duty" of the water.

• Rugosity Coefficient (n): The roughness of the canal surface. A smooth concrete lining has a lower n than a grassy earth canal.

• Bed Slope (S): The longitudinal tilt given to the canal so water flows by gravity.

The Cross-Section (Trapezoidal)

Most irrigation canals are designed with a Trapezoidal shape because it is the most hydraulically efficient and stable for earthwork.

Geometric Formulas:

        Area (A):  A = (b + ny)y

        Wetted Perimeter (P):=b+2√(1+n²)

        Hydraulic Radius (R): R = A / P

(Where b = bed width, y = depth of flow, and n= side slope ratio)

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Design Theories for Unlined Canals

In India, two classic theories are used to design "Regime Channels" (canals that neither silt nor scour):

A. Kennedy’s Theory

Kennedy proposed that the silt is kept in suspension by the "eddy currents" generated from the bed of the canal.

• Critical Velocity (Vo): The velocity that keeps the channel free from silting and scouring.

• Formula: Vo = 0.55•m•y^0.64

        (where m is the critical velocity ratio).

B. Lacey’s Theory

Lacey improved on Kennedy's work by stating that eddies are generated from the sides as well as the bed. He introduced the "Silt Factor" (f).

• Perimeter Formula: P = 4.75√Q

    (This is a famous rule used to find the width of the canal based solely on discharge).

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Design of Lined Canals

Lined canals are much simpler to design because the concrete surface is rigid. We use the Manning’s Formula to find the velocity (V)

V = (1/n)R⅔S½

Because the lining prevents erosion, we can use much higher velocities, which allows the canal to be smaller and cheaper to excavate compared to an unlined one.

$$
r squared

Final Design Steps

1. Calculate Q based on crop requirements.

2. Fix the Side Slopes based on the type of soil (e.g., 1:1 for hard soil, 2:1 for loose sand).

3. Find Dimensions (b and y) using Kennedy’s or Lacey’s equations.

4. Add Freeboard: Usually 0.5m to 0.75m of extra height above the water level for safety.

5. Check for Velocity: Ensure the velocity is between the non-silting and non-scouring limits (usually 0.6 m/s to 1.5 m/s).

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Eddy Currents/Kennedy's theory

Kennedy’s theory is based on the idea that silt is kept in suspension by the vertical components of eddy currents.

• Origin of Eddies: These eddies are generated due to the friction of flowing water against the roughness of the canal bed.

• The Balancing Act: If the velocity is high enough to generate eddies that counteract the weight of the silt, the silt stays suspended. If the velocity drops, silting occurs.

Critical Velocity (Vo)

Kennedy defined "Critical Velocity" as the mean velocity that is just sufficient to keep the channel free from silting and scouring.

The Formula:

Vo = = 0.55•m•y^0.64

Where:

• Vo = Critical velocity (m/s)

• y = Depth of water flow (m)

Critical Velocity Ratio (C.V.R or m)

Kennedy later realized that the type of silt differs by region. He introduced a factor m to account for this:

V = = 0.55•m•y^0.64

• For Fine Silt (Sands of South India): m = 0.7 to 0.9

• For Standard Silt (Upper Bari Doab): m = 1.0

• For Coarse Silt: m = 1.1 to 1.2

Design Procedure

Since Kennedy did not provide a direct formula to find the dimensions ($b$ and $y$), the design is an iterative (trial and error) process:

1. Assume a trial depth (y).

2. Calculate Vo using Kennedy's formula: Vo = 0.55•m•y^0.64

3. Find the Area (A): A = Q / Vo

4. Find Bed Width (b): Use the trapezoidal area formula A = (b + ny)y.

5. Calculate the Actual Velocity (V): Use Manning’s or Kutter’s formula:

   V = (1/n)R⅔S½

6. Compare: If the calculated V matches your Vo, the design is correct. If not, assume a new depth and repeat.

Limitations of Kennedy’s Theory

While revolutionary at the time, the theory has several flaws:

• Bed vs. Sides: He assumed eddies are generated only from the bed. In reality, eddies are also generated from the side slopes of the canal.

• Silt Concentration: He did not account for the amount of silt, only the type (m).

• No Slope Formula: He didn't provide a way to calculate the ideal bed slope; it must be assumed or taken from Kutter's formula.

• b/y Ratio: The theory doesn't specify a fixed ratio between width and depth.