# Lacey’s Silt Theory of Canals

### Lacey’s Silt Theory of Canals

According to what I know, Lacey’s silt theory is a method for designing irrigation canals that considers the interaction between water flow and sediment transport. It was developed by G. Lacey in the early 20th century.

Lacey’s silt theory is based on the idea that a stable canal, one that does not silt up or erode, is in a state of equilibrium where the amount of sediment being transported by the water is equal to the amount of sediment being deposited. This equilibrium is known as the regime condition.

Lacey identified three regime conditions:

• True regime: This is the ideal condition where the canal is in perfect equilibrium, with no silting or scouring. However, Lacey acknowledged that this condition is rarely achieved in practice.
• Initial regime: This condition occurs when the bed slope of the canal is affected by silting or scouring, but other parameters, such as the width and depth, remain relatively constant.
• Final regime: This condition occurs when all the parameters of the canal, including the bed slope, width, and depth, are changing in response to the flow rate and sediment grade.

Lacey’s theory focuses on the final regime condition, which he considered to be the most practical and achievable. He proposed that the ideal shape for a regime channel is a semi-ellipse.

Lacey’s theory uses a number of empirical equations to calculate the design parameters of a canal, including:

• Silt factor: This is a measure of the size and shape of the sediment particles being transported by the water.
• Velocity: This is the speed of the water flow in the canal.
• Area: This is the cross-sectional area of the canal.
• Hydraulic depth: This is the ratio of the area of the canal to its wetted perimeter.
• Bed slope: This is the angle of the canal bed.

Canal Design using Lacey’s Silt Theory

Lacey’s design procedure for building a canal involves the following steps:

• Canal discharge (Q) and mean particle size (dm) should be known.
• From the mean size or diameter of the particle (dm), silt factor is first calculated using the below expression:
• Silt factor values for different types of soils are tabulated here.
• Using discharge and silt factor, velocity (V) can be calculated by the expression as follows:
• After attaining the velocity of canal flow, find the area of the canal by dividing discharge with velocity. Also, find the mean hydraulic depth (R) of the canal and wetted perimeter (P) of the canal.
• Assume the bed slope (S) value or find by substituting the values of silt factor and canal discharge in the following formula:

Drawbacks of Lacey’s Silt Theory

Lacey’s silt theory has several drawbacks, including:

• Lacey did not explain the properties that govern the alluvial channel.
• In general, flow is different at the bed and sides of the channel which requires two different silt factors but Lacey derived only one silt factor.
• The semi-elliptical shape proposed by Lacey as the ideal shape of the channel is not convincing.
• Lacey did not consider the silt concentration in his equations.
• Attrition of silt particles is ignored by Lacey.
• Lacey did not give proper definitions for the silt grade and silt charge.

Numerical Problem:

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