Irrigation Engineering
Crop water requirement, duty, delta and base period, consumptive use, irrigation efficiencies, soil moisture and frequency of irrigation, Lacey's and Kennedy's silt theories, and canal structures.
Irrigation supplies water to crops when rainfall is not enough. GATE asks about water requirement calculations, canal design by the silt theories, and hydraulic structures.
Duty, delta and base period
- Delta (Δ): total depth of water a crop needs over its base period.
- Duty (D): area irrigated per cumec of continuous flow (ha/cumec).
- Base period (B): days from first to last watering.
- Relation: Δ = 8.64 B/D (Δ in m, B in days, D in ha/cumec).
- Duty is higher at the field than at the canal head (losses on the way).
- Crop period ≥ base period.
Water requirement
- Consumptive use (CU): evapotranspiration + water in plant tissue. Net irrigation requirement = CU − effective rainfall.
- Field irrigation requirement = net requirement / application efficiency; gross = field requirement / conveyance efficiency.
- Efficiencies: conveyance, application, storage, and uniformity (distribution).
Soil moisture: field capacity (water held after free drainage), permanent wilting point, and available moisture = FC − PWP. Water depth to apply:
d = (γ_d/γ_w) D (F_c − m₀), with D = root depth and m₀ the moisture content at which irrigation starts. Frequency = d/(daily consumptive use).
Canal design: silt theories
Kennedy's theory: critical velocity V₀ = 0.55 m y^0.64 (m = critical velocity ratio); trial and error with Kutter's formula.
Lacey's regime theory:
- Silt factor f = 1.76 √d (d = particle size in mm).
- Velocity: V = (Q f²/140)^(1/6).
- Hydraulic radius R = (5/2)(V²/f); wetted perimeter P = 4.75 √Q.
- Regime slope S = f^(5/3)/(3340 Q^(1/6)).
Canal structures
- Weirs and barrages on permeable foundations: Bligh's creep theory (creep length L = C × H, safe if the hydraulic gradient H/L ≤ 1/C) and Khosla's theory (uplift pressures from the potential flow; exit gradient G_E = (H/d)(1/(π√λ))).
- Cross-drainage works: aqueduct (canal over drain), super-passage (drain over canal), syphon, level crossing.
- Canal falls, regulators, outlets (modular, semi-modular).
Worked example
A crop has B = 120 days and duty 1728 ha/cumec at the field.
- Δ = 8.64 × 120/1728 = 0.6 m.
Practice
The delta of a crop is 1.2 m and its base period 100 days. What is the duty in ha/cumec?
Show answer and explanation
Answer: 720D = 8.64B/Δ = 864/1.2 = 720 ha/cumec.
By Lacey's theory, what is the wetted perimeter (m) of a regime canal carrying 64 m³/s?
Show answer and explanation
Answer: 38P = 4.75√Q = 4.75 × 8 = 38 m.
Root zone depth 1 m, field capacity 30%, irrigation starts at 18%, dry unit weight of soil 15 kN/m³ (γ_w = 10). What depth of water (mm) should be applied?
Show answer and explanation
Answer: 180d = (γ_d/γ_w) D (F_c − m₀) = 1.5 × 1 × 0.12 = 0.18 m = 180 mm.
A cross-drainage work where the canal passes over a natural drain, with the drain flowing freely below, is called:
Show answer and explanation
Answer: AIn an aqueduct the canal is carried over the drain; in a super-passage the drain passes over the canal.