Hydrology and Irrigation

Syllabus

• Hydrology: hydrologic cycle, precipitation, evaporation, evapotranspiration, infiltration, watersheds, hydrographs and unit hydrographs, flood estimation and routing, reservoir capacity, groundwater and well hydraulics.
• Irrigation: crop water requirements, duty, delta and base period, irrigation methods and efficiencies, design of lined and unlined canals (Kennedy and Lacey), cross-drainage works, gravity dams and spillways.

Key concepts and formulas

Precipitation. Average rainfall over a basin: arithmetic mean, Thiessen polygons (area-weighted), or isohyets. A missing record can be estimated by the normal ratio method: P_x = (N_x/n) Σ (P_i/N_i).

Infiltration. Horton's equation f = f_c + (f₀ − f_c)e^−kt. The φ-index is the constant loss rate such that rainfall above it equals the observed runoff.

Rational method: Q = CIA/3.6, with Q in m³/s, I in mm/h and A in km² (C is the runoff coefficient). The design intensity is for a duration equal to the time of concentration.

Unit hydrograph. The direct runoff hydrograph from 1 cm of effective rain falling uniformly over the basin in a given duration. Runoff from P cm of effective rain is P times the ordinates (linearity). The area under a unit hydrograph equals 1 cm of runoff over the catchment: Σ Q Δt = A × 0.01 m.

Flood routing. Muskingum: storage S = K[xI + (1 − x)Q], and O₂ = C₀I₂ + C₁I₁ + C₂O₁ with C₀ + C₁ + C₂ = 1.

Well hydraulics (steady flow).

• Confined aquifer of thickness b (Thiem): Q = 2πKb(H − h)/ln(R/r)
• Unconfined aquifer (Dupuit): Q = πK(H² − h²)/ln(R/r)
• Transmissivity T = Kb.

Irrigation.

• Delta Δ (total depth of water for a crop), duty D (hectares per cumec), base period B (days): Δ = 8.64B/D metres.
• Consumptive use, effective rainfall, and net and gross irrigation requirements; irrigation efficiencies (conveyance, application).
• Lacey's regime theory: velocity V = √(2fR/5), wetted perimeter P = 4.75√Q, and silt factor f = 1.76√d (d = mean particle size in mm).
• Gravity dam: the resultant must lie within the middle third to avoid tension at the heel; the uplift pressure acts at the base.

Worked example

A crop has a base period of 120 days and a duty of 1728 ha/cumec. Find its delta. A catchment of 2.5 km² with C = 0.4 receives a design storm of 60 mm/h: find the peak runoff by the rational method. Finally, find the discharge from a fully penetrating well in a confined aquifer.

import math

B, D = 120, 1728
print(f"delta = {8.64 * B / D:.3f} m")
C, I, A = 0.4, 60, 2.5
print(f"rational method Q = {C * I * A / 3.6:.3f} m3/s")
K, b, H, h, R, r = 30 / 86400, 20, 40, 34, 500, 0.15   # K in m/s (30 m/day)
Q = 2 * math.pi * K * b * (H - h) / math.log(R / r)
print(f"confined well Q = {Q:.5f} m3/s = {Q * 86400:.1f} m3/day")

delta = 0.600 m
rational method Q = 16.667 m3/s
confined well Q = 0.03227 m3/s = 2788.5 m3/day

Practice questions