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01
Introduction to Irrigation
Why we irrigate, the forms irrigation takes, and how water is finally applied to the field.
Memory Map — Introduction to Irrigation
💧Irrigationartificial supply of water to crops
🌧️Flow / Inundationperennial vs flood (inundation) irrigation
⬇️Lift Irrigationwater lifted by pumps from source
🚿Sprinkler & Dripmicro-irrigation, ~90% efficiency
📏Duty (D)area (ha) irrigated per cumec of water
🌊Delta (Δ)total depth of water (cm); Δ = 8.64B/D
⏱️Base Period (B)days from 1st to last watering of crop
🌾Kharif & Rabimonsoon vs winter cropping seasons
Memory hook
"Lift Big Buckets, Flow Soon, Drip Sub"
Irrigation methods: Lift → Border & Basin (flooding) → Furrow → Sprinkler → Drip → Sub-surface
Classification of irrigation
Irrigation
Surface
Flow (gravity)
Lift (pumped)
Sub-surface
Key definitions — Irrigation glossary
Irrigation
Artificial application of water to soil for growing crops, supplementing rainfall.
Flow / lift irrigation
Flow = water supplied by gravity; lift = water pumped up from a source.
Perennial / inundation
Perennial = continuous supply from a weir/dam; inundation = land flooded only during high river stage.
Base period (B)
The period (days) from the first watering to the last watering of a crop.
Crop period
Time from sowing to harvesting (slightly longer than base period).
Delta (Δ)
Total depth of water (cm/m) required by a crop over its base period.
Duty (D)
Area (ha) that 1 cumec of water can irrigate for the whole base period. Δ = 8.64B/D.
Kor depth / kor period
Depth & duration of the first (most critical) watering of a young crop; fixes the canal's peak capacity.
Paleo watering
Watering done before sowing to prepare the soil.
GCA / CCA
Gross command area = total commandable; culturable command area = the cultivable part of it.
Intensity of irrigation
(Area irrigated in a season ÷ CCA) × 100%.
Outlet / time / capacity factor
Outlet duty · ratio of running days to base period · ratio of mean to design discharge.
Cumec / cumec-day
1 cumec = 1 m³/s; 1 cumec-day = 8.64 hectare-metres of water.
Consumptive use (Cu)
Total water lost by evaporation + transpiration (evapotranspiration) plus that used in plant tissue.
Effective rainfall
The part of rainfall actually useful to the crop (stored in the root zone).
NIR / FIR / GIR
Net = Cu − effective rainfall; Field = NIR ÷ application eff.; Gross = FIR ÷ conveyance eff.
Field capacity
Moisture retained by soil after gravity drainage; upper limit of available water.
Permanent wilting point
Moisture content at which the plant can no longer extract water and wilts permanently.
Regime channel
An unlined channel in which silting = scouring, so the section & slope are stable over time.
Silt factor (f)
Lacey's measure of silt coarseness: f = 1.76√d (d in mm).
Critical velocity (Vo)
The non-silting, non-scouring velocity in a channel (Kennedy: Vo = 0.55 m y^0.64).
CVR (m)
Critical velocity ratio = actual velocity ÷ critical velocity; indicates silt grade.
Afflux
The rise in upstream water level caused by a weir/obstruction across a river.
Freeboard
Vertical margin between the full-supply level and the top of the canal bank.
Creep / uplift
Creep = seepage path under a structure; uplift = upward water pressure on the floor from that seepage.
Exit gradient / piping
Hydraulic gradient where seepage leaves the floor; if it exceeds the critical value, soil is washed out (piping/undermining).
Water-logging
Rise of the water table to the root zone, harming crops; remedied by lining, drainage & controlled irrigation.
Definition, need & ill-effects basics
Irrigation = artificial application of water to soil, at the right time & quantity, to grow crops — supplementing rainfall.
- Need: insufficient / ill-timed rainfall, perennial & cash crops, higher yield & cropping intensity.
- Advantages: more yield, drought protection, hydropower/navigation by-products, prosperity.
- Ill-effects: water-logging, salinity/alkalinity, dampness & water-borne disease, loss of fertile land.
Types of irrigation types
- Flow irrigation — by gravity.
- Perennial: direct (weir/barrage) or storage (dam & reservoir).
- Inundation: land flooded during high river stage only.
- Lift irrigation — water pumped from wells/tanks/rivers.
- Sub-surface — natural (high water table) or artificial (buried perforated pipes).
Methods of application & kor watering field
| Method | Note |
|---|---|
| Border / Check-basin / Furrow / Basin | Surface methods; check-basin most common. |
| Sprinkler | Sprayed like rain; saves water, undulating land. |
| Drip (trickle) | Highest efficiency (~90%); orchards. |
Exam focus Kor watering = first watering to a young crop; kor depth & kor period (rice ≈19 cm/14–21 d; wheat ≈13.5 cm/28 d) fix the maximum canal capacity.
Worked example — Duty, Delta & Area irrigated
A canal carries a discharge of 25 m³/s. The duty of water for a crop is 1000 hectares per cumec. The base period of the crop is 100 days. Find (i) the area irrigated, and (ii) the delta (depth of water) for the crop.
Step 1 Relation between area (A), discharge (Q) and duty (D): A = Q × D. Here Q = 25 m³/s (cumec) and D = 1000 ha/cumec.
Step 2 Area irrigated A = 25 × 1000 = 25000 hectares.
Step 3 Delta–Duty–Base relation: Δ = 8.64 × B ÷ D, where Δ is in metres, B = base period in days, D = duty in ha/cumec.
Step 4 Substitute B = 100 days, D = 1000 ha/cumec: Δ = (8.64 × 100) ÷ 1000 = 864 ÷ 1000 = 0.864 m.
Step 5 Convert delta to cm: Δ = 0.864 × 100 = 86.4 cm of water depth over the field.
Answer: Area irrigated = 25000 hectares and Delta = 0.864 m (86.4 cm).
Kazama says: "Listen carefully! Duty is like one farmer feeding a whole crowd from a single water tap, while Delta is just the puddle of water sitting on one plate. Big Duty means the water is generous and feeds MORE hectares per cumec, so naturally the Delta on each field gets smaller, all over the Base Period the crop is hungry!"
💥 Interactive Flow: Deriving Delta-Duty Relation (Δ = 8.64B / D)
Click "Advance Flow" to pull the derivation step-by-step!
Step 1 A discharge of 1 cumec (1 m³/s) flows continuously for the whole Base Period B (in days). Convert B days to seconds → total seconds = B × 24 × 60 × 60 = 86400B.
Step 2 Volume of water supplied = discharge × time = 1 × 86400B = 86400B m³. By definition, 1 cumec irrigates an area equal to the Duty D (in hectares).
Step 3 Spread this volume over the area D hectares. Convert hectares to m² → Area = D × 104 m².
Step 4 Delta Δ = depth = VolumeArea = 86400 × BD × 104 metres = 8.64 × BD metres.
Kinetic formulas — tap Animate! animated
Tap each formula to watch it rearrange itself in mid-air.
Delta (depth of water) · Δ = (8.64 × B) / D
Δ
×
D
=
8.64
×
B
02
Water Requirements of Crops
The numbers chapter — crop seasons, the delta–duty–base-period triangle, command areas & efficiencies.
Animated lab — duty, delta & base period
1 cumec flowing for the whole base period irrigates D hectares; spread over that area the water stands Δ = 8.64B/D metres deep. Slide either one and watch the water depth on the field respond.
Δnote
Memory Map — Water Requirements of Crops
💧Delta (Δ)total water depth per crop, in cm
⏱️Base Period (B)days from 1st watering to last, in days
🌊Duty (D)area irrigated per cumec, in ha/cumec
📏Delta RelationΔ = 8.64 B / D (cm)
☠️Kor Watering1st watering after sowing; max depth
🌾Crop Period > Basecrop period ≥ base period
🔥Consumptive Useevapotranspiration = E + T (mm/day)
🧪Effective Rainfallrain useful to crop, subtract from CU
Memory hook
"Delta Drinks By the Base"
Stands for: Delta Δ (total depth of water, cm/m) → Duty D (area irrigated per unit discharge, ha/cumec) → Base period B (crop days) — linked by Δ = 8.64×B/D (B in days, D in ha/cumec, Δ in m).
Water Requirements of Crops
Crop Water Need
Water Requirement
Consumptive Use
Evaporation
Transpiration
Effective Rainfall
Duty & Delta
Delta Δ
Duty
Irrigation Frequency
Tap any box to see what it means
Crop SeasonsDelta, Duty & Base PeriodDuty Relations & ImprovementCommand Areas & EfficienciesConsumptive Use & FrequencySoil–Water Classificat...
Crop Seasons & Crop Period basics
Crop period = the time (in days) from sowing of a crop to its harvesting; base period = the time between the first watering at sowing and the last watering before harvest (slightly less than crop period, but taken equal in problems).
| Season | Period (India) | Typical crops |
|---|---|---|
| Kharif (monsoon) | Jun–Oct/Nov | Rice/paddy, jowar, bajra, maize, cotton, groundnut |
| Rabi (winter) | Oct/Nov–Mar | Wheat, barley, gram, mustard, peas |
| Zaid (hot weather) | Mar–Jun | Watermelon, cucumber, vegetables, fodder |
- Kharif (wet) crops: need more water; sown with the monsoon. Paddy is the heaviest user.
- Rabi (dry) crops: need less water, mostly supplied by irrigation since rainfall is low.
- Crop ratio: ratio of area under rabi to area under kharif, usually kept near 1 : 1.
- Crop rotation: growing different crops on the same land in sequence to restore fertility (e.g. legume after cereal fixes nitrogen).
Paleo irrigation
Watering the land BEFORE sowing the crop (pre-sowing watering).
Kor watering
First watering after the plant has grown a few cm high; depth/period are critical and govern outlet design.
Overlap allowance
Extra capacity given to a canal because two crop periods overlap and demand water simultaneously.
Delta, Duty & Base Period core
Delta (Δ) = total depth of water (in cm or m) required by a crop over its entire base period. Duty (D) = area (in hectares) that can be irrigated by a unit discharge (1 cumec) supplied continuously over the base period.
Delta from duty & base period
Δ = 8.64 × BD (metres)
Δ = delta, m; B = base period, days; D = duty, ha/cumec. Multiply by 100 for cm.
Duty from delta & base period
D = 8.64 × BΔ
D = duty, ha/cumec; constant 8.64 comes from 86400 s/day ÷ 10000 m²/ha.
Derivation of 8.64
Δ (m) = VolumeArea = 1 × (B × 86400)D × 10000 = 8.64 BD
1 cumec flowing for B days = B×86400 m³ spread over D×10000 m².
| Crop | Δ (cm) | Duty (ha/cumec) |
|---|---|---|
| Rice / Paddy | 100–130 | ~775 |
| Wheat | 40 | ~1800 |
| Sugarcane | 90–120 | ~600–800 |
| Cotton | 40–45 | ~1400 |
Solved: Base period B = 120 days, duty D = 1500 ha/cumec. Δ = 8.64×120/1500 = 0.6912 m = 69.1 cm.
Exam focus Memorise Δ(m) = 8.64B/D. The 8.64 constant gives Δ in METRES (multiply by 100 for cm). Smaller delta or longer base period → higher duty → more area irrigated per cumec.
Duty Relations & Its Improvement duty
Inverse rule: Duty is inversely proportional to delta — a crop needing less water (small Δ) has a high duty, so a given canal can serve a larger area.
- Flow duty ↔ Quantity duty: flow duty is expressed in ha/cumec; quantity duty (or volumetric) in ha/Mm³.
- Duty rises moving up the system: duty at the field < at the outlet < at the distributary head < at the canal head, because losses (transit + field) are deducted as we go.
- Lower the system point, the more losses already accounted, so a smaller duty value.
- Highest duty is at the field/farm where no transit loss is left.
- Factors increasing duty: good land levelling, lined canals, rotational supply (warabandi), light soil with low percolation handled, proper kor depth, timely watering, less conveyance loss.
- Factors lowering duty: sandy/porous soil, hot climate (high evaporation), undulating land, poor maintenance, water-logging.
Discharge required for an area
Q = AD
Q = discharge, cumec; A = area to irrigate, ha; D = duty, ha/cumec.
Solved: Irrigate 4500 ha of wheat, duty 1800 ha/cumec. Q = 4500/1800 = 2.5 cumec at the field.
Quick revision Q&A
Q1. Where is duty maximum — canal head or field?
At the field (farm), because all conveyance/transit losses have already been deducted upstream.
Q2. If delta doubles and base period is fixed, what happens to duty?
Duty becomes half (D ∝ 1/Δ).
Q3. Name two ways to improve duty.
Canal lining (cut seepage) and rotational/warabandi supply (cut wastage).
Command Areas & Irrigation Efficiencies efficiency
GCA, CCA & intensity describe how much land a canal commands and how much is actually cropped; efficiencies measure water lost between source and root zone.
GCA
Gross Command Area — total area bounded by the canal that can be irrigated (includes uncultivable land, villages, roads).
CCA
Culturable Command Area — the area of GCA fit for cultivation (GCA minus unculturable area).
Intensity of irrigation
% of CCA actually irrigated in a crop season; sum of kharif + rabi intensities = annual intensity.
Intensity of irrigation
I = Area irrigated in seasonCCA × 100%
Express as a percentage of culturable command area.
Conveyance efficiency
ηc = Water delivered to fieldWater entering canal
Accounts for evaporation + seepage losses in canals.
Application (field) efficiency
ηa = Water stored in root zoneWater delivered to field
Fraction of delivered water actually retained for the crop.
Overall efficiency
ηo = ηc × ηa
Source-to-root-zone efficiency = product of all stage efficiencies.
| Efficiency type | Typical value |
|---|---|
| Conveyance ηc (lined) | ~85–90% |
| Application ηa | ~60–80% |
| Water-use efficiency & uniformity | varies |
- Water distribution efficiency: measures how uniformly water spreads over the field; 100% − (mean deviation / mean depth).
- Water-use efficiency: crop yield per unit of water consumed; key for productivity.
Solved: ηc = 90% and ηa = 70%. Overall ηo = 0.90×0.70 = 0.63 = 63%. Of 100 units at source only 63 reach the root zone.
Consumptive Use, Effective Rainfall & Frequency advanced
Consumptive use (Cu) = water evaporated + transpired by the crop + water used in plant tissue ≈ evapotranspiration (ET) for that crop; basis for actual field water demand.
- Potential ET (PET): ET when soil water is unlimited; estimated by Blaney–Criddle, Penman, or Hargreaves methods.
- Effective rainfall: the part of rainfall actually stored in the root zone and usable by the crop (runoff & deep percolation excluded).
- Net irrigation requirement (NIR) = Consumptive use − effective rainfall − ground-water contribution.
- Field/Gross irrigation requirement = NIR ÷ application efficiency (and further by conveyance efficiency for canal head).
Frequency of irrigation
f = Readily available moisture (depth)Daily consumptive use
f = interval between waterings, days. Larger storage or lower Cu → less frequent watering.
Depth of water stored in root zone
d = γd × dr × (FC − w)100
d = depth, m; dr = root depth; FC = field capacity %, w = moisture before watering %; γd relative to water density.
Field capacity
Moisture held by soil against gravity after free drainage; upper limit of available water.
Wilting point
Moisture level below which plant cannot extract water and wilts permanently; lower limit.
Available moisture
Difference between field capacity and permanent wilting point.
Solved: Daily Cu = 5 mm, readily available moisture depth = 40 mm. Frequency f = 40/5 = 8 days between waterings.
Quick revision Q&A
Q1. Consumptive use is approximately equal to which quantity?
Evapotranspiration (ET) of the crop.
Q2. Name one empirical method to estimate PET.
Blaney–Criddle method (or Penman / Hargreaves).
Worked example — Delta from Duty & Base Period
Given Duty D = 1728 ha/cumec and Base period B = 115 days. Find the Delta (depth of water Δ) in cm.
Step 1 Standard relation between Delta, Base period and Duty: Δ = 8.64 × B ÷ D metres (B in days, D in ha/cumec).
Step 2 Substitute the given values: Δ = 8.64 × 115 ÷ 1728 m.
Step 3 Compute the numerator: 8.64 × 115 = 993.6, so Δ = 993.6 ÷ 1728 = 0.575 m.
Step 4 Convert to centimetres (× 100), or use Δ = 864 × B ÷ D cm = 864 × 115 ÷ 1728 = 99360 ÷ 1728 = 57.5 cm.
Answer: Δ ≈ 57.5 cm (0.575 m).
Delta from Duty & Base period
Δ = 864·B/D (cm) · B = base period (days), D = duty (ha/cumec)
Soil–Water Classification (FC, PWP, AW) notes
Gravitational water
Drains out freely under gravity; not retained — not available to plants.
Capillary water
Held by surface tension between soil particles against gravity — the only water actually available to plants for growth.
Hygroscopic water
Held tightly on particle surfaces by loose chemical bonds; unavailable to plants.
- Field Capacity (FC): moisture retained after gravitational water has drained.
- Permanent Wilting Point (PWP): moisture content below which the plant can no longer extract water and wilts/dies.
- Available Water (AW): AW = FC − PWP — the water available for root uptake.
- Readily Available Moisture (RAM): the fraction of AW that the crop can take up with little stress; OMC = optimum moisture content, the lowest level to which soil moisture is allowed to fall before re-irrigating.
Soil-Moisture Tension (SMT)
FC: SMT ≈ 0.1 – 0.33 atm | PWP: SMT ≈ 15 atm
SMT = force per unit area roots must overcome to extract water; measured by a tensiometer. Higher tension → drier soil → harder uptake.
Shin-chan says: "Duty is like how many friends ONE chocolate biscuit can feed at a sleepover! Big Duty means one water-stream irrigates a HUGE area, so each crop only gets a thin sip of Delta (the total water depth). Greedy crops with a long Base Period sip slowly for months... so don't be greedy like me with the biscuits!"
💥 Interactive Flow: Deriving Delta-Duty Relation (Δ = 8.64B/D)
Click "Advance Flow" to pull the derivation step-by-step!
Step 1 Duty D = area (hectares) irrigated by a steady flow of 1 m³/s (cumec) running for the whole Base Period B (days). So 1 cumec irrigates D hectares.
Step 2 Total volume supplied by 1 cumec over B days = flow × time = 1 × (B × 24 × 60 × 60) = 86400 × B m³.
Step 3 This volume is spread over the Duty area D hectares = D × 10⁴ m². Delta (Δ) is the depth of water = Volume ÷ Area → Δ = 86400 × BD × 10⁴ m.
Step 4 Simplify the constant: 86400 ÷ 10⁴ = 0.0864 m = 8.64 cm. Express Δ in cm → Δ = 8.64 × BD cm.
Delta · Duty · Base Period — animated interactive
Watch how the total volume of water forces Duty (D) into the denominator!
Δ
×
D
=
8.64
×
B
Read it: start with Δ × D = 8.64 × B (volume balance); click to fly D under the line → Δ = 8.64B / D.
Kinetic formulas — tap Animate! animated
Tap each formula to watch it rearrange itself in mid-air.
Delta from duty & base period · Δ = (8.64 × B) / D
Δ
×
D
=
8.64
×
B
Duty from delta & base period · D = (8.64 × B) / Δ
D
×
Δ
=
8.64
×
B
Discharge required for an area · Q = A / D
Q
×
D
=
A
Intensity of irrigation · I = (Aₐ × 100) / CCA
I
×
CCA
=
Aₐ
×
100
Conveyance efficiency · ηc = W₃ / Wₐ
ηc
×
Wₐ
=
W₃
03
Design of Canal
Figures: Canal Design - Cross-Sections & Kennedy's Theory
REFERENCE DIAGRAMS
Trapezoidal Canal
A = (B+zD)·D
P = B+2D√(1+z²)
R = A/P
z = side slope (H:V)
P = B+2D√(1+z²)
R = A/P
z = side slope (H:V)
Regime Channel Concept
Silt carried = Silt deposited
Scour: V > Vᵒ
Silting: V < Vᵒ
Regime: V = Vᵒ
Scour: V > Vᵒ
Silting: V < Vᵒ
Regime: V = Vᵒ
Kennedy's Formula
Vᵒ = 0.55·m·y⁰·⁶⁴
m=1.0: standard silt
m=1.2: coarse silt
m=0.8: fine silt/sand
m=1.0: standard silt
m=1.2: coarse silt
m=0.8: fine silt/sand
Lacey's Equations
P = 4.75√Q
A = Q/(0.439f¹⁄³)
R = Q¹⁄³/(2.47f²⁄³)
f = 1.76√dᵗ
A = Q/(0.439f¹⁄³)
R = Q¹⁄³/(2.47f²⁄³)
f = 1.76√dᵗ
Key Formulas: Canal Design
FORMULAS
Manning's Formula
V = R²⁄³ S½ / n
Q = A·V
n = 0.0225 (earthen)
n = 0.014 (concrete)
Q = A·V
n = 0.0225 (earthen)
n = 0.014 (concrete)
Bazin's & Chezy
V = C√(RS)
C = R¹⁄⁶/n (Manning)
C = 87√R/(K+√R) (Bazin)
K=Bazin's constant
C = R¹⁄⁶/n (Manning)
C = 87√R/(K+√R) (Bazin)
K=Bazin's constant
Canal Losses
Δ = 8.64D/d metres
D = duty (ha/cumec)
d = base period (days)
Loss ∼15-50% seepage
D = duty (ha/cumec)
d = base period (days)
Loss ∼15-50% seepage
Canal network & classification, silt-theory design (Kennedy & Lacey), lining economics and the most-economical section.
Memory Map — Design of Canal
🌊Kennedy's theoryV0 = 0.55 m y0.64 (critical velocity)
⚖Lacey's regimeV = 0.4382 (Qf2)1/6 ; silt factor f
🧮Silt factor ff = 1.76√dmm ; sand f ≈ 1.0
📐Lacey wetted PP = 4.75 √Q ; A = 2.28 Q5/6/f1/3
📉Bed slopeS = f5/3 / (3340 Q1/6) (Lacey)
🔢CVR (m)m = V/V0 ; m = 1 → non-silting
🗿Side slope1:1 (cutting) ; 1.5:1 (filling) in earth
▲Free board0.3–0.75 m above FSL of canal
Memory hook
"Kennedy's Velocity Makes Canals Run Smooth"
Kennedy's theory: V0 = 0.55 m y0.64 → m = critical velocity ratio (≈1 for ordinary silt), y = depth of water (m). Silt is kept in suspension by the eddies rising from the canal bed only.
Classification of canals
Canals
By Alignment
Ridge
Contour
Side-slope
By Supply
Perennial
Inundation
By Boundary
Alluvial
Lined/Unlined
Network & WarabandiKennedy's theoryLacey's theoryLining & economical sectionSediment Transport & Tra...Lacey's Normal Scour Depth n...
Canal system & alignment network
- Distribution: primary (main, branch) → secondary (distributary, minor) → tertiary (water-course, field channel).
- Warabandi — rotational water supply with each farmer's turn fixed by roster.
- Ridge canal = no CD works (most economical); contour canal = needs CD works.
Kennedy's theory silt
Channel is in regime when running at the critical velocity V₀ that keeps silt up; eddies rise from the bed.
Critical velocity
V₀ = 0.55 · m · y0.64
m = CVR: 1.3 much-coarser · 1.0 standard (Upper Bari Doab) · 0.6–0.7 very fine. Slope via Kutter's; B/D assumed → trial & error.
Drawback: no slope equation, no fixed B/D; CVR loosely defined.
Lacey's regime theory regime
True-regime channel; eddies rise from the whole wetted perimeter.
Silt factor
f = 1.76 √dmm
Wetted perimeter
P = 4.75 √Q
Regime velocity
V = (Qf²/140)1/6
Hydraulic radius
R = 2.5 V²/f
Regime slope
S = f5/3 / (3340 Q1/6)
Scour depth
R = 0.47 (Q/f)1/3
| Basis | Kennedy | Lacey |
|---|---|---|
| Silt kept up by | bed eddies | whole perimeter |
| Slope eqn | none (Kutter) | given |
| Design | trial & error | direct |
Lining & most-economical section design
- Lining advantages: cuts seepage (~90%), higher velocity → smaller section, prevents weeds/scour, raises duty.
- Economics: lining justified when benefit–cost ratio > 1; best lined section = trapezoidal with circular corners.
| Section | Most economical when | R |
|---|---|---|
| Rectangular | b = 2y | y/2 |
| Trapezoidal | half of a regular hexagon | y/2 |
| Circular (max Q) | depth = 0.95 D | ≈0.29 D |
Manning
V = (1/N)R2/3S1/2
Chezy
V = C√(RS)
Worked example — Canal design by Lacey's regime theory
Design a regime channel to carry Q = 30 m³/s of water in alluvium with silt factor f = 1.0. Find the velocity V, hydraulic radius R, wetted perimeter P and the regime slope S.
Step 1 Regime velocity: V = (Q·f² ÷ 140)1/6. Substitute → V = (30 × 1.0² ÷ 140)1/6 = (0.2143)1/6 = 0.783 m/s.
Step 2 Hydraulic mean radius: R = 2.5 × V² ÷ f = 2.5 × (0.783)² ÷ 1.0 = 2.5 × 0.613 = 1.533 m.
Step 3 Wetted perimeter (Lacey): P = 4.75 √Q = 4.75 × √30 = 4.75 × 5.477 = 26.02 m.
Step 4 Check area A = Q ÷ V = 30 ÷ 0.783 = 38.32 m²; also A = P × R = 26.02 × 1.533 = 39.9 m² (close → consistent regime section).
Step 5 Regime slope: S = f5/3 ÷ (3340 × Q1/6) = 1.0 ÷ (3340 × 301/6) = 1.0 ÷ (3340 × 1.763) = 1 ÷ 5890.
Answer: V = 0.783 m/s, R = 1.53 m, P = 26.0 m, bed slope S ≈ 1 in 5890.
Sediment Transport & Tractive Force notes
Bed load
Moves on or near the bed by sliding, rolling and hopping (saltation).
Suspended load
Remains in suspension and floats along with the flowing water.
Total / silt load
Total suspended sediment flowing with the water (bed load + suspended load).
Mechanism: flowing water exerts a tractive (shear) stress τ0 along the bed/sides; when it exceeds the permissible/critical tractive stress τc, sediment movement begins.
Shield's Theory — no-scour condition
τactual < τc → no scour / no movement
τc = critical (permissible) tractive stress for the boundary material; below it the channel boundary is stable.
Exam focus Tractive-force method is the basis of designing a non-scouring, stable channel boundary (alternative to regime/Kennedy approaches).
Lacey's Normal Scour Depth notes
Normal regime scour depth
R = 1.35 (q2 / f)1/3
R = normal scour depth below high flood level (m), q = discharge per unit width (m3/s per m), f = Lacey's silt factor. Used when the river/channel is in regime.
- Silt factor: f = 1.76 √dmm, where dmm is the mean particle size; coarser silt → higher f → shallower scour.
- Normal scour depth is the depth measured below the high flood level (HFL).
- For abnormal/concentrated flow conditions the scour depth is increased by an empirical multiplier of R.
Exam focus Scour depth governs the founding levels of weirs, bridge piers, guide bunds and launching aprons in river training works.
Kazama says: "Designing a canal is like Goldilocks picking porridge - if velocity is too slow, silt settles and the canal chokes; too fast, and it scours the bed away. Kennedy found the 'just right' non-silting non-scouring speed depends on depth: V0 = 0.55 m × y0.64. Memorize the eddies rising from the bed - they keep the silt dancing instead of dropping!"
💥 Interactive Flow: Deriving Kennedy's Critical Velocity
Click "Advance Flow" to pull the derivation step-by-step!
Step 1 Kennedy observed that silt is kept in suspension by eddies generated from the canal bed, so the non-silting velocity must depend on the flow depth y(depth).
Step 2 He proposed the critical velocity varies as a power of depth: V0 ∝ yn → V0 = C × yn, where C and n are constants from field data.
Step 3 Fitting observations from the Upper Bari Doab Canal gave C = 0.55 (in m units) and n = 0.64, so V0 = 0.55 × y0.64.
Step 4 To handle different silt grades, a critical velocity ratio m (m = V÷V0) is introduced for the actual silt type.
Kinetic formulas — tap Animate! animated
Tap each formula to watch it rearrange itself in mid-air.
Critical velocity · 0.55m = V₀ / y⁰∙⁶⁴
V₀
=
0.55m
×
y⁰∙⁶⁴
Hydraulic radius · R = 2.5V² / f
R
×
f
=
2.5V²
Regime slope · S = f⁵⁄³ / 3340Q¹⁄₆
S
×
3340Q¹⁄₆
=
f⁵⁄³
🔒
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