UNIT 3: WATER RESOURCE ENGINEERING – COMPREHENSIVE STUDY NOTES

(Based on RGPV CE-603(A) Past Examination Analysis)

1.0 FUNDAMENTALS OF HYDROLOGY AND PRECIPITATION

1.1 Hydrological Cycle

Definition: The continuous circulation of water on, above, and below the Earth's surface through evaporation, transpiration, condensation, precipitation, runoff, infiltration, and groundwater flow.

Key Components & Process:

1. Evaporation & Transpiration (Evapotranspiration): Water moves from surface/soil/plants to atmosphere.

2. Condensation: Water vapor cools to form clouds.

3. Precipitation: Water returns to Earth as rain, snow, etc.

4. Runoff: Water flows over land surface to streams/rivers.

5. Infiltration: Water enters soil, recharging groundwater.

6. Groundwater Flow: Subsurface movement to springs, oceans, or wells.

Exam Tip: Always sketch the cycle showing all major pathways (atmospheric, surface, subsurface) with directional arrows. Label key processes.

1.2 Precipitation

1.2.1 Rainfall Measurement

Methods of Areal Estimation:

• Point Measurement: Single gauge reading.

• Areal Estimation: Required for catchment rainfall. Methods:

  1. Arithmetic Mean: Simple average of all station readings. Suitable for uniform rainfall areas with uniform gauge distribution.

  2. Thiessen Polygon Method: Weighted average based on area of influence.

  3. Isohyetal Method: Contour mapping of rainfall, then planimeter area between contours.

1.2.2 Thiessen Polygon Method – Step-by-Step

1. Plot locations of all rain gauge stations on a map.

2. Connect adjacent stations with straight lines to form a network of triangles.

3. Construct perpendicular bisectors for each connecting line.

4. The polygon formed around each station by the bisectors defines its area of influence.

5. Measure the area of each polygon (planimeter or graph paper).

6. Compute weighted average:

$$P_{avg} = \frac{\sum (P_i \times A_i)}{\sum A_i}$$

where $$\displaystyle P_i $$ = rainfall at station $i$, $$\displaystyle A_i $$ = area of its polygon.

Common Pitfall: Forgetting to use polygon areas as weights; just averaging station values is incorrect for non-uniform gauge spacing.

1.2.3 Depth-Area-Duration (DAD) Curves

• Definition: Curves showing the maximum average depth of precipitation over a given area for a given duration.

• Significance:

  • Design Storm: Used to estimate Probable Maximum Precipitation (PMP) for large dams.

  • Flood Estimation: Higher intensity for smaller areas/durations; DAD curves help select appropriate storm for catchment.

  • Spatial Variation: Illustrates how rainfall becomes less intense as area increases (areal reduction factor).

• Construction:

  1. For a given duration (e.g., 24-hr), plot maximum rainfall isohyets.

  2. Calculate average rainfall for successively larger enclosed areas.

  3. Plot points (Area, Avg. Depth) and draw curve.

  4. Repeat for other durations (6-hr, 12-hr, 48-hr).

1.3 Evaporation (Analytical Methods for Lakes/Reservoirs)

• Energy Balance Method: Based on conservation of energy at water surface.

$$E = \frac{R_n - G - H - \lambda E}{\lambda}$$

where $$\displaystyle R_n $$ = net radiation, $G$ = soil heat flux, $H$ = sensible heat, $\lambda E$ = latent heat (often combined as *Bowen ratio*).

• Aerodynamic Method: Based on turbulent transfer of vapor.

$$E = C \cdot (e_s - e_a) \cdot u$$

where $C$ = coefficient, $$\displaystyle e_s $$ = saturation vapor pressure, $$\displaystyle e_a $$ = actual vapor pressure, $u$ = wind speed.

• Combination Method (Penman): Most widely used. Combines energy balance and aerodynamic principles.

$$E = \frac{\Delta (R_n - G) + \gamma \frac{900}{T+273} u_2 (e_s - e_a)}{\Delta + \gamma (1 + 0.34 u_2)}$$

where $\Delta$ = slope of vapor pressure curve, $\gamma$ = psychrometric constant, $T$ = temp (°C), $$\displaystyle u_2 $$ = wind speed at 2m.

2.0 SOIL-WATER-PLANT RELATIONSHIPS & CROP WATER REQUIREMENTS

2.1 Soil Moisture Characteristics

Calculation of Available Water (Depth):

$$\text{Depth of ASW (cm)} = (\theta_{FC} - \theta_{PWP}) \times \text{Depth of Root Zone (cm)} \times \text{Bulk Density}$$

where $\theta$ = volumetric or gravimetric moisture content.

Exam Tip: Problems often ask for "days between irrigation." Use ASW and daily consumptive use.

2.2 Crop Water Requirements

2.2.1 Consumptive Use (Evapotranspiration, ET)

• Definition: Total water used by a crop through transpiration + evaporation from soil/plant surfaces.

• Factors: Climate (temp, humidity, wind, solar radiation), Crop type & growth stage, Soil moisture, Management practices.

• Methods of Determination:

  • Direct (Soil Moisture Depletion): Measure change in soil water storage over a period.

  • Indirect (Empirical/Thornthwaite):

    • Blaney-Criddle: $$\displaystyle ET = K \cdot f \cdot p $$ (K = crop coeff, f = temp/daylight hrs factor, p = % annual daytime hrs).

    • Penman: Most accurate, based on energy balance & aerodynamics (see 1.3).

    • Hargreaves, Modified Penman-Monteith (FAO-56): Modern standards.

2.2.2 Duty, Delta, and Base Period

• Definitions:

  • Duty (D): Area (hectares) irrigated by 1 cumec (m³/s) of water during the base period. [Unit: ha/cumec]

  • Delta (Δ): Total depth of water (cm) required by a crop during its entire growth period (base period).

  • Base Period (B): Number of days between first and last watering of a crop for a particular irrigation season.

• Relationship:

  Volume of water required = Area × Depth = $A \times \Delta$

  Volume supplied = Duty × Base Period × 86400 seconds/day = $D \times B \times 86400$ (since 1 cumec = 1 m³/s)

  Equating: $$\displaystyle A \times \Delta = D \times B \times 86400 $$

  For 1 hectare ($$\displaystyle 10^4 $$ m²) and $\Delta$ in cm ($\Delta/100$ m):

$$1 \times 10^4 \times \frac{\Delta}{100} = D \times B \times 86400$$

$$\boxed{\Delta \text{ (cm)} = \frac{8.64 \times D}{B}}$$

where D is in ha/cumec, B in days.

2.2.3 Irrigation Scheduling

• Frequency of Irrigation (N): Number of days between irrigations.

$$N = \frac{\text{Allowable Depletion (mm)}}{\text{Daily Consumptive Use (mm/day)}}$$

Allowable Depletion = (FC - PWP) × Root Depth × BD - (Minimum permissible moisture level).

• Depth of Irrigation:

  • Net Depth ($$\displaystyle d_n $$): Depth needed to bring soil moisture to FC.

$$d_n = (\theta_{FC} - \theta_{\text{current}}) \times \text{Root Depth}$$

*   **Gross Depth ($$\displaystyle d_g $$):** $$\displaystyle d_g = d_n / \eta_a $$, where $$\displaystyle \eta_a $$ = application efficiency.

• Kor Period & Depth: Initial critical growth stage period requiring frequent, heavy irrigation. Kor depth = depth applied during kor period.

2.3 Crop Terminology & Rotation

3.0 IRRIGATION ENGINEERING: METHODS, SYSTEMS, AND CANAL DESIGN

3.1 Necessity & Assessment

• Advantages: Increased yield, multiple cropping, drought protection, income stability, groundwater recharge.

• Disadvantages: Waterlogging, salinity, high cost, water-borne diseases, displacement.

• Types:

  • Flow (Gravity) Irrigation: Water flows by gravity from source.

  • Lift Irrigation: Water lifted by pumps (from wells, reservoirs).

3.2 Methods of Irrigation

3.2.1 Surface Irrigation

3.2.2 Pressurized Systems

3.2.3 Subsurface Irrigation

• Methods: Use of porous pipes (tile drains), underground channels.

• Applicability: High water table areas, certain soil types, to minimize evaporation.

3.3 Irrigation Efficiencies & Duty Improvement

Methods to Improve Duty (Increase Area per Unit Discharge):

1. Land Leveling: Reduces deep percolation & runoff.

2. Watercourse Improvement: Lining, reducing travel time.

3. Cropping Pattern: Use less water-intensive crops.

4. Improved Irrigation Methods: Shift from flood to drip/sprinkler.

5. Reducing Losses: Seepage control, scheduling.

3.4 Canal Systems

3.4.1 Classification

• Based on Function:

  • Main Canal: From headworks to major distributaries. No direct irrigation.

  • Branch Canal: Off-takes from main canal. May irrigate directly if discharge small.

  • Distributary: Takes from branch/main, supplies water to minors/watercourses.

  • Minor: Takes from distributary, supplies to watercourses (field channels).

  • Watercourse (Field Channel): Smallest channel, directly irrigates fields.

• Based on Discharge/Importance:

  • Primary (Main): Largest discharge.

  • Secondary (Branch/Distributary): Medium discharge.

  • Tertiary (Minor/Watercourse): Smallest discharge.

3.4.2 Alignment of Canals

• Factors:

  1. Topography: Follow contour lines to avoid steep slopes (reduces erosion) & deep cuttings. May use ridge canal (on watershed) or valley canal (in valley).

  2. Soil & Geology: Avoid unstable slopes, seepage zones, poor foundation.

  3. Drainage: Must cross natural drains via cross-drainage works; avoid parallel alignment to streams.

  4. Utility Services: Avoid roads, railways, towns where possible.

  5. Command Area: Should serve maximum area with shortest length.

  6. Cost: Balance between earthwork (cut/fill) and structure costs.

3.5 Canal Design Theories

3.5.1 Kennedy’s Theory (Critical Velocity Theory)

• Concept: Silt is carried in suspension if flow velocity is critical ($$\displaystyle V_0 $$). Too low → silt deposition; too high → scouring.

• Critical Velocity: $$\displaystyle V_0 = 0.55 \, m \sqrt{(m)} $$ for sandy soils (m = hydraulic mean depth).

  • For other soils: $$\displaystyle V_0 = 0.84 \, (D)^{1/6} $$ (D in m, V in m/s).

• Design Equation (Trapezoidal Channel):

$$Q = A \cdot V = A \cdot V_0$$

where $$\displaystyle A = (b + my)y $$, $m$ = side slope (H:V), $y$ = depth of flow.

**Steps:**

1.  Assume $y$ (or $b$).

2.  Calculate $A$, $P$, $$\displaystyle m = A/P $$.

3.  Find $$\displaystyle V_0 $$ from $m$.

4.  Check $$\displaystyle Q = A V_0 $$. Iterate until match.

5.  Check slope using Manning’s: $$\displaystyle Q = \frac{1}{N} A R^{2/3} S^{1/2} $$.

• Limitations: Empirical, based on alluvial soils of UP, doesn't account for silt properties.

3.5.2 Lacey’s Regime Theory

• Concepts:

  • Regime Channel: Channel in equilibrium with silt load; dimensions stable over time.

  • Silt Factor ($f$): $$\displaystyle f = 1.76 \sqrt{d_{50}} $$ (mm), where $$\displaystyle d_{50} $$ = median silt size. Indicates siltiness.

  • Perimeter ($P$) & Slope ($S$): Related to discharge and silt factor.

• Design Equations:

  1. Perimeter: $$\displaystyle P = 4.75 \sqrt{Q} $$ (Q in cumecs, P in m) – for $$\displaystyle f=1 $$.

  2. Area: $$\displaystyle A = \frac{Q}{V} $$, where $$\displaystyle V = \sqrt{RS} $$ (Lacey’s velocity formula).

  3. Slope: $$\displaystyle S = \frac{f^{5/3}}{1640} \cdot \frac{1}{Q^{1/6}} $$ (for $$\displaystyle f=1 $$, $$\displaystyle S \propto 1/Q^{1/6} $$).

  • For given $f$, $P \propto \sqrt{Q}$, $$\displaystyle S \propto f^{5/3} Q^{-1/6} $$.

• Procedure:

  1. Calculate $P$ from $Q$.

  2. Assume side slope (usually 1.5H:1V for alluvial).

  3. Solve $$\displaystyle P = b + 2y\sqrt{1+m^2} $$ and $$\displaystyle A = (b+my)y $$ simultaneously for $b$, $y$.

  4. Calculate $S$ from silt factor.

• Drawbacks:

  • Based on empirical data from specific canals.

  • Assumes channel is in true regime (often not initially).

  • Doesn't consider channel roughness ($N$) explicitly.

  • Not suitable for cohesive (clayey) soils.

3.5.3 Kutter’s Formula

• Used for lined/unlined channels with known roughness.

$$V = \frac{\sqrt{RS}}{N} \cdot \frac{23 + \frac{0.00155}{S}}{1 + 23 \cdot \frac{N}{\sqrt{R}} \cdot \frac{1}{\sqrt{S}}}$$

Simplified Chezy’s: $$\displaystyle V = C \sqrt{RS} $$, where $$\displaystyle C = \frac{23 + \frac{0.00155}{S}}{N \left(1 + 23 \frac{N}{\sqrt{R}} \frac{1}{\sqrt{S}}\right)} $$.

• Application: Given $N$, $m$, $S$, $Q$ → solve for $b$, $y$ using $$\displaystyle Q = A V $$.

3.6 Canal Lining

• Importance:

  1. Reduces seepage loss (conserve water, increase duty).

  2. Increases flow velocity (reduces channel size).

  3. Prevents waterlogging & salinity.

  4. Reduces maintenance (weed growth, bank erosion).

• Types:

  • Hard Lining: Concrete, masonry, brick, stone – durable, smooth, high initial cost.

  • Soft Lining: Soil cement, bentonite, geomembranes (HDPE, PVC) – flexible, cheaper, less durable.

• Materials: Cement concrete (most common), shotcrete, precast slabs, clay tiles, synthetic membranes.

3.7 Hydraulic Structures in Irrigation

3.7.1 Cross-Drainage Works

• Purpose: Carry canal across a natural drain/river.

• Types & Selection:

  | Structure | Description | When Used | | :--- | :--- | :--- | | Aqueduct | Canal over drain; drain flows subcritical under. | Common, drain bed lower than canal bed. | | Siphon Aqueduct | Canal over drain; drain flows supercritical through siphons (pressurized). | High flood levels in drain. | | Super Passage | Drain over canal (inverted aqueduct). | Canal bed lower than drain bed. | | Inlet & Outlet | Small drains enter/exit canal through closed conduits. | Minor cross-drainage. | | Level Crossing | Canal & drain at same level with regulators. | Rare, high maintenance. |

Selection Factors: Discharge of canal & drain, relative bed levels, topography, cost, silt load.

3.7.2 Canal Regulation Structures

• Head Regulator: At canal head; controls flow into canal from source.

• Cross Regulator: On main canal; raises water level to supply off-taking distributaries.

• Outlets (Module): Structures at minor/watercourse offtakes.

  • Non-Modular: Discharge varies with head (e.g., orifice).

  • Semi-Modular: Discharge independent of upstream head, sensitive to downstream (e.g., submerged pipe).

  • Modular: Discharge independent of both heads (e.g., Khanna’s module, Khosla’s module).

3.7.3 Weirs and Barrages

4.0 RUNOFF HYDROLOGY AND FLOOD MANAGEMENT

4.1 Infiltration

• Definition: Process of water entering soil surface.

• Infiltration Capacity ($$\displaystyle f_p $$): Maximum rate at which soil can absorb rainfall (decreases with time).

• Actual Infiltration ($f$): Rate at which water actually enters soil.

  • If $i$ (rainfall intensity) > $$\displaystyle f_p $$: $$\displaystyle f = f_p $$ (ponding occurs).

  • If $$\displaystyle i \leq f_p $$: $$\displaystyle f = i $$ (all rain infiltrates).

• Factors Affecting:

  • Soil: Texture, structure, porosity, initial moisture.

  • Vegetation: Cover reduces impact, increases organic matter.

  • Slope: Steeper → faster runoff, less infiltration.

  • Antecedent Precipitation: Wet soil → lower infiltration.

  • Rainfall: Intensity, duration, drop impact.

• Infiltration Indices:

  • φ-index: Constant infiltration rate that, when subtracted from total rainfall, gives direct runoff. Assumes constant $f$ after initial abstraction.

$$\phi = \frac{P - R}{t_r}$$

    where $P$ = total storm rainfall, $R$ = total runoff, $$\displaystyle t_r $$ = duration of rainfall excess (time when $$\displaystyle i > \phi $$).

*   **W-index:** Average infiltration rate during the period of rainfall excess (more accurate than φ-index, accounts for varying $f$).

4.2 Runoff and Hydrograph

4.2.1 Unit Hydrograph (UH)

• Definition: Direct runoff hydrograph (DRH) from 1 cm (or 1 mm) of effective rainfall occurring uniformly over the entire catchment in a specified duration ($$\displaystyle T_e $$).

• Assumptions:

  1. Temporal distribution of effective rainfall is uniform.

  2. Catchment characteristics are constant.

  3. Effective rainfall is linearly related to direct runoff.

  4. Baseflow separation is consistent.

• Derivation from Single Storm Hydrograph:

  1. Separate baseflow from observed hydrograph.

  2. Calculate total direct runoff volume (DRV) from DRH.

  3. Calculate effective rainfall depth: $$\displaystyle P_e = \frac{\text{DRV (ha-cm)}}{\text{Catchment Area (ha)}} $$.

  4. Scale DRH ordinates by factor $$\displaystyle \frac{1}{P_e} $$ to get UH of that duration.

• S-Curve Hydrograph: Summation of UHs of same duration offset by $$\displaystyle T_e $$. Used to derive UH of different duration.

  • To get UH of duration $$\displaystyle nT_e $$: From S-curve, take ordinates at intervals of $$\displaystyle nT_e $$, subtract lagged S-curve ordinates.

  • To get UH of duration $$\displaystyle T_e/n $$: Differentiate S-curve (take differences over $$\displaystyle T_e/n $$).

4.2.2 Flood Frequency Analysis

• Objective: Estimate magnitude of flood with given return period ($$\displaystyle T_r $$) or exceedance probability ($p$).

• Methods:

  1. Graphical (Gumbel/EV1): Fits extreme value distribution to annual series.

$$y = -\ln[-\ln(1 - \frac{1}{T_r})]$$

    Plot $y$ vs. $Q$ on Gumbel probability paper, fit line, find $Q$ for given $$\displaystyle T_r $$.

2.  **Log-Pearson Type III (USGS/Recommended):** Fit distribution to logarithms of flood peaks.

$$\log Q = \bar{x} + K \cdot S_x$$

    where $\bar{x}$ = mean of log $Q$, $$\displaystyle S_x $$ = std dev of log $Q$, $K$ = frequency factor (from tables for skewness $$\displaystyle C_s $$).

• Design Discharge: Selected based on risk (return period), economic loss, dam safety.

4.3 Flood Control Measures

• Structural:

  • Reservoirs: Store floodwater, release slowly.

  • Channel Improvement: Straightening, widening, deepening to increase capacity.

  • Levees/Embankments: Contain flood within channel.

  • Detention/Retention Basins: Temporarily store runoff, reduce peak.

  • Bypass Channels: Divert excess flow.

• Non-Structural:

  • Flood Forecasting & Warning: Evacuation, preparedness.

  • Floodplain Zoning: Regulate development in flood-prone areas.

  • Flood Insurance: Financial recovery.

  • Watershed Management: Afforestation, check dams to reduce runoff.

4.4 Channel Routing – Muskingum Method

• Concept: Storage in reach is function of both inflow ($I$) and outflow ($O$): $$\displaystyle S = K [x I + (1-x) O] $$

  where $K$ = storage time constant (time for flood wave to travel reach), $x$ = weighting factor (0 ≤ x ≤ 0.5).

• Routing Equation:

$$O_{t+\Delta t} = C_0 I_t + C_1 I_{t+\Delta t} + C_2 O_t$$

where coefficients:

$$C_0 = \frac{-Kx + 0.5\Delta t}{K(1-x) + 0.5\Delta t}, \quad C_1 = \frac{Kx + 0.5\Delta t}{K(1-x) + 0.5\Delta t}, \quad C_2 = \frac{K(1-x) - 0.5\Delta t}{K(1-x) + 0.5\Delta t}$$

with $$\displaystyle C_0 + C_1 + C_2 = 1 $$.

• Steps:

  1. Estimate $K$ (from travel time) and $x$ (from storage-discharge relationship, usually 0.2-0.3 for natural channels).

  2. Choose $\Delta t$ (usually $K/5$ to $K/10$).

  3. Compute $$\displaystyle C_0, C_1, C_2 $$.

  4. Apply equation sequentially for each time step.

4.5 Stream Types

5.0 GROUNDWATER ENGINEERING

5.1 Aquifers and Properties

• Aquifer: Geologic formation that stores & transmits water economically.

• Types:

  • Unconfined (Water Table): Upper surface is water table; atmospheric pressure.

  • Confined (Artesian): Between two impermeable layers; under pressure > atmospheric.

  • Artesian Well: Taps confined aquifer; water rises above top of aquifer (may flow at surface if pressure sufficient).

• Properties:

  • Porosity ($n$): Ratio of void volume to total volume. $$\displaystyle n = \frac{V_v}{V} $$.

  • Specific Yield ($$\displaystyle S_y $$): Volume of water drained per unit aquifer volume under gravity (drainable porosity). $$\displaystyle S_y < n $$.

  • Specific Retention ($$\displaystyle S_r $$): Volume of water retained against gravity. $$\displaystyle n = S_y + S_r $$.

  • Coefficient of Permeability ($K$) / Hydraulic Conductivity: Rate of flow under unit hydraulic gradient. Units: m/day, cm/s.

  • Transmissivity ($T$): $$\displaystyle T = K \cdot b $$ (for confined), where $b$ = aquifer thickness. Rate of flow through entire saturated thickness under unit gradient.

5.2 Wells and Well Hydraulics

Types of Wells:

• Dug Well: Large diameter (3-10m), shallow, manual excavation.

• Tube Well: Small diameter (10-30 cm), deep, drilled/cased.

• Artesian Well: Taps confined aquifer.

• Infiltration Gallery: Horizontal perforated pipe in shallow aquifer near surface (for induced recharge).

Discharge Equations:

1. Dupuit-Thiem Equation (Unconfined Aquifer):

   For steady flow to a fully penetrating well:

$$Q = \frac{\pi K (h_1^2 - h_2^2)}{\ln(r_2 / r_1)}$$

where $$\displaystyle h_1, h_2 $$ = head at radii $$\displaystyle r_1 $$ (well), $$\displaystyle r_2 $$ (observation well/radius of influence).

*   **Drawdown ($s$):** $$\displaystyle s = h_0 - h_w $$, where $$\displaystyle h_0 $$ = static head, $$\displaystyle h_w $$ = pumping head.

*   Often written: $$\displaystyle Q = \frac{\pi K (2h_0 s - s^2)}{\ln(R / r_w)} $$, where $R$ = radius of influence.

2. Confined Aquifer (Theim/Dupuit):

$$Q = \frac{2\pi K h (h_1 - h_2)}{\ln(r_2 / r_1)}$$

where $h$ = aquifer thickness (constant), $$\displaystyle h_1, h_2 $$ = piezometric heads.

3. Artesian Well (Confined, given $s$, $K$, $R$):

$$Q = \frac{2\pi K h s}{\ln(R / r_w)}$$

(Assuming $$\displaystyle s << h $$).

Exam Tip: Identify aquifer type first. For unconfined, use $$\displaystyle h^2 $$ term; for confined, use linear $h$.

5.3 Groundwater Recharge

• Natural: Precipitation infiltration, seepage from rivers/lakes.

• Artificial Methods:

  1. Infiltration Galleries: Horizontal perforated pipes buried near stream/river to capture floodwater.

  2. Check Dams & Percolation Ponds: Small barriers across streams to slow flow, increase infiltration.

  3. Recharge Wells: Direct injection of surface water into aquifer through wells.

  4. Spreading Basins/Contour Trenching: Large shallow basins or trenches to spread water over large area.

  5. Canal Lining: Paradoxically, lining canals in some areas can raise water table by reducing seepage from canals; but lining in recharge areas reduces natural recharge.

5.4 Waterlogging

• Causes:

  • Poor Natural Drainage: Flat terrain, clayey soil.

  • Over-Irrigation: Excessive application.

  • High Water Table: Due to seepage from canals, reservoirs, or inadequate subsurface drainage.

  • Obstructed Surface Drainage: Lack of proper drains.

• Effects:

  • Soil Salinization: Capillary rise brings salts to surface.

  • Reduced Aeration & Root Growth: Water-filled pores.

  • Reduced Crop Yield & Land Productivity.

  • Structural Damage: Foundations, roads.

• Prevention & Reclamation:

  • Surface Drainage: Open ditches, buried pipes.

  • Subsurface Drainage: Tile drains, mole drains.

  • Land Leveling: Prevent localized over-irrigation.

  • Crop Rotation: With less water-intensive crops.

  • Drainage + Leaching: Flush salts below root zone.

5.5 Salinity and Salt-Affected Lands

• Salt Efflorescence: White crust of salts (NaCl, Na₂SO₄, etc.) on soil surface after evaporation.

• Effects: Ion toxicity, osmotic stress (reduces water uptake), soil structure degradation (sodium dispersion).

• Reclamation Strategies:

  1. Leaching: Apply excess water to dissolve and move salts below root zone. Requires good drainage.

  2. Soil Amendments: Add gypsum (CaSO₄) to replace sodium on exchange sites with calcium, improving structure.

  3. Drainage: Essential to remove leached salts.

  4. Cropping: Salt-tolerant crops (barley, sugar beet) during reclamation.

  5. Mulching: Reduces evaporation, prevents salt accumulation.

5.6 Groundwater Flow Analysis

• Water Table Contouring: Plot water table elevations from well data, draw contours. Flow is perpendicular to contours from high to low head.

• Flow Direction & Gradient:

  • Connect three wells (A, B, C). Calculate gradient between known points.

  • Example: Given A(160.00, 157.00), B(159.00, 156.50) → gradient $$\displaystyle i = \frac{\Delta h}{\Delta l} $$.

  • Use gradient to interpolate unknown elevation.

• Specific Yield Estimation:

  From volume balance: $$\displaystyle S_y = \frac{\text{Volume of water withdrawn}}{\text{Area} \times \text{Decline in water table}} $$.

  From pumping test: $$\displaystyle S_y $$ derived from time-drawdown data (Theis recovery).

5.7 Specific Problems

• Estimation of Specific Yield:

  Given: Basin area $A$, volume pumped $V$, water table drop $\Delta h$.

$$S_y = \frac{V}{A \cdot \Delta h}$$

(Ensure consistent units: e.g., $A$ in m², $\Delta h$ in m, $V$ in m³).

• Water Table Elevation in Extensive Aquifer:

  Use flow net or Dupuit-Thiem. For two points with known head, gradient is constant. Extrapolate linearly if flow is uniform.

• Well Discharge (Artesian):

  Use $$\displaystyle Q = \frac{2\pi K h s}{\ln(R / r_w)} $$. Ensure $K$ in consistent units (m/day → m³/day by multiplying by $h$).

6.0 INTEGRATED APPLICATIONS AND ADVANCED TOPICS

6.1 Design Problems (Step-by-Step Approaches)

A. Canal Design – Kennedy’s Theory

Given: $Q$, $S$, $m$, $N$ (Manning’s $N$).

1. Assume $y$.

2. Calculate $$\displaystyle A = (b+my)y $$, $$\displaystyle P = b + 2y\sqrt{1+m^2} $$, $$\displaystyle R = A/P $$.

3. Calculate $$\displaystyle m = A/P $$.

4. Find $$\displaystyle V_0 = 0.55 m^{1/2} $$ (or $$\displaystyle 0.84 D^{1/6} $$).

5. Check $$\displaystyle Q_{calc} = A V_0 $$. Adjust $y$ (and $b$) to match given $Q$.

6. Verify with Manning: $$\displaystyle Q_{Manning} = \frac{1}{N} A R^{2/3} S^{1/2} $$. Should be close to given $Q$; if not, adjust $N$ or $y$.

B. Regime Channel Design – Lacey’s Theory

Given: $Q$, $f$ (silt factor), $m$ (side slope).

1. Calculate perimeter: $$\displaystyle P = 4.75 \sqrt{Q} \cdot \left(\frac{f}{1.0}\right)^{5/3} $$? [Note: Original Lacey: $$\displaystyle P = 4.75\sqrt{Q} $$ for $$\displaystyle f=1 $$. For $f \neq 1$, some texts use $$\displaystyle P \propto f^{5/3} $$; check standard formula.]

2. Solve simultaneously:

   $$\displaystyle P = b + 2y\sqrt{1+m^2} $$

   $$\displaystyle A = (b+my)y = Q / V $$, with $$\displaystyle V = \sqrt{RS} $$ and $$\displaystyle S = \frac{f^{5/3}}{1640 Q^{1/6}} $$.

   Simpler: Often $A \approx Q / 1.0$ (velocity ~1 m/s for regime). Use $$\displaystyle A = Q / V_{design} $$ (1-2 m/s).

3. Find $b$, $y$ from $P$ and $A$ equations.

4. Calculate $S$ from Lacey’s formula.

C. Irrigation Scheduling

Given: FC%, PWP%, BD (g/cm³), root depth (cm), daily CU (mm).

1. ASW depth (mm): $$\displaystyle (\theta_{FC} - \theta_{PWP}) \times \text{depth (mm)} \times \text{BD} $$.

   • Convert % to decimal, depth to mm.

2. Frequency (days): $$\displaystyle N = \frac{\text{ASW}}{\text{Daily CU}} $$.

3. Net depth ($$\displaystyle d_n $$): If irrigating at FC → PWP, $$\displaystyle d_n = \text{ASW} $$. If irrigating to FC from current moisture, calculate difference.

4. Gross depth: $$\displaystyle d_g = d_n / \eta_a $$.

D. Unit Hydrograph Transformation

• Given UH of duration $T$, derive UH of $nT$ or $T/n$:

  1. To longer duration ($nT$): Construct S-curve by summing $n$ UHs offset by $T$. Then, take ordinates of S-curve at intervals of $nT$, subtract ordinates lagged by $nT$.

  2. To shorter duration ($T/n$): From S-curve, take differences over interval $T/n$.

6.2 Data Estimation and Analysis

• Missing Rainfall:

  • Arithmetic Mean: Simple average of all stations (including missing? No, only reporting stations). Less accurate if stations not uniformly distributed.

  • Thiessen Polygon: More accurate if stations unevenly spaced. Use polygon areas as weights.

• φ-index & W-index:

  • From storm hyetograph and runoff volume.

  • φ-index: Constant rate that gives correct runoff for total storm. Solve $$\displaystyle \phi = (P - R)/t_r $$, where $$\displaystyle t_r $$ is time when $$\displaystyle i > \phi $$ (found by trial).

  • W-index: Weighted average of $f$ during rainfall excess period. $$\displaystyle \sum (f_i \cdot \Delta t) / t_r $$.

• Thiessen Polygon Construction: (See 1.2.2).

6.3 Comparative Studies

Final Exam Strategy:

1. Definitions First: Always start 7-mark answers with clear, boxed definitions (e.g., \boxed{\text{Duty is...}}).

2. Diagrams: Sketch where possible (hydrological cycle, canal cross-section, hydrograph, UH derivation, cross-drainage types).

3. Formulas: Box key equations (Δ = 8.64D/B, Dupuit-Thiem, Lacey’s P, Muskingum coefficients).

4. Numericals: Show step-by-step procedure, state assumptions, box final answer.

5. Comparative Questions: Use tables for clarity (sprinkler vs. drip, weir vs. barrage).

6. High-Yield Topics: Prioritize: Duty-Delta, Canal Design (Kennedy/Lacey), UH, Infiltration indices, Aquifers/Well equations, Waterlogging/Salinity, Irrigation methods. These appear in every past paper.