GATE Agricultural Engineering Irrigation and Drainage Engineering Syllabus

What is the condition for the most economical (best hydraulic) trapezoidal channel section?

For a given area, the section is most efficient when the hydraulic radius is maximum, i.e. half the top width equals the sloping side ($\tfrac{b + 2my}{2} = y\sqrt{1+m^{2}}$) and the hydraulic radius $R = y/2$. The section is then tangent to a semicircle.

State Kennedy's theory critical velocity relation for stable channel design.

$$V_0 = 0.55\,m\,y^{0.64}$$ where $V_0$ = critical (non-silting, non-scouring) velocity (m/s), $y$ = depth of water (m), and $m$ = critical velocity ratio (CVR) depending on silt grade.

State Lacey's regime velocity and silt factor relations.

Lacey's regime velocity: $V = 0.4382\,(Q f^{2})^{1/6}$ (SI). Silt factor $f = 1.76\sqrt{d_{mm}}$ where $d_{mm}$ is mean particle size in mm. Wetted perimeter $P = 4.75\sqrt{Q}$.

List key advantages of underground (buried) pipeline irrigation conveyance over open channels.

No conveyance seepage or evaporation losses, no land lost to channel width, no weed growth or maintenance of banks, water can be delivered across undulating land under pressure, reduced operation labour, and elimination of cross-drainage works.

Name the major surface irrigation methods.

Border (border strip) irrigation, basin (check basin) irrigation, furrow irrigation (including corrugation), and wild flooding/free flooding. They distribute water over the soil surface by gravity flow.

Compare furrow and border irrigation in terms of crop suitability and wetting.

Furrow irrigation wets only part of the surface (between ridges) and suits row crops (maize, cotton, vegetables, potato), reducing evaporation and crusting. Border irrigation wets the whole strip and suits close-growing crops (wheat, alfalfa, pasture) on uniform slopes.

What is the advance and recession phase in surface irrigation hydraulics?

Advance is the phase during which the water front moves from the inlet to the downstream end of the field. Recession is the phase after inflow stops, during which surface water infiltrates/drains and the water disappears, starting from the upstream end.

State the components of total head needed for a sprinkler irrigation system.

Total head $H = H_n + H_r + H_f + H_e + H_s$: operating pressure at nozzle ($H_n$), riser height ($H_r$), friction losses in pipes/fittings ($H_f$), elevation difference ($H_e$), and suction lift ($H_s$).

How is the application rate of a sprinkler computed?

$$I = \frac{Q}{S_l \times S_m}$$ where $I$ = application rate (mm/h), $Q$ = sprinkler discharge (L/h or m³/h converted), $S_l$ = spacing along lateral, $S_m$ = spacing between laterals (moves). The application rate must not exceed the soil infiltration rate to avoid runoff.

Why must the sprinkler application rate be less than the soil's basic infiltration rate?

If the application rate exceeds the basic (steady) infiltration capacity, water ponds and runs off, causing non-uniform distribution, surface sealing, and erosion. Keeping $I < f_c$ ensures all applied water infiltrates where it lands.

How is sprinkler uniformity quantified using Christiansen's Uniformity Coefficient (CU)?

$$CU = 100\left(1 - \frac{\sum |x_i - \bar{x}|}{n\,\bar{x}}\right)$$ where $x_i$ = individual catch-can depths, $\bar{x}$ = mean depth, $n$ = number of observations. A well-designed system gives $CU \geq 85\%$.

Distinguish drip (trickle) and sprinkler micro-irrigation in terms of how water is applied.

Drip irrigation applies water slowly drop-by-drop directly to the root zone through emitters at low pressure, wetting only part of the soil. Sprinkler simulates rainfall over the whole area at higher pressure. Drip has the highest application efficiency.

What is the emission uniformity (EU) of a drip system and a typical design target?

$$EU = 100\,\frac{q_{min}}{q_{avg}}\quad\text{or}\quad EU = 100\left(1 - 1.27\,\frac{C_v}{\sqrt{n}}\right)\frac{q_{min}}{q_{avg}}$$ where $q_{min}$ = minimum emitter discharge, $q_{avg}$ = average, $C_v$ = manufacturer's coefficient of variation, $n$ = emitters per plant. Good design: $EU \geq 90\%$.

Define the emitter flow (discharge) equation for micro-irrigation emitters.

$$q = K_d\,H^{x}$$ where $q$ = emitter discharge, $H$ = operating pressure head, $K_d$ = emitter constant, and $x$ = emitter discharge exponent. $x = 0$ for a fully pressure-compensating emitter; $x = 0.5$ for an ordinary orifice emitter.

List the main advantages of drip irrigation.

Very high water-use efficiency (90–95%), reduced weed growth (only root zone wetted), suitability for saline water/saline soils, ability to apply fertilizer through the system (fertigation), suitability for undulating terrain, and reduced evaporation and deep percolation losses.

Define water conveyance efficiency.

$$E_c = \frac{W_f}{W_r}\times 100$$ where $W_f$ = water delivered to the farm (field) and $W_r$ = water released at the source/headworks. It measures losses (seepage, evaporation) in the conveyance system.

Define water application efficiency.

$$E_a = \frac{W_s}{W_f}\times 100$$ where $W_s$ = water stored in the root zone available to the crop, and $W_f$ = water delivered to the field. It accounts for deep percolation and runoff losses during application.

Define water storage efficiency and water use efficiency.

Storage efficiency $E_s = \dfrac{\text{water stored in root zone}}{\text{water needed in root zone}}\times100$. Water use efficiency $WUE = \dfrac{\text{crop yield}}{\text{water used (ET or applied)}}$ (e.g. kg/m³).

Define water distribution (uniformity) efficiency in surface irrigation.

$$E_d = \left(1 - \frac{\bar{d}}{D}\right)\times 100$$ where $\bar{d}$ = average numerical deviation of stored depth from the mean stored depth $D$. It measures how uniformly water is distributed over the field.

Define drainage coefficient.

Drainage coefficient is the depth of water (in mm or cm) to be removed from a drainage area in 24 hours to prevent crop damage. For surface drainage of agricultural land it is the design rate at which excess water is taken off the area.

What is the difference between surface and subsurface (sub-surface) drainage?

Surface drainage removes excess water ponded on the soil surface using graded land, open ditches/field drains and removes water before it infiltrates. Subsurface drainage lowers a high water table by removing excess gravitational water from within the soil profile via buried perforated pipes (tile) or mole drains.

State the ellipse (Hooghoudt) equation for spacing of subsurface drains in steady-state.

$$S^{2} = \frac{4K\,(2\,d_e\,h + h^{2})}{q}$$ where $S$ = drain spacing, $K$ = hydraulic conductivity, $h$ = height of water table above drain level at midpoint, $d_e$ = equivalent depth to impermeable layer (Hooghoudt's correction), $q$ = drainage coefficient (recharge rate).

What is the equivalent depth $d_e$ in Hooghoudt's drain spacing theory?

$d_e$ is a reduced (corrected) depth to the impermeable barrier that accounts for the extra resistance to radial (converging) flow near the drains. Using $d_e < d$ corrects the simple Donnan/ellipse equation, which otherwise overestimates flow because it ignores radial convergence.

Define leaching requirement (LR) for salinity control.

Leaching requirement is the fraction of irrigation water that must pass through (drain below) the root zone to keep root-zone salinity below a crop-tolerance limit: $$LR = \frac{EC_{iw}}{EC_{dw}} = \frac{D_{dw}}{D_{iw}}$$ where $EC_{iw}$ = EC of irrigation water and $EC_{dw}$ = EC of drainage water (or $5\,EC_e - EC_{iw}$ in the denominator for the FAO form).

How is the gross (total) irrigation depth obtained when a leaching fraction is required?

$$D_{gross} = \frac{D_{net}}{(1 - LR)}$$ where $D_{net}$ is the depth to meet crop ET and $LR$ is the leaching requirement (fraction). The extra water leaches salts below the root zone.

What three parameters classify irrigation water quality, and what does SAR measure?

Salinity (EC), sodium hazard (SAR), and specific ion toxicity/residual carbonate. The Sodium Adsorption Ratio: $$SAR = \frac{Na^{+}}{\sqrt{\dfrac{Ca^{2+}+Mg^{2+}}{2}}}$$ (concentrations in meq/L) measures the sodium hazard — its tendency to deflocculate clay and reduce permeability.

What is a non-conventional drainage system? Give examples.

Non-conventional drainage uses methods other than conventional open ditches or buried tile pipes. Examples: mole drainage (unlined channels formed by a mole plough in clay soils), bio-drainage (deep-rooted trees like Eucalyptus that pump water by transpiration), vertical drainage (pumped tubewells lowering the water table), and interceptor drains.

State Darcy's law for flow through a saturated porous medium.

$$Q = -K\,A\,\frac{dh}{dl}\qquad\text{or}\qquad v = -K\,i$$ where $Q$ = discharge, $K$ = hydraulic conductivity, $A$ = cross-sectional area, $i = dh/dl$ = hydraulic gradient, and $v = Q/A$ = Darcy (apparent) velocity. The negative sign indicates flow toward decreasing head.

Differentiate a confined and an unconfined aquifer, and define storage coefficient.

A confined (artesian) aquifer is bounded above and below by impermeable layers and is under pressure greater than atmospheric; water is released by compression (storativity $S \sim 10^{-5}$–$10^{-3}$). An unconfined (water-table) aquifer has its upper surface at the water table; water is released by gravity drainage, so $S$ = specific yield ($\sim 0.1$–$0.3$).

State the Thiem (Dupuit) steady-state radial flow equation for a confined aquifer well.

$$Q = \frac{2\pi K b\,(h_2 - h_1)}{\ln(r_2/r_1)} = \frac{2\pi T\,(h_2 - h_1)}{\ln(r_2/r_1)}$$ where $T = Kb$ = transmissivity, $b$ = aquifer thickness, $h_1,h_2$ = heads at radii $r_1,r_2$ from the well.

State the Dupuit steady-state radial flow equation for an unconfined aquifer well.

$$Q = \frac{\pi K\,(h_2^{2} - h_1^{2})}{\ln(r_2/r_1)}$$ where $K$ = hydraulic conductivity and $h_1,h_2$ = saturated thicknesses (heads measured from the impermeable base) at radii $r_1,r_2$. This uses the Dupuit assumptions (nearly horizontal flow, small gradient).