Agricultural Engineering · Land & Water Resources Engineering · also Groundwater Hydrology, Groundwater Development, Wells and Pumps
Aquifers, well hydraulics, well design and the pumps that lift the water — asked in some form in every GATE AG paper.
In the exams: GATE AG Section 5 (well hydraulics in 7 of 8, pumps in 5 of 8 papers 2019–26); ICAR AIEEA-PG Unit VII; ICAR AICE subjects 40 and 43; NCEES PE pumps; IA CID pumps 15–20%; RPSC AAE
Groundwater is the water that fills the pores and fractures of soil and rock below the water table. It supplies a large share of the world's irrigation through pumped wells, and in many regions — the Indo-Gangetic plain, the North China plain, the High Plains of the United States — it is pumped faster than it is replenished.
The subject has two halves. The first is groundwater hydraulics: how aquifers store and transmit water, how Darcy's law governs flow through porous media, how water levels fall around a pumped well (the Thiem, Dupuit, Theis and Cooper-Jacob solutions), how a pumping test is run and analysed, how wells interfere, how a well is designed, drilled and developed, how groundwater is found by resistivity survey, and how recharge is estimated and augmented. The second half is pumps: their classification, the characteristic curves of centrifugal pumps, specific speed and the affinity laws, net positive suction head and cavitation, selection and installation, and solar photovoltaic pumping.
In India's GATE Agricultural Engineering paper some groundwater item appears in most years — usually Thiem or Dupuit discharge, transmissivity or interference — and pump specific speed, affinity laws and power recur. Other PG, licensing and certification exams expect a candidate to compute a drawdown or a pump duty quickly and to know which formula applies to which aquifer. Where practice or law differs by country, this manual says so.
In the unsaturated (vadose) zone pores hold both air and water at less than atmospheric pressure; below it, in the saturated zone, every pore is full. The boundary is the water table: the surface at which pore-water pressure equals atmospheric pressure, and the level at which water stands in a shallow well. Just above the water table is the capillary fringe, saturated or nearly so but at negative pressure, so it does not drain into a well.
A geological formation that stores water and transmits it in useful quantities to wells and springs is an aquifer (sand and gravel, sandstone, karstic limestone, fractured basalt, weathered granite). An aquitard transmits water, but so slowly that it cannot supply a well; it can still leak substantial volumes to the aquifers it separates. An aquiclude stores water but transmits practically none (a thick clay), and an aquifuge neither stores nor transmits it (massive unfractured granite). Texts draw the aquitard–aquiclude line differently.
An unconfined (water-table) aquifer has the water table as its upper boundary. A confined (artesian) aquifer is bounded above and below by confining beds and is under pressure, so water in a well that penetrates it rises above the top of the aquifer. The surface joining these levels is the piezometric (potentiometric) surface; where it is above ground the well flows. A leaky or semi-confined aquifer is overlain or underlain by an aquitard through which it gains or loses water. A perched aquifer is a local saturated lens resting on a small impermeable layer above the main water table.
Porosity n is the ratio of void volume to total volume. Primary porosity forms with the rock or sediment (the spaces between sand grains); secondary porosity develops later through fractures, joints and solution channels. In hard-rock terrains such as the granites and basalts of peninsular India and much of Africa, usable groundwater sits in the weathered mantle and fractures, so yields are small and vary sharply between sites.
Not all pore water can be drained. When a saturated soil drains under gravity, the volume released per unit volume of material is the specific yield Sy; the volume retained against gravity by surface tension and adsorption is the specific retention Sr. Their sum is the porosity: n = Sy + Sr. Fine-grained materials hold water tightly, so clay can have a porosity above 0.4 and yet a specific yield of only a few per cent, while a medium sand of lower porosity may yield 0.2 or more. Effective porosity, the fraction of connected pores that carry flow, converts a Darcy flux into a water velocity; it is close to Sy in sands but defined for a different purpose.
The storage coefficient or storativity S is the volume of water released from storage per unit surface area of aquifer per unit decline in head. It is dimensionless. In an unconfined aquifer the water comes mainly from draining pores as the water table falls, so S is practically equal to Sy. In a confined aquifer the pores stay full; water is released only because the water expands slightly and the aquifer skeleton compresses as pressure drops. The specific storage Ss (per metre) expresses this per unit thickness, and S = Ss × b, where b is the aquifer thickness. Confined storativities are therefore tiny, typically of the order of 10⁻⁵ to 10⁻³, against 0.01 to 0.3 for unconfined aquifers.
For a head decline Δh over area A, the volume released is ΔV = S × A × Δh. Take an area of 2 km² with a 1.5 m decline. If the aquifer is unconfined with Sy = 0.12, ΔV = 0.12 × 2,000,000 × 1.5 = 360,000 m³. If it is confined with S = 2 × 10⁻⁴, the same decline releases only 600 m³. Pressure changes in confined aquifers therefore spread far with little water removed, so deep tube wells in confined systems interfere over long distances.
Transmissivity T is the rate at which water is transmitted through a unit width of the whole aquifer thickness under unit hydraulic gradient: T = K × b, with units of m²/day. In an unconfined aquifer b is the saturated thickness, so T falls as the water table falls. T and S are the parameters every well formula needs; a pumping test measures them.
In 1856 Henry Darcy found, from sand-filter experiments at Dijon, that the discharge Q through a column of sand is proportional to the cross-sectional area A and to the head loss Δh, and inversely proportional to the length L over which the loss occurs. In differential form Q = −K A (dh/dl), where dh/dl is the hydraulic gradient i and the minus sign shows that flow is towards decreasing head. The constant K is the hydraulic conductivity, with the dimensions of a velocity (m/s or m/day). The quantity q = Q/A = K i is the specific discharge or Darcy flux.
Separating medium from fluid gives the intrinsic permeability k (m², or the oil-industry unit darcy), a property of the pore geometry alone: K = k ρ g / μ, where ρ is fluid density and μ its dynamic viscosity. Because the viscosity of water falls as temperature rises, the same sand has a higher K for warm water than for cold water. K spans more than ten orders of magnitude from clean gravel to unfractured clay; texts give ranges, and a site value must be measured.
Hydraulic head h at a point is the sum of elevation head z and pressure head p/ρg; velocity head is negligible in groundwater. Groundwater flows from higher to lower head, not necessarily from higher pressure or elevation.
The Darcy flux q is a fictitious velocity: it assumes the whole cross-section carries flow. Water in fact moves only through the connected pores, so the average linear or seepage velocity is v = q / nₑ, where nₑ is the effective porosity. Use v for travel times.
Example: an aquifer with K = 30 m/day under a gradient of 0.004 has q = 30 × 0.004 = 0.120 m/day. With nₑ = 0.25, v = 0.48 m/day, and water takes about 150 / 0.48 ≈ 312 days to travel 150 m to a well.
Darcy's law holds for laminar flow, where viscous forces dominate. The check is a Reynolds number Re = q d / ν, with d a representative grain diameter (often d₁₀ or d₅₀) and ν the kinematic viscosity. The law is generally reliable for Re below about 1 and begins to fail somewhere between 1 and 10. It can break down in karst conduits, open fractures, very coarse gravel and in the zone immediately around a heavily pumped well screen, where velocities are high and part of the head loss becomes non-linear (the source of the "well loss" discussed in Chapter 5).
For flow parallel to the layers, each layer carries flow in proportion to its K and thickness, so the equivalent horizontal conductivity is the thickness-weighted arithmetic mean: Kh = Σ(Kᵢ bᵢ) / Σbᵢ. For flow perpendicular to the layers the same flow must pass through each layer in series, so the equivalent vertical conductivity is the thickness-weighted harmonic mean: Kv = Σbᵢ / Σ(bᵢ / Kᵢ). The harmonic mean is controlled by the least permeable layer, so Kv is always less than or equal to Kh.
Example: three layers 4 m of K = 20 m/day, 2 m of K = 0.5 m/day and 6 m of K = 8 m/day. Kh = (80 + 1 + 48) / 12 = 10.75 m/day. Kv = 12 / (0.2 + 4 + 0.75) = 2.42 m/day. The thin 2 m silt layer barely affects Kh but dominates Kv.
Combining Darcy's law with conservation of mass gives the groundwater flow equation. For steady flow in a homogeneous, isotropic medium it reduces to Laplace's equation, ∇²h = 0, which can be solved graphically with a flow net of flow lines and equipotential lines crossing at right angles. For transient confined flow, ∇²h = (S/T) ∂h/∂t; T/S is the hydraulic diffusivity, which sets how fast a pressure change spreads. The well formulas that follow solve these equations.
When a well is pumped, water levels around it fall in a cone of depression. The fall at any point is the drawdown s. At steady state — when the cone has stopped growing — the flow through every cylinder of radius r around the well equals the pumping rate. The classical solutions assume a homogeneous, isotropic, infinite aquifer, a fully penetrating well, horizontal radial Darcian flow and negligible well storage.
For a confined aquifer of thickness b, Darcy's law across a cylinder of area 2πrb gives Q = 2πrbK (dh/dr). Integrating between two radii r₁ and r₂ with heads h₁ and h₂ gives the Thiem equation: Q = 2πT (h₂ − h₁) / ln(r₂/r₁) = 2πT (s₁ − s₂) / ln(r₂/r₁). If r₂ is taken as the radius of influence R (where drawdown is zero) and r₁ as the well radius r_w, then Q = 2πT s_w / ln(R/r_w).
Example: a well pumps from a confined aquifer with T = 400 m²/day. Observation wells at 12 m and 90 m show steady drawdowns of 2.6 m and 1.1 m. Then Q = 2π × 400 × 1.5 / ln(7.5) = 1,871 m³/day. Using log₁₀ instead of the natural logarithm inflates the answer by 2.303 — a common slip.
Because Q is proportional to drawdown in a confined aquifer, specific capacity Q/s is constant (apart from well losses) and doubling the pumping rate doubles the drawdown.
In an unconfined aquifer the saturated thickness itself falls as the water table is drawn down, so the flow area 2πrh changes with r. Dupuit's assumptions — that flow is horizontal and that the hydraulic gradient equals the slope of the water table and is uniform with depth — give Q = 2πrhK (dh/dr), which integrates to Q = πK (h₂² − h₁²) / ln(r₂/r₁), where h₁ and h₂ are saturated thicknesses (heads above the aquifer base) at r₁ and r₂. Note the squares of heads, not the square of their difference, and π rather than 2π.
Example: K = 20 m/day; saturated thickness 18.0 m at 15 m and 20.5 m at 75 m from the well. Q = π × 20 × (420.25 − 324) / ln 5 = 3,758 m³/day.
The Dupuit assumptions fail close to the well, where flow has a strong vertical component and the water level inside the well is lower than the water table just outside it (a seepage face forms). The equation still predicts discharge well, but water-table elevations near the well are underestimated. When drawdown is small compared with the saturated thickness, an unconfined aquifer behaves almost like a confined one; Jacob's correction s′ = s − s²/(2b) converts observed unconfined drawdowns to equivalent confined drawdowns so that confined-aquifer methods can be used.
In an infinite aquifer without recharge the cone never stops growing; true steady state needs a source — a river, leakage, or recharge — that supplies the pumping rate. The radius of influence R therefore depends on pumping time and boundaries, not on the aquifer alone. Empirical formulas such as Sichardt's R = 3000 s √K (s in m, K in m/s), from construction dewatering, exist. These give orders of magnitude only. Fortunately R appears inside a logarithm, so the computed yield is not very sensitive to it. For a well of radius 0.15 m, changing R from 300 m to 600 m changes ln(R/r_w) from 7.60 to 8.29, and the computed discharge by only about 8 per cent. Two observation wells avoid R entirely. A well whose drawdown keeps falling on a straight line against log time is still unsteady (Chapter 4), and steady formulas should not be applied to its data.
In 1935 C. V. Theis solved the transient flow equation for a well pumping at constant rate from a confined aquifer. Keeping the Thiem assumptions but allowing storage to change with time, and assuming water is released instantaneously from storage as head falls, the drawdown at distance r and time t is s = (Q / 4πT) W(u), with u = r²S / (4Tt). W(u) is the well function, the exponential integral ∫ₓ^∞ (e⁻ˣ/x) dx from u to infinity, which can be expanded as W(u) = −0.5772 − ln u + u − u²/(2·2!) + u³/(3·3!) − … .
Drawdown is directly proportional to Q and inversely proportional to T. Because r and t appear only together as r²/t, the drawdown at 20 m after 4 hours equals that at 10 m after 1 hour. A small storativity (confined aquifer) gives a small u and a large, fast-spreading cone; a large storativity (unconfined) slows the spread.
The Theis solution has two direct uses: forward prediction of drawdown for known T and S, and inverse estimation of T and S from observed drawdowns by type-curve matching (Chapter 5).
When u is small the series for W(u) is dominated by its first two terms, giving W(u) ≈ −0.5772 − ln u. Substituting and converting to common logarithms gives the Cooper-Jacob (1946) equation: s = (2.3Q / 4πT) log₁₀(2.25Tt / r²S). The approximation is usually accepted when u < 0.01; some texts accept u < 0.05 with a small error. Because u falls as t rises and as r falls, the condition is met near the well and at later times.
The equation predicts that drawdown plotted against log t is a straight line, and that for each tenfold increase in time drawdown increases by Δs = 2.3Q/(4πT). It equally predicts a straight line of s against log r at a fixed time, with Δs = 2.3Q/(2πT) per log cycle of distance.
Example: Q = 2000 m³/day, T = 600 m²/day, S = 3 × 10⁻⁴; find drawdown at r = 40 m after 1 day. u = 1600 × 0.0003 / (4 × 600 × 1) = 2 × 10⁻⁴, well below 0.01. Cooper-Jacob gives s = (2.3 × 2000 / (4π × 600)) × log₁₀(2.25 × 600 / (1600 × 0.0003)) = 2.10 m. The full Theis series gives W(u) = 7.940 and s = 2.11 m — the same to within a centimetre.
Theis assumes that all water comes from storage within the aquifer. Two common departures change the curve.
In a leaky (semi-confined) aquifer, pumping lowers head in the aquifer and induces flow through the overlying aquitard. Hantush and Jacob (1955) solved this case: the drawdown curve rises like Theis at first, then flattens and may reach a true steady state as leakage balances pumping. The leakage factor B = √(T b′ / K′), with K′ and b′ the aquitard's vertical conductivity and thickness, controls it; the flattening can be mistaken for a recharge boundary.
In an unconfined aquifer water is not released instantaneously: pores drain gradually as the water table falls. The time-drawdown curve on log-log paper is typically S-shaped. Early data follow a Theis curve with a small, confined-like storativity (elastic release); a middle segment flattens as delayed gravity drainage begins; late data follow another Theis curve with storativity equal to the specific yield. Boulton described this empirically and Neuman (1972, 1975) gave the widely used analytical solution, which also handles partial penetration and anisotropy. Fitting one Theis curve to all the data gives neither storage value correctly, so tests in unconfined aquifers must run long enough to reach the late segment.
An aquifer pumping test pumps a well at a known, constant rate and records water levels in the pumped well and in one or more observation wells over time. It is the most reliable way to measure T and S.
Good practice: record static levels before the test to detect trends and nearby pumping; place observation wells at several distances (commonly tens to a few hundred metres), screened in the same aquifer; keep discharge constant and measure it with a calibrated meter, orifice or weir; record levels at logarithmically increasing intervals (every few seconds at first, then minutes, then hours), because the analysis uses log time; discharge the pumped water well away from the test site so it does not recharge the aquifer; and continue long enough for the relevant behaviour — often one to three days for a confined aquifer and longer for an unconfined one. After pumping stops, recovery is recorded with the same care.
Observation-well data are preferred for calculating S. Drawdown in the pumped well includes non-linear well losses, and its effective radius is uncertain, so S computed from it is unreliable even when T is acceptable.
Theis type-curve matching: plot observed s against t (or t/r²) on log-log paper, overlay the W(u)–1/u type curve drawn to the same scale, and slide it (keeping axes parallel) until the data fit. A match point gives T = QW(u)/(4πs) and S = 4Ttu/r².
Cooper-Jacob time-drawdown: plot s against log t for an observation well; fit the straight late-time portion. Then T = 2.3Q/(4πΔs), where Δs is drawdown per log cycle, and S = 2.25Tt₀/r², where t₀ is the time at which the straight line crosses zero drawdown. Time units must match: if T is in m²/day, t₀ must be in days. Example: Q = 1800 m³/day, Δs = 0.48 m, r = 30 m, t₀ = 0.9 min. T = 2.3 × 1800 / (4π × 0.48) = 686 m²/day; t₀ = 0.9/1440 day; S = 2.25 × 686 × 0.000625 / 900 = 1.07 × 10⁻³. Forgetting to convert minutes to days inflates S by a factor of 1440.
Distance-drawdown: with three or more observation wells at one time, plot s against log r; T = 2.3Q/(2πΔs) and S = 2.25Tt/r₀², where r₀ is the distance at which the line meets zero drawdown.
Theis recovery: plot residual drawdown s′ against log(t/t′), where t is time since pumping started and t′ time since it stopped; T = 2.3Q/(4πΔs′).
Step-drawdown test: the well is pumped at three or more increasing rates. Jacob's relation s_w = BQ + CQ² separates aquifer loss BQ from non-linear well loss CQ². Well efficiency is BQ/s_w. Example: B = 1.5 × 10⁻³ day/m², C = 3 × 10⁻⁷ day²/m⁵, Q = 1500 m³/day gives s_w = 2.25 + 0.675 = 2.925 m, efficiency 77%.
When two or more wells pump from the same aquifer their cones overlap and each well's drawdown increases. Because the confined flow equation is linear, drawdowns add: the drawdown at any point is the sum of drawdowns caused by each well acting alone (superposition). For unconfined aquifers superposition is applied to h² (or to Jacob-corrected drawdowns) and is approximate.
Example: two wells 120 m apart each pump 1200 m³/day from a confined aquifer with T = 500 m²/day; take R = 600 m. The extra drawdown at one well caused by the other is (1200/(2π × 500)) ln(600/120) = 0.61 m. Several countries and Indian states regulate minimum spacing between irrigation wells; the distances are set by local law and vary.
Boundaries are handled with image wells. A straight recharge boundary (a river in good hydraulic connection) is represented by an imaginary recharging well of equal rate placed at the mirror-image position across the boundary; its negative drawdown holds the head fixed at the boundary, and drawdown eventually stabilises. A straight impermeable (barrier) boundary is represented by an imaginary pumping well at the mirror position; once its effect arrives, the slope of the Cooper-Jacob time-drawdown line doubles. A change in slope on a semi-log plot is therefore the field signature of a boundary, and its timing can be used to estimate the distance to it.
A drilled well in unconsolidated material has, from the top: a sanitary seal of cement or bentonite grout in the annulus near the surface, which stops surface water running down the outside of the casing; the pump-housing casing, large enough to take the pump with clearance; the casing string down to the aquifer; the screen (or slotted pipe) opposite the water-bearing layers; a short blank sump or sediment trap at the bottom; and, where needed, a gravel (filter) pack in the annulus between screen and borehole wall.
Design proceeds in a fixed order. First the required yield and the expected pumping level set the pump type and size, which fixes the diameter of the pump-housing casing; it must pass the pump bowls or motor with clearance for installation and, for submersibles, for cooling flow. Next the borehole log and sieve analyses of aquifer samples fix where the screen goes and its slot size. Then screen length and diameter are chosen so that entrance velocity is low. Finally the need for, and grading of, a gravel pack is decided. Materials (mild steel, stainless steel, thermoplastics, fibreglass) follow water chemistry: corrosive water attacks mild steel, encrusting water (carbonate, iron) clogs slots.
Screen length depends on aquifer type and thickness. In a homogeneous confined aquifer, standard guidance (for example Driscoll's Groundwater and Wells) is to screen most of the aquifer — commonly about 70 to 80 per cent of its thickness, placed centrally — because drawdown does not reduce the saturated thickness. In a homogeneous unconfined aquifer the upper part will be dewatered during pumping, so the screen is placed in the lower portion, commonly the lower third to half. In layered aquifers the most permeable layers are screened.
Slot size is chosen from the grain-size distribution of the aquifer. In a naturally developed well (no artificial pack), the slot is sized to let the finer fraction pass during development while retaining the coarser fraction, which forms a natural graded filter around the screen. Texts give a slot that retains a stated percentage of the formation — often in the range of about 40 to 60 per cent — and the exact percentage depends on the uniformity of the sand, the corrosivity of the water and confidence in the samples.
Entrance velocity through the screen openings is kept low, commonly at or below about 0.03 m/s, to limit head loss, sand movement, incrustation and corrosion. The required open area is Q/v. Example: Q = 35 L/s, screen diameter 200 mm, open area 15 per cent of the screen surface: open area per metre = π × 0.2 × 0.15 = 0.0942 m²/m, required open area = 0.035/0.03 = 1.167 m², so length ≥ 12.4 m. Continuous-slot wire-wound screens have V-shaped openings widening inwards (so grains do not jam) and the highest open area.
An artificial gravel pack is placed when the aquifer is too fine or uniform for a natural pack to form, or is a sloughing weak sandstone; coarse, well-graded aquifers do not need one.
The uniformity coefficient Cu = D₆₀/D₁₀ (the grain sizes at which 60 and 10 per cent of the sample by weight is finer) describes the grading. A uniform fine sand has a low Cu; texts commonly treat Cu below about 2 to 3 together with a fine effective size as indicating that a pack is needed.
Pack grain size is set by a pack-aquifer ratio: a characteristic size of the pack is made a fixed multiple of the corresponding size of the aquifer. Many texts use a multiple of about 4 to 6 (smaller for fine uniform aquifers, larger for coarser graded ones), though the grain percentile it is applied to differs between texts, so the method used must be stated. The pack itself should be uniform (low Cu), composed of clean, well-rounded siliceous grains that do not dissolve, and the screen slot is then chosen to retain most of the pack (commonly 90 per cent or more).
Pack thickness is typically in the range of about 75 to 200 mm. Thin packs risk gaps; thick ones defeat development, because surging energy cannot reach the formation. Packs are placed through a tremie pipe to avoid segregation.
The method is chosen by geology, depth, diameter, water availability and cost.
Shallow wells are dug (wide, lined, storing water), bored with augers, driven as well points, or jetted with water in sand.
The cable-tool (percussion) method repeatedly lifts and drops a heavy bit; a bailer removes the slurry. It is slow but simple, uses little water, works in boulders and fractured rock, and gives good formation samples and water-level observations during drilling.
Direct rotary drilling turns a bit on a drill-pipe string while drilling fluid is pumped down the pipe and returns up the annulus carrying cuttings. The fluid — water with bentonite clay or polymer additives — cools and lubricates the bit, lifts cuttings, holds the hole open by hydrostatic pressure and by forming a thin filter cake on the wall, and suspends cuttings when circulation stops. It is fast in unconsolidated sediments, but the filter cake must later be removed by development.
Reverse-circulation rotary reverses the flow: fluid (often mainly water) runs down the annulus and returns, with cuttings, up the large-bore drill pipe under suction or air lift. It suits large-diameter wells in unconsolidated sediments and causes less mud invasion, but needs a lot of water.
Air rotary drilling uses compressed air in place of liquid, and the down-the-hole (DTH) hammer adds a pneumatic percussion hammer behind the bit. DTH drilling is the standard method for boreholes in hard crystalline rock and basalt.
Development removes fines and drilling mud from around the screen, repairs drilling damage and stabilises the formation so the well yields sand-free water with higher specific capacity and longer life.
The principle is to reverse flow through the screen repeatedly, breaking grain bridges and drawing fines in for removal while coarser grains settle into a graded filter. Common methods are: overpumping — pumping at a rate higher than the design rate, simple but inefficient because flow is in one direction only; backwashing or rawhiding — starting and stopping a pump without a check valve, so the water column surges back through the screen; mechanical surging — moving a surge block (a close-fitting plunger) up and down inside the casing above or within the screen, then bailing or pumping out the fines; air-lift surging and pumping — injecting compressed air through an eductor pipe to surge and lift water; high-velocity jetting — rotating horizontal water jets directed through the screen openings, very effective with continuous-slot screens.
Chemical dispersants such as polyphosphates can help break down clay and drilling mud, though some texts caution that phosphate residues may encourage bacterial growth. In hard-rock boreholes, hydraulic fracturing — pumping water at high pressure into a sealed section — is used to open and extend fractures. Development continues until the water is clear and specific capacity stops improving; acceptable sand content is set by standards or contract and varies.
After development the well is tested (at least a short yield test, ideally a step test), disinfected with a chlorine solution to kill bacteria introduced during construction, and sealed at the surface with a grouted annulus, a concrete apron sloping away from the casing and a sanitary cap. The driller's log is the well's permanent record, and many countries require it to be filed.
Yields decline over time for several reasons: incrustation of the screen by carbonate or iron compounds precipitating as pressure and temperature change at the screen; biofouling by iron and sulphur bacteria; corrosion; sand pumping; and falling regional water levels. Monitoring specific capacity once or twice a year is the simplest early warning — a steady fall points to clogging at the well rather than aquifer decline. Rehabilitation uses mechanical cleaning (brushing, surging, jetting), acid treatment for carbonate incrustation, and chlorine or other oxidising treatment for biofouling, followed by redevelopment. Chemicals and contact times follow national guidance and safety rules.
Alongside electromagnetics, seismic refraction, magnetics and remote sensing of lineaments, electrical resistivity is the most widely used method for water wells because it is cheap and responds to water content, salinity and clay.
Most rock-forming minerals are poor conductors; current flows mainly through the water in pores and fractures, and along the surfaces of clay minerals. The bulk resistivity of a formation therefore falls as porosity and saturation rise, as pore water becomes more saline, and as clay content rises. Archie's empirical law for clean (clay-free) saturated rock expresses this as ρ_rock = a ρ_w φ⁻ᵐ, where ρ_w is pore-water resistivity, φ porosity and a and m empirical constants; the ratio ρ_rock/ρ_w is the formation factor.
Clays and saline-water sands have low resistivities, fresh-water sands and gravels and weathered or fractured rock have moderate values, and dry sand or unweathered crystalline rock have very high values. Published ranges overlap widely, so a low reading may mean clay or salty water and a moderate one may mean a good aquifer or a clayey weathered layer. Interpretation must be calibrated against borehole logs in the area.
Current I is passed into the ground through two current electrodes A and B, and the potential difference ΔV is measured between two potential electrodes M and N. For a homogeneous ground ΔV/I depends only on resistivity and electrode geometry, so resistivity = K × ΔV/I, where K is the geometric factor. Over layered ground the same formula gives an apparent resistivity ρₐ, a weighted average of the layers sampled.
In the Wenner array the four electrodes are equally spaced at distance a, in the order A M N B, and K = 2πa. Example: a = 15 m, ΔV/I = 0.8 Ω; ρₐ = 2π × 15 × 0.8 = 75.4 Ω·m.
In the Schlumberger array the potential electrodes are close together at the centre, and the current electrodes are moved outward. With L = AB/2 and l = MN/2, K = π(L² − l²)/(2l). Example: L = 40 m, l = 2.5 m, ΔV/I = 0.12 Ω; K = π(1600 − 6.25)/5 = 1,001.4 m, ρₐ = 120.2 Ω·m. A frequent error is to divide by l instead of 2l (that is, by MN/2 instead of MN), which doubles the answer. Setting L = 1.5a and l = 0.5a returns the Wenner factor 2πa, a useful check.
The Schlumberger array needs fewer electrode moves and is less affected by near-surface variation, so it is the usual choice for sounding.
A vertical electrical sounding (VES) keeps the centre fixed and progressively increases the current-electrode spacing. As the current penetrates deeper, ρₐ reflects deeper layers; plotting ρₐ against AB/2 on log-log paper gives a sounding curve. Resistivity profiling keeps the spacing fixed and moves the whole array along a line, mapping lateral changes such as a buried channel or a fracture zone at roughly constant depth.
Three-layer curves are named by the relation between layer resistivities: H type (ρ₁ > ρ₂ < ρ₃, a conductive middle layer — the classic hard-rock case of dry topsoil over a saturated weathered layer over fresh rock); K type (ρ₁ < ρ₂ > ρ₃); A type (ρ₁ < ρ₂ < ρ₃); and Q type (ρ₁ > ρ₂ > ρ₃). Curves are interpreted by master-curve matching or computer inversion.
Interpretation is not unique. By the principle of equivalence, a thin conductive layer between resistive ones is resolved only through its longitudinal conductance (thickness divided by resistivity), and a thin resistive layer between conductive ones only through its transverse resistance (thickness times resistivity); different thickness-resistivity pairs give the same curve. By suppression, a thin layer whose resistivity is intermediate between its neighbours may not show at all. VES results must be tied to borehole logs.
Recharge is water that reaches the water table. In agricultural areas it comes from rainfall, seepage from canals, tanks and rivers, and return flow from irrigation. Estimates are uncertain, so several methods are compared.
The water-table fluctuation (WTF) method multiplies the rise of the water table after a recharge season by the specific yield: R = Sy × Δh. Example: a monsoon rise of 2.8 m in an aquifer with Sy = 0.10 gives 280 mm of recharge (plus any groundwater pumped during the season, which must be added back in a full balance). It is sensitive to the uncertain Sy.
The chloride mass balance (CMB) assumes chloride in rain is concentrated by evapotranspiration and carried to the water table conservatively: R = P × Cl_p / Cl_gw. Example: P = 700 mm/year, chloride in rainfall (including dry deposition) 3 mg/L and in groundwater 60 mg/L gives R = 35 mm/year. It fails where there are other chloride sources such as fertiliser, irrigation water or evaporite rocks.
Other methods: soil-water balance, lysimeters, tracers and groundwater models. Government assessments often use norms: India's Central Ground Water Board uses the Ground Water Estimation Committee methodology (GEC-2015), which combines the WTF method with rainfall-infiltration factors and categorises assessment units by stage of groundwater extraction — annual extraction as a percentage of annual extractable resource — as safe (up to 70 per cent), semi-critical (70–90), critical (90–100) or over-exploited (above 100), together with long-term water-level trends.
Artificial recharge, now usually called managed aquifer recharge (MAR), deliberately adds water to aquifers for later use or for environmental benefit. The method depends on where the aquifer is and what lies above it.
Surface spreading — basins, ditches and furrows, flooding of fields — needs permeable soil and an unconfined aquifer without clay layers above it; it is cheap and the soil provides some treatment. In-channel structures slow and spread stream flow: check dams, nala (gully) bunds, gabion structures, and percolation tanks sited on permeable ground upstream of the wells they are meant to support. Recharge pits, trenches and shafts penetrate a shallow clay or silt layer to reach permeable material beneath. Recharge wells and injection wells place water directly into a deeper or confined aquifer; aquifer storage and recovery (ASR) uses the same well to inject in the wet season and pump in the dry season. Induced bank infiltration draws river water through the riverbed by pumping wells near the bank. Subsurface dykes (groundwater dams) built across a narrow valley hold water in the sediments.
The main operational problem is clogging: suspended sediment, algae and bacterial growth seal the infiltration surface or the well screen. Basins are managed by alternating wetting and drying and by scraping the surface layer; injection wells need clean, pre-filtered water and regular backflushing. Recharge with treated wastewater or stormwater is regulated in most countries.
Positive-displacement pumps trap a fixed volume and push it out; discharge is nearly independent of head, so they must never run against a closed valve without a relief device. They include reciprocating (piston, plunger, diaphragm) and rotary types (gear, vane, screw, and the progressive-cavity or helical-rotor pump common in small solar deep-well systems). For a single-acting piston pump the theoretical discharge is Q = A × L × N / 60, with A the piston area, L the stroke and N the speed in rpm; a double-acting pump delivers twice this. Example: bore 100 mm, stroke 200 mm, 50 rpm gives Q = 0.00785 × 0.2 × 50/60 = 1.31 L/s. Slip is (theoretical − actual)/theoretical; air vessels smooth the pulsating flow.
Rotodynamic pumps add velocity with a rotating impeller and convert it to pressure. They are classified by flow direction through the impeller: radial-flow (centrifugal, high head, low flow), mixed-flow, and axial-flow (propeller, low head, very high flow).
For wells: a surface-mounted centrifugal pump works only while the pumping level is within its suction lift; a vertical turbine pump has multistage diffuser bowls in the well driven by a line shaft from a surface motor; a submersible pump has the motor close-coupled below the bowls, both submerged, with power fed by cable. A jet (ejector) pump recirculates part of its discharge through a nozzle down the well to lift water to a surface centrifugal pump; it is simple but inefficient. An airlift pump injects compressed air into a submerged eductor pipe so the lighter air-water mixture rises; it tolerates sand but is inefficient and needs deep submergence. The hydraulic ram uses the water-hammer pressure of a falling stream to lift a fraction of that water higher, with no external power.
The total dynamic head (TDH) a pump must supply is the sum of static suction lift (or minus static suction head), static delivery head, friction and minor losses in suction and delivery pipes, the velocity head at discharge, and any pressure required at the outlet (for a sprinkler or drip system). For a well, static lift is measured from the pumping water level — the static water level plus drawdown plus any expected seasonal decline — not from the static level.
Water (hydraulic) power is P_w = ρgQH. Shaft (brake) power is P_w/η_p, where η_p is pump efficiency, and electrical input is shaft power divided by motor efficiency η_m. Example: Q = 20 L/s, H = 30 m, η_p = 0.65, η_m = 0.85. P_w = 1000 × 9.81 × 0.02 × 30 = 5.89 kW; shaft power = 9.06 kW; motor input = 10.65 kW. Using 1 hp = 746 W, shaft power is 12.1 hp. (A metric horsepower is about 735.5 W.)
The Euler equation gives the ideal head of a rotodynamic impeller: H = (u₂V_w2 − u₁V_w1)/g, where u is blade speed (πDN/60) and V_w the whirl component of absolute velocity at outlet (2) and inlet (1). With radial (shock-free) entry V_w1 = 0 and H = u₂V_w2/g. Actual head is lower because of slip and losses.
Manufacturers publish constant-speed characteristic curves against discharge: head (H–Q), shaft power (P–Q), efficiency (η–Q) and required NPSH (NPSHr–Q). For a radial-flow centrifugal pump the head is highest at zero flow (the shutoff head) and falls as flow increases; efficiency rises to a peak — the best efficiency point (BEP) — and then falls; power rises with flow. For axial-flow pumps the head curve is steep and power is highest at shutoff.
This difference governs starting: a radial-flow pump is started with the delivery valve closed (minimum power), whereas an axial-flow pump is started with the valve open to avoid overloading the motor.
The system curve gives the head the piping system needs at each flow: H_sys = H_static + kQ², the static lift plus friction and minor losses that rise roughly with the square of flow. The pump operates where its H–Q curve crosses the system curve. Throttling a delivery valve steepens the system curve and moves the operating point to a lower flow — a wasteful way to control flow; changing speed with a variable-frequency drive or trimming the impeller is more efficient.
Pumps in series add heads at the same flow, for high lifts. Pumps in parallel add flows at the same head. Because the system curve rises with flow, two identical pumps in parallel deliver less than twice the flow of one, and the shortfall is largest on a steep, friction-dominated system. A pump should be selected so that its operating point lies close to its BEP.
Specific speed classifies impeller shape by the combination of speed, flow and head at the best efficiency point: N_s = N√Q / H^(3/4). For a multistage pump H is the head per stage; for a double-suction impeller many conventions use half the flow. Geometrically similar pumps operating at corresponding points have the same specific speed, so it is a property of the design, not of one operating point.
Low N_s means a narrow radial impeller of large diameter (high head, low flow); high N_s means a wide, open axial propeller (low head, high flow); mixed-flow impellers lie between. Specific speed is not dimensionless in its usual form, so its numerical value depends on units. In US customary units (rpm, US gpm, ft), radial pumps are commonly below about 4,000, mixed-flow roughly 4,000 to 9,000–10,000, and axial above that. In metric units (rpm, m³/s, m) the values are about 51.6 times smaller. Band edges vary between texts.
Example: N = 1450 rpm, Q = 0.04 m³/s, H = 20 m. N_s = 1450 × 0.2 / 20^0.75 = 30.7 (rpm, m³/s, m), a radial-flow impeller. Turbines use N√P / H^(5/4) instead.
The affinity (similarity) laws predict how a pump's performance changes with speed or impeller diameter, at hydraulically similar points (constant efficiency): Q ∝ N D³, H ∝ N² D², P ∝ N³ D⁵ for geometrically similar pumps of different size; for one pump at changed speed, Q ∝ N, H ∝ N², P ∝ N³; for small trims of the same impeller at constant speed, approximately Q ∝ D, H ∝ D², P ∝ D³.
Example: a pump absorbs 7.5 kW at 1450 rpm. Driven at 2900 rpm, power rises by a factor of 2³ = 8, to 60 kW.
The laws move the pump curve, not the operating point directly. Each point on the old curve moves along a parabola H ∝ Q² through the origin. If the system curve is itself a parabola through the origin (pure friction, no static lift), the new operating point is simply scaled by the laws. If the system has a large static lift — typical of well pumping — reducing speed reduces flow much more than proportionally, and below a certain speed the pump cannot overcome the static lift at all. The new operating point must be found by intersecting the scaled pump curve with the actual system curve.
Cavitation occurs when the local static pressure in the liquid falls to its vapour pressure, usually at the eye of the impeller. Vapour bubbles form and then collapse violently when they reach higher-pressure regions. The results are gravel-like noise, vibration, loss of head and efficiency, and pitting of the vanes.
Net positive suction head available is the absolute head at the pump suction above vapour pressure: NPSHa = p_atm/ρg − p_v/ρg − z_s − h_fs, where z_s is the static suction lift (negative if the liquid level is above the pump) and h_fs the suction-pipe friction and minor losses. NPSH required (NPSHr) is a property of the pump, found by test; the Hydraulic Institute and ISO define it at the flow where head has fallen by 3 per cent because of cavitation, so some cavitation already exists at NPSHr. A margin, set by standards and application, is needed.
Example at sea level: p_atm = 101.3 kPa, water at 20 °C with p_v = 2.34 kPa and ρ = 998 kg/m³, suction lift 4.5 m, suction losses 0.7 m. (101.3 − 2.34) × 1000 / (998 × 9.81) = 10.11 m, so NPSHa = 10.11 − 4.5 − 0.7 = 4.91 m.
NPSHa falls with altitude (lower atmospheric pressure), with warmer water (higher vapour pressure), with greater suction lift and with more suction friction. Hence the practical suction lift at sea level is about 6 to 7 m, not the theoretical 10.3 m. Remedies: lower the pump, shorten and enlarge the suction pipe, remove fittings, reduce speed or flow, or choose a pump with lower NPSHr. Throttling on the suction side makes cavitation worse and is never used for flow control. Thoma's cavitation coefficient σ = NPSHr/H relates required NPSH to head and rises with specific speed.
Selection starts from two numbers: the discharge wanted and the total dynamic head at that discharge, and both must respect the well. The design discharge comes from peak irrigation demand and pumping hours but must not exceed the safe yield of the well found from a pumping test; overpumping draws in sand and wastes energy.
The head is built up from the lowest expected pumping level (static level in the driest season plus drawdown at design discharge, plus an allowance for long-term decline), the elevation to the outlet, pipe friction (Darcy-Weisbach or Hazen-Williams), fittings, and any operating pressure required by a sprinkler or drip system.
With Q and TDH known, the type follows. If the pumping level stays within the practical suction lift, a surface centrifugal pump is cheapest and easiest to maintain. If not, a vertical turbine or a submersible pump is used; submersibles dominate small and medium bore wells, line-shaft turbines persist in large-diameter wells and where motors must stay accessible. Large flows at low lift suit mixed- or axial-flow pumps.
The chosen model's H–Q curve should pass through the duty point close to its BEP, with NPSH margin (for surface pumps), a motor rated to cover the maximum power over the likely range of operating points, and a power supply — grid, diesel engine, or solar — that matches the duty. Ask for test results to a recognised national or international pump test standard rather than catalogue claims.
Surface centrifugal pumps: set the pump as close to the water as possible on a rigid foundation, with pump and motor shafts aligned. Keep the suction pipe short, airtight, at least as large as the pump inlet, and rising steadily towards the pump so no air pockets form; use an eccentric reducer with its flat side on top at the pump inlet. Fit a foot valve with strainer at the suction end to hold the prime and keep out debris, submerged deeply enough to avoid vortices drawing in air. On the delivery side fit a non-return (check) valve to protect the pump from reverse flow and water hammer, then a gate or sluice valve for isolation. Prime fully before starting.
Submersible pumps: install below the lowest expected pumping level with some margin, but above the sump so sand is not drawn in. The motor depends on water flowing past it for cooling; where the well diameter is much larger than the motor or the water enters above the pump, a flow sleeve (shroud) is fitted to force water past the motor. Size the cable for voltage drop and protect the motor against dry running, overload and phase loss.
Common faults: no delivery — not primed, suction air leak, blocked foot valve, wrong rotation, excessive suction lift; low delivery — worn impeller, blocked strainer, falling pumping level; overload — head far below design (a radial pump's power rises), low voltage; noise — cavitation, misalignment, worn bearings.
A solar pumping system has a PV array, a controller or inverter, a pump and motor, and usually a storage tank instead of batteries. Motors are DC brushless or AC with a variable-frequency inverter. The controller performs maximum power point tracking (MPPT): it continuously adjusts the operating voltage and current (and hence pump speed) so the array delivers the most power available at the current irradiance and temperature. Output follows the sun, peaking near solar noon.
Water is stored instead of electricity because a tank is cheaper and longer-lived than batteries, and crops need a daily volume, not continuous flow; systems are designed for daily volume.
Sizing: hydraulic energy per day E = ρgVH. With V in m³ and H in m, E (kWh) = V × H / 367. Example: 40 m³/day at 35 m TDH needs 3.81 kWh/day of hydraulic energy. With an overall subsystem (motor-pump-controller) efficiency of 45 per cent, 5.5 peak sun hours and a derating factor of 0.8 for temperature, dust and mismatch, the array must be about 3.81 / (0.45 × 5.5 × 0.8) = 1.93 kWp. Peak sun hours come from the critical design month; efficiencies and derating vary by product and site. Fixed arrays are commonly tilted near the site latitude, facing the equator.
Solar pumps have high capital cost and very low running cost. Many governments subsidise them — India's PM-KUSUM scheme is one example. Because the marginal cost of pumping is almost zero, studies have raised the concern that solar pumps can accelerate groundwater depletion where extraction is not otherwise controlled; grid-connected designs that pay farmers for surplus electricity have been proposed partly to give them a reason to pump less.
Learn to recognise instantly which equation fits: confined or unconfined, steady or unsteady, observation-well data or pumped-well data. Practise the ten standard calculations until the unit conversions are automatic: storage change, Darcy flux and travel time, Thiem, Dupuit, Cooper-Jacob drawdown and T and S from a straight line, interference by superposition, screen length from entrance velocity, Wenner and Schlumberger apparent resistivity, pump power, specific speed, affinity scaling and NPSHa. Draw a sketch of the well and cone for every problem. In the lab, run a small pumping test or a VES if your department has the equipment; one field dataset teaches more than twenty textbook examples.
A young engineer with a state groundwater department, an irrigation contractor or a drilling firm designs and supervises tube wells: reading driller's logs and sieve analyses to set screen positions and slot sizes, deciding whether a gravel pack is needed, checking development until the water runs clear, and running step and constant-rate tests to set the safe pumping rate. On the pump side the daily work is selecting a submersible or surface pump for a stated area and crop, calculating TDH from the lowest pumping level, sizing solar arrays for subsidised pumps, and diagnosing field complaints — low discharge, tripping motors, sand in the water — by checking levels, curves and installation before blaming the pump.
After twenty-five years the decisions are about well fields and basins rather than single wells. A senior engineer sets spacing and pumping schedules to limit interference, reads decades of water-level and specific-capacity records to separate well deterioration from aquifer decline, decides where recharge structures will actually work, and writes the technical specifications and acceptance tests for drilling and pump procurement. He or she also advises regulators on groundwater categorisation, permits and energy policy — for example how solar-pump subsidies and electricity pricing affect extraction — and trains drilling crews and junior engineers, whose field habits determine whether wells last five years or forty.
A researcher with long field experience works where the classical assumptions fail: heterogeneous and fractured hard-rock aquifers, delayed yield, partial penetration, leaky multi-aquifer systems and non-Darcian flow near wells. Typical work includes calibrating numerical groundwater models against pumping-test and long-term monitoring data, quantifying recharge with tracers and multiple independent methods, evaluating managed aquifer recharge at scale, and studying the coupled economics of energy and groundwater — how electricity subsidies, solar pumps and water markets change farmer behaviour and aquifer trajectories. Such a researcher also designs monitoring networks and teaches the uncertainty in every T, S and recharge estimate that practitioners are tempted to treat as exact.
This manual does not cover numerical groundwater modelling, well-hydraulics solutions for partially penetrating wells and large-diameter dug wells (Papadopulos-Cooper), slug-test analysis in detail, fractured-rock and karst hydraulics, groundwater quality and contaminant transport, or geophysical methods other than resistivity beyond a mention. It gives screen-slot and gravel-pack criteria only as the ranges that textbooks agree on, because the exact percentile rules differ between texts and national standards; use your national well-construction code. Well-spacing rules, groundwater permits and solar-pump subsidies are country- and state-specific and are named, not tabulated. It has no diagrams yet (type curves, pump curves and electrode layouts are described in words).
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions.
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