Question 1

Groundwater engineering: In which type of tube well is shrouding (gravel packing around the screen) specifically provided to control sand entry and improve yield?

Accepted Answer

Introduction / Context: Shrouding, also known as gravel packing, is a standard development technique in well engineering. It improves well efficiency by stabilizing the aquifer formation around the screen and filtering out fine particles that would otherwise be carried into the well. Given Data / Assumptions: Well construction involves a well screen or strainer to admit water. Formation contains sands/silts prone to migration under pumping. Objective is to minimize sand entry and maintain higher specific capacity. Concept / Approach: In strainer (screen) type tube wells, a graded gravel envelope (shroud) is placed between the borehole wall and the screen. The gravel gradation is selected to retain formation fines while allowing water to pass, reducing head losses and wear of pumping equipment due to sand. Step-by-Step Solution: Identify well type: presence of screens/strainers indicates suitability for gravel packing.Shrouding design: choose filter gradation satisfying empirical retention criteria (e.g., D15(filter) / D85(formation) ratios).Performance: gravel pack increases open area and reduces entrance velocity, improving yield and longevity. Verification / Alternative check: Field experience shows significant reduction in sand pumping and improved efficiency after proper gravel packing in screen-type wells compared with unshrouded installations. Why Other Options Are Wrong: Cavity type wells rely on developed cavities in coarse formations; shrouding is not typical.Generic slotted or perforated pipes without designed screens may not employ engineered gravel packs. Common Pitfalls: Using poorly graded or too fine gravel leading to clogging; omitting a centralizer, causing uneven pack thickness; ignoring uniformity coefficient in filter design. Final Answer: Strainer (screen) type tube wells

Question 2

Irrigation engineering: During the growth period of a crop, what does its consumptive use represent?

Accepted Answer

Introduction / Context: Consumptive use (also termed crop water use) is central to irrigation planning. It quantifies the water actually used and lost to the atmosphere by a crop and its immediate environment, guiding irrigation scheduling and water resource allocation. Given Data / Assumptions: Crop actively growing over a defined season. Loss pathways include transpiration through leaves and evaporation from soil and wet canopy. Standard agronomic definition of consumptive use as evapotranspiration (ET). Concept / Approach: Consumptive use is effectively ET = evaporation + transpiration. Many texts also consider evaporation from intercepted rainfall on leaves as part of the evaporative component. Hence, interception loss, direct soil/water surface evaporation, and plant transpiration collectively constitute consumptive use. Step-by-Step Solution: Recognize ET components: E (soil/canopy evaporation) + T (transpiration).Interception contributes to E when intercepted water re-evaporates from plant surfaces.Therefore, consumptive use during growth is the sum of these losses. Verification / Alternative check: Crop coefficients (Kc) applied to reference ET (ETo) encapsulate all such losses for practical irrigation design, implicitly covering evaporation and transpiration. Why Other Options Are Wrong: Any single-component answer underestimates true crop water demand. Common Pitfalls: Ignoring interception when canopy is frequently wetted; double-counting percolation losses (not part of consumptive use) as ET; confusing effective rainfall with ET. Final Answer: All of the above (combined evapotranspiration components)

Question 3

Flood estimation for catchment shape: For a fan-shaped catchment area, which empirical formula is commonly recommended for estimating high floods in Indian practice?

Accepted Answer

Introduction / Context: Peak flood estimation for ungauged basins in India often relies on empirical formulae tailored to regional hydrology and catchment geometry. The plan shape of a catchment (fan-shaped vs elongated) influences concentration time and peak runoff characteristics. Given Data / Assumptions: Fan-shaped catchment, promoting rapid concentration of flow. No long-term gauge data available; empirical formula needed. Use of classical Indian formulae: Dicken's, Ryve's, Inglis, each with regional context. Concept / Approach: Fan-shaped basins tend to yield higher, sharper floods due to short travel times. Traditional Indian practice commonly associates Ryve's formula with catchments in southern regions and situations where quick concentration is expected, making it suitable for fan-shaped basins in standard MCQ conventions. Step-by-Step Solution: Identify shape (fan-shaped) ⇒ expect higher peak.Select an empirical relation aligned with quick concentration characteristics.Ryve's formula is generally cited in teaching problems for fan-shaped catchments; hence it is the accepted choice here. Verification / Alternative check: Where data permit, regional calibration should be used. In absence of data, shape-based selection using widely taught heuristics is acceptable for preliminary estimates. Why Other Options Are Wrong: Dicken's and Inglis are region-specific or tuned differently; they are not the standard selection for a generic fan-shaped-case MCQ.'None of these' is incorrect because a suitable option exists. Common Pitfalls: Applying a formula outside its regional validity without adjustment; ignoring catchment lag and storage effects; forgetting to check units and return period consistency. Final Answer: Ryve's formula

Question 4

Hydrometeorology instrumentation: What is the standard rim height of a standard (Symons-type) rain gauge above ground level used for measuring rainfall?

Accepted Answer

Introduction / Context: Rain gauges must be installed at a prescribed height above ground to minimize splash-in/splash-out errors and interference from surrounding features. In Indian practice (Symons rain gauge), a standard mounting height is adopted to ensure consistency across stations. Given Data / Assumptions: Standard non-recording rain gauge installation. Open exposure, away from obstructions per siting guidelines. Rim elevation above ground is fixed by standard. Concept / Approach: The standard rim height is maintained to reduce local turbulence and ground splash effects while keeping access practical. In the Symons gauge commonly used, the rim is set at approximately 30 cm above ground level. Step-by-Step Solution: Install the gauge on a level base.Adjust stand so that the orifice rim is 30 cm above the soil surface.Verify verticality and unobstructed exposure as per siting recommendations. Verification / Alternative check: Field manuals and bureau standards specify the rim height; periodic inspections confirm compliance and calibration. Why Other Options Are Wrong: 10 cm or 20 cm: too low, prone to splash and local effects.50 cm: higher than standard; increases wind-induced error potential. Common Pitfalls: Placing the gauge near walls or tall vegetation; mounting at non-standard heights; poor leveling leading to biased catch. Final Answer: 30 cm

Question 5

Atmospheric moisture concepts: Which statements regarding absolute humidity, relative humidity, and measurement methods are correct?

Accepted Answer

Introduction / Context: Atmospheric moisture parameters are foundational in hydrology, irrigation scheduling, and weather analysis. Understanding absolute and relative humidity along with practical measurement approaches helps interpret evapotranspiration and rainfall processes. Given Data / Assumptions: Standard thermodynamic definitions of humidity metrics. Air assumed to be a mixture of dry air and water vapour. Psychrometry used in field practice for humidity estimation. Concept / Approach: Absolute humidity is defined as mass of water vapour per unit volume of air (e.g., g/m^3). Relative humidity (RH) is the ratio of actual vapour pressure to saturation vapour pressure at the same temperature; equivalently, RH can be expressed as the ratio of actual to saturation mixing ratios or densities under the same conditions. Psychrometers (dry-bulb/wet-bulb thermometers) infer humidity from wet-bulb depression. Step-by-Step Solution: Recognize absolute humidity as a volumetric measure of vapour content.Define RH via vapour pressures: RH = e / e_s at the same T.Confirm measurement: sling or Assmann psychrometers provide RH through psychrometric charts or equations. Verification / Alternative check: Cross-check with dew point and temperature to compute RH; hygrometers (resistive/capacitive) are modern alternatives, but psychrometer remains a reference method. Why Other Options Are Wrong: Each individual statement (a–d) is correct; hence the combined correct choice is 'All the above.' Common Pitfalls: Confusing specific humidity, mixing ratio, and absolute humidity; using RH without specifying the temperature; instrument exposure errors affecting readings. Final Answer: All the above.

Question 6

Hydrologic cycle comprehension: Which of the following statements about sources of atmospheric moisture, precipitation, and the continuity of the hydrologic cycle are correct?

Accepted Answer

Introduction / Context: The hydrologic (water) cycle describes the endless movement of water among the atmosphere, lithosphere, hydrosphere, and biosphere. Understanding its continuity and pathways supports water resources engineering and climate analysis. Given Data / Assumptions: Evaporation and transpiration supply atmospheric moisture. Condensation and precipitation return moisture to the surface. Surface and subsurface flows redistribute water into water bodies. Concept / Approach: Solar energy drives evaporation from oceans, lakes, and rivers; transpiration adds plant-sourced vapour. Moist air masses condense to clouds and precipitate, replenishing surface and ground waters. Water remains in the atmosphere as vapour, completing the cycle with continuous exchanges rather than a one-time process. Step-by-Step Solution: Identify sources: major evaporation from oceans, supplemented by inland waters and soils.Transport and transformation: advection and uplift lead to condensation, cloud formation, and precipitation.Return flows: precipitation feeds runoff to rivers/lakes and infiltration to aquifers, sustaining springs; re-evaporation continues the cycle. Verification / Alternative check: Water balance over long periods confirms mass conservation: precipitation ≈ evaporation + runoff + storage change on global scales. Why Other Options Are Wrong: Each statement (a–d) is individually correct; therefore the inclusive option 'All the above.' is the appropriate answer. Common Pitfalls: Assuming the hydrologic cycle is linear or seasonal only; neglecting groundwater-surface water interactions; ignoring sublimation/deposition pathways in cold regions. Final Answer: All the above.

Question 7

In surface hydrology, who originally enunciated the Unit Hydrograph theory that relates excess rainfall of unit depth to direct runoff hydrograph at a watershed outlet?

Accepted Answer

Introduction / Context: The Unit Hydrograph is a cornerstone concept in engineering hydrology. It provides a linear-response tool that converts a specific depth of effective rainfall over a catchment into a direct runoff hydrograph at the outlet, enabling design flood estimations and storm hydrograph synthesis. Given Data / Assumptions: The question asks for the original proponent of the Unit Hydrograph theory. Assumes familiarity with basic hydrology terms like excess rainfall, direct runoff, and watershed response. Historical attributions are important for exam recall. Concept / Approach: The Unit Hydrograph assumes linearity and time invariance of the catchment response for small storms. The original method describes a 1 cm (or 1 inch) effective rainfall pulse of specified duration and the resulting runoff hydrograph. Step-by-Step Solution: Identify key hydrology pioneers associated with runoff theory and hydrograph analysis.Robert E. Horton is known for infiltration and overland flow concepts, not for enunciating the Unit Hydrograph.Le-Roy K. Sherman published the Unit Hydrograph concept in the early 1930s, formalizing the linear unit response approach.Therefore, the correct attribution is to Le-Roy K. Sherman. Verification / Alternative check: Standard hydrology textbooks and historical reviews consistently credit Sherman with the first formal articulation of the Unit Hydrograph method. Why Other Options Are Wrong: W. W. Horner: not associated with origination of the Unit Hydrograph. Robert E. Horton: renowned for infiltration and hydrologic cycle insights but not for the Unit Hydrograph origination. Merrill Bernard: not credited with this specific theory. Common Pitfalls: Confusing Horton infiltration theory with Sherman Unit Hydrograph development. Assuming any early hydrology pioneer originated all common methods. Final Answer: Le-Roy K. Sherman

Question 8

In the derivation of Thiem’s formula for steady radial flow to a well, which of the following assumptions is NOT applicable for an unconfined aquifer case?

Accepted Answer

Introduction / Context: Thiem’s formula is widely used to analyze steady, laminar, radial groundwater flow to pumping wells. Correct identification of its modeling assumptions is critical to avoid applying it incorrectly. Given Data / Assumptions: Steady state flow conditions around a well. Question asks which assumption is not applicable. Focus on well penetration, aquifer properties, and flow geometry. Concept / Approach: Thiem’s derivation for both confined and unconfined aquifers assumes that the pumping well fully penetrates the saturated thickness so that streamlines are essentially horizontal and radial, and vertical gradients are negligible. Step-by-Step Solution: List standard assumptions: homogeneous and isotropic aquifer; steady laminar flow; fully penetrating well; negligible well losses; radial and horizontal flow; small water surface slope for unconfined.Evaluate each option against these assumptions.The statement that the well is sunk only up to the water table (not fully penetrating) contradicts the fully penetrating assumption.Hence this statement is not applicable to the classical derivation. Verification / Alternative check: Texts show partial penetration induces vertical flow components and requires more complex solutions; classical Thiem flow net assumes full penetration. Why Other Options Are Wrong: Homogeneous and isotropic: core assumption. Radial and horizontal flow: key simplification. Small water surface slope: used in unconfined analysis to linearize the drawdown surface. Common Pitfalls: Using Thiem with partially penetrating wells without correction factors. Ignoring anisotropy which alters effective hydraulic conductivity. Final Answer: The well has been sunk only up to the water table surface and does not fully penetrate the aquifer

Question 9

In catchment water balance terminology, the initial basin recharge is equal to which combination of early storm abstractions?

Accepted Answer

Introduction / Context: At the beginning of a storm, a portion of rainfall is abstracted before it contributes to surface runoff. Understanding these initial abstractions is essential for hydrograph separation and rainfall–runoff modeling. Given Data / Assumptions: Definitions of interception, depression storage, and infiltration to satisfy soil moisture deficit. Focus is on what constitutes initial basin recharge or initial abstraction. Concept / Approach: Initial basin recharge accounts for water that first replenishes storage compartments such as vegetation surfaces and depressions, and restores the soil profile up to field capacity, before runoff begins. Step-by-Step Solution: Interception: rainfall retained on vegetation and surfaces that later evaporates.Depression storage: water held in microtopographic hollows that must be filled prior to runoff.Infiltration to satisfy antecedent soil moisture deficit: initial infiltration used to restore near-surface storage.Summing these components represents the initial basin recharge or initial abstraction before runoff starts. Verification / Alternative check: Hydrologic models like SCS-CN explicitly account for initial abstraction as a combination of such storages prior to runoff generation. Why Other Options Are Wrong: Single-component choices ignore other equally important abstractions. Common Pitfalls: Confusing continuing losses (infiltration after runoff starts) with initial abstractions. Final Answer: All of the above (interception + depression storage + initial infiltration to satisfy moisture deficit)

Question 10

Identify the named relationship used to determine the average linear velocity of groundwater flow (in metres per day) based on hydraulic conductivity, hydraulic gradient, and effective porosity.

Accepted Answer

Introduction / Context: Groundwater movement is commonly analyzed using Darcy-based relationships. Translating discharge to average linear (seepage) velocity requires the concept of effective porosity to account for the actual flow pathways. Given Data / Assumptions: Steady laminar groundwater flow through a porous medium. Hydraulic conductivity K, hydraulic gradient i, and effective porosity n_e. Concept / Approach: Darcy’s law states Q = K i A. The Darcy or superficial velocity v_d = Q/A = K i. The average linear (seepage) velocity v is v = v_d / n_e = (K i) / n_e. Step-by-Step Solution: Start with Darcy: Q = K i A.Superficial velocity: v_d = Q/A = K i.Average linear velocity accounting for flow through voids: v = v_d / n_e = (K i)/n_e.This velocity is often expressed in metres per day when K and i are in compatible units. Verification / Alternative check: Field tracer tests typically show that groundwater moves at the seepage velocity which exceeds the Darcy velocity by roughly 1/n_e. Why Other Options Are Wrong: Hazen, Slichter, Meinzer: associated with empirical correlations for K from grain-size data, not the fundamental velocity relation. Common Pitfalls: Confusing Darcy velocity with seepage velocity; forgetting to divide by effective porosity. Final Answer: Darcy’s formula

Question 11

Precipitation caused by lifting of an air mass due specifically to pressure differences and atmospheric disturbances is termed as which type of precipitation?

Accepted Answer

Introduction / Context: Classifying precipitation mechanisms helps interpret storm patterns and design hydrologic structures. The lifting mechanism of the air mass determines the precipitation type. Given Data / Assumptions: Lifting of air due to pressure differences and frontal systems. Distinguish from thermal and orographic lifting. Concept / Approach: Three broad precipitation mechanisms: cyclonic (frontal) due to pressure systems, convective due to surface heating and buoyancy, and orographic due to terrain forcing. Step-by-Step Solution: Identify key phrase: pressure difference causes large-scale ascent.Cyclonic or frontal systems create pressure gradients and convergence lifting air masses along fronts.Therefore, precipitation is classified as cyclonic. Verification / Alternative check: Weather charts show fronts and low-pressure centers inducing widespread stratiform precipitation typical of cyclonic systems. Why Other Options Are Wrong: Convective: driven by strong surface heating, not primarily pressure gradients. Orographic: driven by airflow over topography. Common Pitfalls: Misreading pressure-driven lifting as convective because both can produce heavy rain. Final Answer: Cyclonic precipitation

Question 12

According to standard observational practice in India, at what local time is the daily rainfall typically recorded and entered in the gauge register?

Accepted Answer

Introduction / Context: Consistency in rainfall observation time is essential for hydrologic data quality and inter-station comparability. India follows a standard observation hour for daily totals. Given Data / Assumptions: Daily rain gauge readings must be taken at a fixed local time. Question asks the conventional time used in India. Concept / Approach: Indian meteorological and hydrological services traditionally observe daily precipitation at 8 A.M. local time to define the 24-hour accumulation period. Step-by-Step Solution: Identify the standard practice per national guidelines.Record the rainfall depth accumulated during the previous 24 hours at 8 A.M.Enter the measured value into the daily register for data continuity. Verification / Alternative check: Hydrology lab manuals and rain gauge operation instructions in India specify the 8 A.M. observation. Why Other Options Are Wrong: Noon, 4 P.M., 8 P.M.: not standard for daily recording in India. Common Pitfalls: Confusing synoptic observation hours with daily rainfall recording conventions. Final Answer: 8 A.M.

Question 13

Which factor primarily governs the infiltration capacity of a soil during a storm, acknowledging the roles of surface detention and saturated layer thickness as well?

Accepted Answer

Introduction / Context: Infiltration capacity describes the maximum rate at which soil can absorb water. It is central to runoff generation, erosion, and irrigation design. Given Data / Assumptions: Focus on physical controls of infiltration capacity. Recognize both subsurface and surface conditions. Concept / Approach: Infiltration depends on soil properties and boundary conditions. As the wetting front advances, hydraulic gradients and conductivity change, and surface detention modifies effective head. Step-by-Step Solution: Soil moisture: higher antecedent moisture reduces available storage and intake rate.Saturated layer thickness: as saturation grows, conductivity and gradients adjust, affecting capacity.Surface detention depth: ponded water increases head and may raise short-term infiltration until sealing or saturation limits appear.Therefore, all listed factors affect infiltration capacity. Verification / Alternative check: Experimental infiltration curves (e.g., Horton and Green-Ampt frameworks) reveal sensitivity to moisture conditions and head at the surface. Why Other Options Are Wrong: Single-factor answers ignore important interacting influences during storms. Common Pitfalls: Treating infiltration capacity as constant in time despite evolving saturation and crusting. Final Answer: All of the above

Question 14

In open channel control design, how can critical depth be produced for a given discharge in a prismatic channel?

Accepted Answer

Introduction / Context: Critical depth controls are used for flow measurement and to stabilize flow regimes. Creating critical depth involves modifying specific energy conditions at a control section. Given Data / Assumptions: Steady, prismatic channel with given discharge. Objective is to induce critical state (Froude number = 1) at a section. Concept / Approach: For a fixed discharge, critical depth corresponds to minimum specific energy. A control structure that increases specific energy demand relative to depth can force the flow to pass through the critical state. Step-by-Step Solution: Raising the bed (hump) effectively reduces available specific energy at a section, pushing the flow toward critical depth.Decreasing the width (contraction) increases velocity for the same discharge, increasing velocity head and promoting a critical state.Lowering the bed or increasing width generally moves conditions away from critical for the same discharge.Thus, both a hump and a contraction can produce critical depth. Verification / Alternative check: Specific energy diagrams show a control shifting the operating point onto the critical curve for the given discharge. Why Other Options Are Wrong: Lowering the bed or increasing width typically increases depth for the same energy and does not enforce criticality. Common Pitfalls: Ignoring energy losses; real controls introduce minor head losses but the critical condition remains a useful design target. Final Answer: Both (a) and (c)

Question 15

For estimating average annual precipitation over a catchment, which method generally provides the most reliable spatial average when adequate contouring of isohyets is possible?

Accepted Answer

Introduction / Context: Catchment-average precipitation is a fundamental input for hydrologic design. Accuracy improves when spatial variability is represented properly. Given Data / Assumptions: Several rain gauges with known long-term records. Topography and storm tracks cause non-uniform rainfall fields. Concept / Approach: Three classical methods exist: simple average, Thiessen polygons (area weighting per gauge), and isohyetal method (area weighting of precipitation bands bordered by isohyets). Step-by-Step Solution: Arithmetical mean ignores spatial distribution and is least accurate for heterogeneous fields.Thiessen assigns fixed areas to gauges but still assumes uniform rain within each polygon.Isohyetal method contours precipitation to create belts of near-equal rainfall, then area-weights each belt, capturing gradients better.Therefore, isohyetal method is generally most reliable when adequate data allow contouring. Verification / Alternative check: When gauge density is high and orography strong, isohyets track spatial patterns more realistically than polygons. Why Other Options Are Wrong: Arithmetical and Thiessen can be used but are less accurate where variability is significant. Common Pitfalls: Poor isohyet drawing yields bias; expert contouring is essential. Final Answer: Isohyetal method

Question 16

Select the correct water balance identity that defines total runoff from a basin in terms of its component contributions.

Accepted Answer

Introduction / Context: Total streamflow at a catchment outlet comprises quick components and delayed components. Correctly expressing this identity helps in hydrograph separation and modeling. Given Data / Assumptions: Surface runoff (direct runoff) and groundwater flow (baseflow) are additive components of streamflow. Units are consistent so volumetric or rate addition is meaningful. Concept / Approach: At any instant or over an event period, total runoff equals the sum of direct runoff and baseflow. Additional minor components like interflow are often grouped with one of these terms depending on the method. Step-by-Step Solution: Define total runoff Q_total.Let Q_surface denote the overland and quick channel contributions.Let Q_base denote delayed contributions from groundwater discharge.Identity: Q_total = Q_surface + Q_base. Verification / Alternative check: Hydrograph separation techniques decompose observed discharge into baseflow and direct runoff, whose sum reconstructs the measured hydrograph. Why Other Options Are Wrong: Subtraction, division, or multiplication do not represent mass-conserving combination of independent flow contributions. Common Pitfalls: Double counting interflow or misclassifying contributions; ensure consistent component definitions. Final Answer: Runoff = Surface runoff + Groundwater flow

Question 17

In India, which recording rain gauge is most commonly used in routine hydrological practice?

Accepted Answer

Introduction: Accurate rainfall recording underpins hydrology, flood forecasting, irrigation scheduling, and water-resources design. Several recording (automatic charting) gauges exist, but one has traditionally been preferred across India for routine network deployment and long-term climatological records. Given Data / Assumptions: Context: recording (not non-recording) rain gauges. Options: weighing, tipping bucket, float (syphon), none. Goal: identify the type generally used in India. Concept / Approach: Recording gauges provide a continuous trace of rainfall depth against time. Common types are: weighing (measures accumulated weight), tipping bucket (counts fixed-volume tips), and float (water rises in a chamber and the float–pen records depth; a syphon resets the level periodically). Step-by-Step Solution: Step 1: List the operational characteristics of each type (cost, maintenance, calibration needs, robustness).Step 2: Map these to typical Indian field conditions and legacy IMD/irrigation department practices.Step 3: The float (syphon) recording gauge has long been the standard due to simplicity, reliability, and wide legacy support (charts, spares, technician familiarity). Verification / Alternative check: Network manuals and long-standing hydromet practice in India document prevalent use of float (syphon) recording gauges for continuous charts, especially at conventional stations. Why Other Options Are Wrong: Weighing type: precise but costlier/maintenance-heavy for dense national networks. Tipping bucket type: common in modern AWS, but historically less prevalent than float in conventional networks. None of these: incorrect because the float type is indeed widely used. Common Pitfalls: Confusing current AWS deployments with historically standard conventional gauges. Equating higher accuracy with wider field adoption. Final Answer: Float (syphon) recording type.

Question 18

A pumping test is conducted in an unconfined aquifer: a well penetrates 30 m below the static water table and is pumped at 31.40 L/min for 24 hours. Drawdown is 1.0 m at r = 20 m and 0.5 m at r = 80 m in observation wells. Using the steady-state Thi…

Accepted Answer

Introduction: This problem tests steady-state well hydraulics for a water-table (unconfined) aquifer using the Thiem equation. The goal is to compute transmissibility T from a constant-rate pumping test with drawdowns observed at two different radial distances. Given Data / Assumptions: Pumping discharge Q = 31.40 L/min = 0.03140 m^3/min. Observation wells: r1 = 20 m with s1 = 1.0 m; r2 = 80 m with s2 = 0.5 m. Steady-state conditions are assumed; aquifer is laterally extensive and homogeneous in the test zone. Use natural logarithm in Thiem equation; flow is radial and horizontal toward the pumped well. Concept / Approach: For steady radial flow in a confined/unconfined aquifer of thickness large enough relative to drawdown, the Thiem equation between two observation wells is: T = (Q / (2 * pi * (s1 - s2))) * ln(r2 / r1) where T is transmissibility (m^2/min), Q is discharge, s are drawdowns (m), and r are radial distances (m). The formula exploits the difference in head at two radii to eliminate unknowns like the effective radius of the well. Step-by-Step Solution: Step 1: Convert discharge: 31.40 L/min = 0.03140 m^3/min. Step 2: Compute drawdown difference: s1 - s2 = 1.0 - 0.5 = 0.5 m. Step 3: Compute ln(r2 / r1) = ln(80 / 20) = ln(4) ≈ 1.3863. Step 4: Apply Thiem: T = (0.03140 / (2 * pi * 0.5)) * 1.3863. Step 5: Numerical value: T ≈ 0.01386 m^2/min. Verification / Alternative check: Check units: Q (m^3/min) divided by length (m) yields m^2/min after multiplying by the dimensionless ln term, which is consistent for T. Magnitude is reasonable for a moderately permeable aquifer under the given low discharge. Why Other Options Are Wrong: 0.01285 m^2/min, 0.01185 m^2/min, 0.01485 m^2/min, 0.01585 m^2/min: These are near-miss distractors obtained by slightly perturbing ln(4) or the denominator 2 * pi * 0.5, but they do not match the correct computation. Common Pitfalls: Forgetting to convert litres to cubic metres or minutes to consistent time units. Using log base 10 instead of natural log; if log10 is used, replace ln with 2.303 * log10. Using the wrong order for s1 and s2 or r1 and r2; only the difference s1 - s2 matters with the matching r2 / r1 inside the logarithm. Final Answer: 0.01386 m^2/min.

Question 19

If the area of a storm hydrograph corresponds to 102 cm of effective rainfall depth, the ordinates of the 1-cm unit hydrograph are obtained by dividing the storm hydrograph ordinates by which factor?

Accepted Answer

Introduction: This question checks your understanding of unit hydrograph scaling. A unit hydrograph (UH) is defined as the direct runoff hydrograph (DRH) produced by 1 cm of effective rainfall (excess) uniformly distributed over the catchment for a specified duration. Given Data / Assumptions: The storm (direct runoff) hydrograph integrates to an effective rainfall depth of 102 cm over the basin for the same effective rainfall duration as the desired UH duration. We need the 1-cm unit hydrograph. Concept / Approach: Unit hydrograph linearity states that if a storm produces D cm of effective rainfall, then the corresponding DRH ordinates are D times the ordinates of the 1-cm UH for the same duration. Therefore, the 1-cm UH ordinates are obtained by dividing the DRH ordinates by D. Step-by-Step Solution: Step 1: Identify the effective rainfall depth D from the storm hydrograph area: D = 102 cm. Step 2: Apply linear scaling: UH_1cm ordinate = DRH ordinate / D. Step 3: Substitute D = 102 to get the divisor as 102. Verification / Alternative check: If you multiply the obtained 1-cm UH ordinates by 102, you should recover the original storm DRH ordinates, confirming internal consistency (superposition and proportionality). Why Other Options Are Wrong: 51: Would imply D = 51 cm; not given by the problem. 10.2: Would correspond to D = 10.2 cm (i.e., 102 mm), which is not the stated value. 204: Double the stated D; incorrect. 1: Dividing by 1 would leave the storm hydrograph unchanged; it would not be a 1-cm UH. Common Pitfalls: Confusing millimetres and centimetres. Always keep units consistent with the UH definition. Trying to change the duration; duration must match between the storm hydrograph and the UH. Final Answer: 102.

Question 20

In a drainage-basin water balance, runoff is obtained from precipitation after accounting for initial recharge (initial abstractions) and groundwater accretion. Which relationship is correct?

Accepted Answer

Introduction: Basin runoff represents the part of precipitation that appears as streamflow after deducting initial abstractions (interception, depression storage, and early infiltration) and considering baseflow contributions from groundwater. Understanding the sign convention for each term is essential for consistent water-balance equations. Given Data / Assumptions: Precipitation (P) supplies water to the basin. Initial recharge (initial abstractions, Ia) represents early losses before runoff forms. Groundwater accretion (G) denotes net baseflow that augments streamflow during/after events. Other long-term terms like evapotranspiration and change in storage are omitted here to focus on the three listed quantities. Concept / Approach: A simplified event water-balance for direct runoff and baseflow can be expressed as: Runoff R = P - Ia + G where P increases streamflow potential, Ia reduces it as an initial loss, and G (if positive as accretion) adds to streamflow through groundwater contribution. Step-by-Step Solution: Step 1: Start from inputs and losses: P is input; Ia is an early-time loss. Step 2: Include groundwater accretion as a gain to channel flow. Step 3: Combine with signs: R = P - Ia + G. Verification / Alternative check: Check limiting cases: If G = 0 (no baseflow), then R = P - Ia, which matches classic initial-loss concepts. If Ia = 0 and G > 0 (e.g., wet antecedent conditions), runoff increases by the baseflow amount, consistent with observed hydrographs where groundwater sustains flow. Why Other Options Are Wrong: Precipitation + initial recharge - groundwater accretion: Adds a loss and subtracts a gain; sign convention reversed. Precipitation - groundwater accretion - initial recharge: Subtracts the baseflow gain; incorrect. Initial recharge + groundwater accretion + precipitation: Treats all as gains; ignores that Ia is a loss. Precipitation + groundwater accretion + initial recharge: Same issue—adds the loss term. Common Pitfalls: Interchanging terms: 'initial recharge' (initial abstractions/losses) versus later groundwater contributions. Ignoring the time scale: event-based balances differ from long-term averages where evapotranspiration and storage changes play major roles. Final Answer: Precipitation - initial recharge + groundwater accretion.

Water Resources Engineering Questions