Question 1

Uplift on floors downstream of a weir crest: minimum floor thickness If the hydraulic gradient line is h metres above a floor of thickness t and the material of the floor has specific gravity G, what minimum thickness t is required downstream of the…

Accepted Answer

Introduction / Context: Hydraulic structures on pervious foundations are subjected to upward seepage pressures. The floor thickness must be adequate so that its submerged weight can counter the uplift to prevent heave or failure. Given Data / Assumptions: Hydraulic gradient line (HGL) lies h metres above the floor soffit. Floor material has specific gravity G (with respect to water). Objective: minimum floor thickness t to prevent uplift at that section. Concept / Approach: Upward water pressure per unit area at the floor = γ_w * h. Downward resisting force per unit area due to the floor = (γ_floor − γ_w) * t = γ_w * (G − 1) * t. For safety at the limiting case, set resisting pressure equal to uplift pressure and solve for t. Step-by-Step Solution: Uplift pressure = γ_w * h.Resisting pressure = γ_w * (G − 1) * t.Equate: γ_w * (G − 1) * t = γ_w * h ⇒ t = h / (G − 1). Verification / Alternative check: The relation is dimensionally correct (both sides have length units). Additional safety may be provided by factors of safety or by drains/relief wells that lower h, reducing t required. Why Other Options Are Wrong: t = h * (G − 1): Overestimates thickness; not derived from equilibrium.t = h / G or G / h: Do not reflect the buoyancy reduction (G − 1) term. Common Pitfalls: Using total unit weight instead of submerged unit weight. Ignoring reduction in uplift due to floor drains or cutoffs (which would lower h). Final Answer: t = h / (G − 1)

Question 2

Best irrigation method for standing crops on undulating, sandy fields: Which method is most suitable under these site conditions?

Accepted Answer

Introduction / Context: Field topography and soil texture strongly influence the selection of an irrigation method. Undulating terrain and sandy soils pose challenges for uniform distribution and water-use efficiency. Given Data / Assumptions: Undulating land surface. Sandy soil (high infiltration, low water-holding). Standing crops already established. Concept / Approach: Sprinkler systems apply water under pressure through nozzles, simulating rainfall. They distribute water uniformly on uneven topography, reduce conveyance losses, and suit light-textured (sandy) soils by allowing frequent, light applications that match high infiltration rates. Step-by-Step Solution: Assess topography: undulations discourage surface methods that depend on level fields.Assess soil: sandy soils benefit from controlled, small, frequent applications.Select sprinkler irrigation to achieve uniform coverage and reduce runoff/ponding. Verification / Alternative check: On flat heavy soils, check or furrow methods can be effective; however, in undulating sandy fields, they lead to non-uniform distribution and deep percolation losses. Sprinklers mitigate both issues. Why Other Options Are Wrong: Free flooding: Highly non-uniform on undulations; excessive deep percolation on sands.Check method: Needs proper levelling; not ideal on undulations.Furrow method: Works for row crops on moderate slopes but still sensitive to slope variations and intake rates. Common Pitfalls: Choosing surface methods without adequate land levelling. Ignoring high infiltration of sands which demands frequent light irrigations. Final Answer: Sprinkler irrigation

Question 3

Baffle walls for holding hydraulic jumps are provided in which type of canal fall?

Accepted Answer

Introduction / Context: Energy dissipation below falls is essential to prevent scour. Baffle blocks/walls are devices in stilling basins that force formation and stabilization of hydraulic jumps, enhancing dissipation at shorter lengths. Given Data / Assumptions: Comparing fall types by appurtenances for energy dissipation. Interest: which fall incorporates baffles to hold the jump. Concept / Approach: Montague (baffle) fall provides a baffle platform and a baffle wall (block) downstream of the glacis so that the hydraulic jump is formed and sustained on the basin, preventing its migration. Other falls like Sarda or simple vertical drops rely more on glacis length and end sills without baffle walls. Step-by-Step Solution: Identify the fall explicitly designed with baffles.Montague fall includes a baffle wall to anchor the jump.Hence it best answers the question. Verification / Alternative check: Design drawings of Montague falls show a baffle platform, baffle wall, and an end sill, a classic baffle-type stilling arrangement. Why Other Options Are Wrong: Sarda type fall: Trapezoidal notch and glacis; no dedicated baffle wall for jump control.English type fall/Vertical fall: Typically rely on hydraulic jump formation with glacis and end sill; not primarily baffle-wall designs. Common Pitfalls: Assuming all stilling basins contain baffle walls; many use only end sills. Confusing “baffle platform” with a simple floor glacis. Final Answer: Montague type fall (baffle fall)

Question 4

Siphon aqueduct floor level estimation: How is the floor level of a siphon aqueduct obtained relative to the canal bed level?

Accepted Answer

Introduction / Context: In a siphon aqueduct, the drainage passes through barrels below the canal prism; the canal is carried on a structure and the drainage flows under pressure. Determining the structural floor level is a layout step for vertical alignment and hydraulic capacity. Given Data / Assumptions: Known canal bed level (CBL). Required culvert (barrel) depth and floor/roof thicknesses. Concept / Approach: The floor level beneath the canal has to accommodate the total structural depth of the barrel (its internal waterway depth) plus the structural thickness (roof/floor). Therefore, the finished floor level is obtained by lowering from the canal bed level by the sum of the culvert depth and its structural thickness. Step-by-Step Solution: Start with CBL (canal bed level).Subtract the structural thickness + barrel (waterway) depth.Floor level = CBL − (thickness + depth). Verification / Alternative check: Check freeboard and head losses to ensure the hydraulic gradient for drainage remains acceptable and that the canal waterway clearances are maintained above. Why Other Options Are Wrong: Subtracting only the culvert depth ignores the required structural thickness; resulting level would be too high.“Both (a) and (b)” is incorrect because (a) is incomplete. Common Pitfalls: Neglecting the slab or roof thickness in vertical alignment. Forgetting allowances for wearing courses or protection layers if provided. Final Answer: By subtracting the thickness of the culvert plus the depth of the culvert from the canal bed level

Question 5

High groundwater table effects on irrigation canals: If the water table is comparatively high, why can an irrigation canal become ineffective or problematic?

Accepted Answer

Introduction / Context: Groundwater conditions strongly influence canal performance. A high water table near the ground surface increases the risk of seepage interactions, waterlogging, and public health issues, potentially undermining the utility of the canal network. Given Data / Assumptions: Canal traversing areas with shallow groundwater depth. Unlined or partially lined canals common in many command areas. Concept / Approach: When groundwater is high, the hydraulic gradient between canal water level and the adjacent soil can encourage seepage. Persistent seepage raises the soil moisture regime of adjoining fields, causing waterlogging and salinity issues. With soils already wet, irrigation demand becomes uncertain and intermittent. Stagnant, waterlogged patches can promote mosquito breeding and disease. Step-by-Step Solution: Recognize head difference drives seepage from canal to soil.Seepage raises water table further, causing waterlogging and reduced aeration of root zones.Public health concerns arise from stagnant water in depressions and drains. Verification / Alternative check: Field observations—rising piezometric levels, salinization signs, and waterlogged spots—corroborate the mechanism. Lining canals and improving drainage often alleviates the issues. Why Other Options Are Wrong: Each listed effect is real; none alone captures the breadth of impacts; therefore “All the above” best represents the situation. Common Pitfalls: Assuming only seepage loss matters and ignoring agronomic and health impacts. Underestimating long-term salinity hazards due to shallow water tables. Final Answer: All the above

Question 6

Dowla (road crossing bund) sizing: If the width of a dowla is generally kept between 30 cm and 60 cm, its height above the road level should invariably be more than how much?

Accepted Answer

Introduction / Context: A “dowla” is a small earthen or masonry bund/hump constructed across rural roads for safely carrying a watercourse or to check overtopping at crossings. Proper sizing ensures safe conveyance and prevents vehicular damage while maintaining drainage continuity. Given Data / Assumptions: Width specified between 30 cm and 60 cm. We need the minimum practical height above road level to ensure functionality and visibility. Concept / Approach: The height must be sufficient to prevent accidental run-through during low visibility, assist in water control, and avoid frequent damage. A practical minimum of more than 30 cm is often adopted as a field standard in low-volume rural settings to balance hydraulic and traffic considerations. Step-by-Step Solution: Consider hydraulics: small rise needed to impound/control shallow flows.Consider safety: too low (10–20 cm) may be ineffective and easily eroded or unnoticed by drivers.Adopt > 30 cm as robust and commonly accepted practice. Verification / Alternative check: Local rural road and irrigation departments commonly specify humps/dowlas around this magnitude to ensure durability and visibility while not impeding traffic excessively. Why Other Options Are Wrong: 10 cm or 20 cm: Too low, prone to wear and insufficient hydraulic control.40 cm: Acceptable but not a minimum; the question asks the least reliable threshold more than which it should be kept. Common Pitfalls: Confusing dowlas with speed breakers having different geometric standards. Ignoring erosion protection on upstream/downstream faces. Final Answer: 30 cm

Question 7

Understanding the water table and capillary zone: Which of the following statements are correct regarding water table behavior and pore-water pressures?

Accepted Answer

Introduction / Context: The water table separates saturated zones with positive pore pressures from the capillary zone where suction prevails. Recognizing these fundamentals is essential in irrigation design, drainage, and groundwater studies. Given Data / Assumptions: Unconfined aquifer conditions. Open wells tapping the phreatic surface. Typical soil behavior in the vadose (unsaturated) zone. Concept / Approach: The water table (phreatic surface) is the locus of points with zero gauge pressure. Above it, capillary rise creates negative pore pressures. In plan, the water table tends to mimic land-surface undulations, smoothed by hydraulic conductivity contrasts and recharge/discharge patterns. Open wells in unconfined settings reflect the local water table elevation when static. Step-by-Step Solution: Statement A: True—though subdued compared with the ground surface.Statement B: True—well water level equals local water table in static equilibrium.Statement C: True—capillary tension above the water table causes negative pore pressure.Statement D: True—by definition, gauge pressure = 0 at the phreatic surface. Verification / Alternative check: Field piezometers and tensiometers verify these pressure regimes; soil–water characteristic curves quantify suction above the water table. Why Other Options Are Wrong: Each individual assertion is correct; therefore the comprehensive choice “All the above” is the best answer. Common Pitfalls: Confusing piezometric head in confined aquifers with water table elevations. Assuming capillary rise is negligible in coarse sands; it can still be significant relative to root depths. Final Answer: All the above

Question 8

Effective precipitation (effective rainfall) for crops: Which definition best captures the concept used in irrigation planning and scheduling?

Accepted Answer

Introduction / Context: Effective precipitation (also called effective rainfall) is a key input to crop water requirement analysis. It determines how much of the crop’s consumptive use can be met by rainfall, reducing required irrigation depths and frequencies. Given Data / Assumptions: Irrigation scheduling framework (soil–water balance). Root-zone storage governs usefulness of rainfall to the crop. Concept / Approach: Not all rain is beneficial: some runs off, some percolates beyond the root zone, and some evaporates promptly. Effective precipitation is that fraction that remains stored within the root zone and is subsequently taken up by the crop (transpiration) and surface soil evaporation contributing to ET over time. Step-by-Step Solution: Define a soil–water balance for the root zone.Subtract immediate runoff, deep percolation below root depth, and non-beneficial evaporation.The remaining stored water that the crop can use is the effective precipitation. Verification / Alternative check: Empirical methods (e.g., USDA SCS methods) estimate effective rainfall from monthly rainfall and ET; field lysimeters and neutron probes provide direct validation of storage changes. Why Other Options Are Wrong: Total minus evaporation or minus infiltration: too simplistic; infiltration can be partly useful if stored in the root zone; evaporation losses may not be immediate and can still benefit soil moisture dynamics indirectly.Total precipitation during crop period: ignores effectiveness. Common Pitfalls: Treating all infiltrated water as effective without checking deep percolation. Ignoring root-depth changes during the season, which alters storage capacity. Final Answer: The portion of precipitation stored in the root zone and available for crop use

Question 9

Fluvial geomorphology: The process of meandering in alluvial rivers primarily arises due to which combined set of factors?

Accepted Answer

Introduction / Context: River meandering is a hallmark of alluvial channels and is central to river engineering, river training works, and the design of hydraulic structures. Understanding the drivers of meandering helps engineers plan guide banks, spurs, and bank protections to stabilize alignments near barrages, bridges, and canal offtakes. Given Data / Assumptions: Alluvial river with mobile bed and banks. Natural planform evolution without artificial straightening. Typical ranges of discharge and sediment supply. Concept / Approach: Meanders result from feedback between flow, sediment transport, and bank erodibility. Non-uniform velocity distribution creates zones of higher shear on outer bends (erosion) and lower shear on inner bends (deposition). Sediment size and load influence transport thresholds and bar formation, while bank material (cohesion and roughness) controls resistance to erosion. Step-by-Step Solution: 1) Identify drivers: (a) sediment load and size distribution, (b) hydraulics governed by discharge/velocity/shear, (c) material properties of bed and banks.2) Recognize feedback: outer-bank erosion and inner-bank deposition amplify curvature.3) Conclude that meandering is not due to a single parameter but the combined action of all three. Verification / Alternative check: Empirical observations across alluvial rivers show meanders develop where banks are erodible, sediment is available for transport, and flow has sufficient energy to rework the planform. Reducing any one can dampen meander growth. Why Other Options Are Wrong: Solely sediment load: without hydraulic forcing and weak banks, meanders do not propagate. Solely discharge/hydraulics: with resistant banks, channels can remain straight despite high flows. Solely erodibility: requires hydraulic action and sediment movement to form bends. None of the above: contradicted by field and theory. Common Pitfalls: Attributing meanders to “Coriolis effect” in engineering practice—local hydraulics dominate. Ignoring cohesive strength of banks in meander migration rates. Final Answer: All of the above.

Question 10

Canal control works: In a main canal, what is the primary functional purpose of a cross regulator?

Accepted Answer

Introduction / Context: Cross regulators are gated control structures provided in the body of a main canal. They play a crucial role in maintaining pond levels that allow distributary head regulators to receive their intended discharge, particularly when the parent canal is running with reduced supplies. Given Data / Assumptions: Main canal with offtaking distributaries. Variable supply conditions across seasons. No special measuring flume specified at the cross regulator site. Concept / Approach: By partially closing gates, a cross regulator increases the upstream water level (creates a pond), ensuring sufficient head at the distributary head regulators. This helps maintain design discharge into distributaries and stabilizes flow division during low-supply periods. Step-by-Step Solution: 1) Identify the control need: maintain sufficient head for offtakes.2) Provide a gated cross regulator in the main canal.3) Operate gates to raise upstream level during low flows, enabling accurate offtake regulation. Verification / Alternative check: Operation manuals commonly pair cross regulators (to set pond level) with distributary head regulators (to set offtake discharge). Escapes and measuring flumes are separate structures for different functions. Why Other Options Are Wrong: Measuring discharge: dedicated flumes or measuring structures are used instead. Passing excessive flows: that is the job of canal escapes or surplus weirs. Permanently closing or desilting by vortex: not the cross regulator’s primary function. Common Pitfalls: Confusing cross regulators with head regulators and escapes. Assuming regulators are primarily for measurement rather than level control. Final Answer: To raise and control the upstream water level so that distributaries can draw their design discharge during low supplies.

Question 11

Earthwork management in canals: The extra excavated earth is commonly utilized to provide spoil banks on which side(s) of the canal alignment?

Accepted Answer

Introduction / Context: Canal excavation generates large volumes of surplus earth. Efficient use of this material reduces hauling costs and enhances canal safety. A common practice is to form spoil banks (bunds) adjacent to the canal to protect against external drainage inflows and to provide access and containment. Given Data / Assumptions: Standard irrigation canal in alluvial terrain. Surplus earth beyond that needed for forming canal banks. Local design may specify distances/setbacks for spoil banks. Concept / Approach: Depending on terrain and drainage patterns, spoil banks can be placed on one or both sides. In many projects, forming spoil banks on both sides ensures protection from external runoff, offers maintenance access, and minimizes breaches from overtopping by adjacent flood flows. Step-by-Step Solution: 1) Identify surplus earth volumes from excavation quantities.2) Locate spoil banks suitably on one or both sides to avoid blocking natural drains.3) Provide cross-drainage or gaps where necessary to prevent ponding outside the canal. Verification / Alternative check: Standard practice notes and design manuals allow flexibility—placement on both sides is common, subject to hydrological constraints and right-of-way availability. Why Other Options Are Wrong: Left-only or right-only: too restrictive; site conditions usually determine side(s). Removal from site: uneconomical unless mandated; material is usually reused locally. Only downstream of regulators: unrelated to where surplus earth should be placed. Common Pitfalls: Blocking natural drainage with continuous spoil banks without culverts or gaps. Placing spoil too close to canal leading to slides into the prism. Final Answer: Both sides of the canal alignment as required.

Question 12

Regime channel parameters: If m is the average silt particle size (in millimetres), Lacey’s silt factor f varies proportionally to which power of m?

Accepted Answer

Introduction / Context: Lacey’s regime theory relates stable alluvial channel dimensions to discharge and sediment properties. The silt factor f captures the effect of sediment size on regime depth, velocity, and hydraulic radius. Correctly identifying how f scales with particle size is essential for preliminary canal sizing. Given Data / Assumptions: Average sediment size m in millimetres (representative of bed load/suspended size influencing regime). Application of Lacey’s empirical relations. Concept / Approach: Lacey proposed f = 1.76 * sqrt(m) when m is in millimetres. Hence, f is proportional to m^0.5. This scaling reflects that coarser sediments require higher velocities and greater hydraulic radii for mobility without deposition or excessive erosion. Step-by-Step Solution: 1) Recall Lacey’s expression: f = 1.76 * m^0.5.2) Identify proportionality: f ∝ m^0.5.3) Compare options and select m^1/2. Verification / Alternative check: Dimensionless trends in field canals support higher velocities (thus higher f) for larger sediment sizes. The square-root dependence is consistent with Lacey’s empirical datasets. Why Other Options Are Wrong: m, m^3, m^2/3, m^1/3: do not match the empirically established square-root dependence. Common Pitfalls: Confusing Lacey’s f with Shields parameter or fall velocity exponents from other theories. Final Answer: m^1/2.

Question 13

Outlet performance terminology: The ratio of head recovered to head put in for a device or system is termed as what?

Accepted Answer

Introduction / Context: In irrigation outlet and hydraulic device evaluation, several indices are used. “Efficiency” specifically quantifies how much input head (or energy) is converted into useful output head or work. It is a foundational metric used across hydraulic machines and control structures. Given Data / Assumptions: Head put in H_in and recovered head H_out are measurable. Losses due to friction, turbulence, and separation are present. Concept / Approach: Efficiency η is defined as beneficial output over input. For head-based systems, η = H_out / H_in. This succinctly captures how effectively a device converts or transmits energy without loss. Step-by-Step Solution: 1) Define η = output / input.2) For head: η = head recovered / head put in.3) Choose the corresponding term: efficiency. Verification / Alternative check: Equivalent definitions exist for power and energy. In all cases, efficiency is a ratio less than or equal to 1 (or 100%). Why Other Options Are Wrong: Sensitivity: relates change in outlet discharge to canal discharge changes. Flexibility: relates outlet discharge change to head change in parent channel. Modular limit: relates to range over which an outlet behaves as a module. Common Pitfalls: Mixing up head-based efficiency with discharge-based flexibility or sensitivity metrics used for outlets. Final Answer: Efficiency.

Question 14

Guide bank protection: The water face (river-side) of guide banks is generally protected using what class of stone pitching?

Accepted Answer

Introduction / Context: Guide banks are vital river training works used near barrages and bridges. Their water face is exposed to high velocities, turbulence, and attack from eddies. Appropriate stone pitching provides erosion resistance and stability against wave action and drawdown. Given Data / Assumptions: Alluvial river with seasonal floods. Standard practice categories of hand-placed stones (e.g., one-man, two-man stones) based on size and handling. Proper underlayers (filter/graded bedding) provided beneath pitching. Concept / Approach: “Two-man stone” pitching uses stones large enough that two workers are typically needed to handle one piece. This size provides better resistance to dislodgement under attack than one-man stones, yet is still practical for placement over large areas of guide bank slopes. Step-by-Step Solution: 1) Identify hydraulic loading on the water face of guide banks.2) Select stone size class adequate to resist design shear and uplift.3) Two-man stones are a commonly adopted standard for water face pitching, with appropriate thickness and toe protection. Verification / Alternative check: Design manuals often specify pitching thickness and stone weight based on velocity and depth. For many Indian river projects, two-man stone pitching on the water face has proven effective when laid over filter layers and combined with toe aprons. Why Other Options Are Wrong: One-man stones: may be too small and susceptible to movement. Three-, four-, five-man stones: heavier than typically necessary and costlier unless very severe conditions demand them. Common Pitfalls: Lack of filter/graded bedding under pitching leading to piping of fines. Insufficient toe protection causing undermining of pitching. Final Answer: Two-man stone pitching.

Question 15

Head regulator silt control: King’s vanes used at distributary heads are provided with which typical geometric and construction characteristics?

Accepted Answer

Introduction / Context: At distributary head regulators, King’s vanes (guide walls/vanes) are installed to streamline approach flow, reduce cross currents, and minimize excessive silt entry into the offtake. Their geometry and placement are empirical, based on experience and model studies. Given Data / Assumptions: Main canal with offtake distributary at an angle. Objective: improve approach hydraulics and silt exclusion. Typical dimensions and spacing used in practice. Concept / Approach: King’s vanes are low-height walls that align streamlines toward the offtake, reducing transverse components that carry silt. The construction (R.C.C. or steel plates), height relative to flow depth, spacing as multiples of height, and extension beyond a 2:1 guide line are all characteristic features used to achieve the objective. Step-by-Step Solution: 1) Provide robust vanes (R.C.C./steel) of adequate thickness (~8 cm).2) Set vane height to about 1/3–1/4 of canal depth so they influence surface/subsurface flow without acting as barriers.3) Space vanes at multiples of their height to create progressive alignment.4) Extend vanes ~1 m beyond a line at 2:1 to-axis to complete flow guidance toward the head regulator. Verification / Alternative check: Physical and numerical models show improved intake conditions and reduced silt ingress with properly proportioned vanes. Field retrofits often follow similar proportions. Why Other Options Are Wrong: Choosing any one feature alone misses the integrated geometric arrangement needed for efficacy. Common Pitfalls: Oversized vanes causing stagnation zones and sediment deposition at the head. Too small or widely spaced vanes yielding negligible guidance. Final Answer: All of the above.

Question 16

Concrete-lined canals: The approximate permissible mean velocity of water in a concrete canal should not exceed which value for general design practice?

Accepted Answer

Introduction / Context: Concrete lining increases permissible non-erosive velocities in canals by providing a smooth, erosion-resistant boundary. Selecting a reasonable upper bound for design velocity is important to balance economy (smaller section) against risks of cavitation, joint distress, or local scour at transitions. Given Data / Assumptions: Well-constructed concrete lining with proper joints and bedding. Normal sediment load and no sharp hydraulic transitions. Mean (section-averaged) velocity for preliminary design. Concept / Approach: Empirical guidance suggests that concrete-lined canals can safely carry higher velocities than earth sections. Typical upper-bound design values are around 2.5 m/sec (sometimes up to ~3 m/sec for special cases). A value of 2.5 m/sec serves as a conservative ceiling for many irrigation canals. Step-by-Step Solution: 1) Identify material: concrete lining allows higher permissible velocities.2) Compare with standard ranges: earth (0.6–1.0 m/sec), masonry (up to ~2.0 m/sec), concrete (up to ~2.5 m/sec or more).3) Select the standard approximate upper value: 2.5 m/sec. Verification / Alternative check: Project specifications often cap velocities near transitions and structures. Many canal design manuals treat 2.5 m/sec as a practical limit to avoid maintenance problems while enabling economical cross-sections. Why Other Options Are Wrong: 0.5–1.5 m/sec: overly conservative for concrete lining, closer to earth channels. 2.0 m/sec: acceptable in many cases, but commonly not the upper bound. Common Pitfalls: Ignoring localized velocities at bends and structures which can exceed mean values. Overlooking cavitation risks at high velocities in undersluices or steep drops. Final Answer: 2.5 m/sec.

Question 17

Lined canal geometry: A triangular-sided channel with a circular bottom of radius D has hydraulic mean depth (R = A/P) approximately equal to which of the following?

Accepted Answer

Introduction / Context: Hydraulic mean depth (also called hydraulic radius) R = A / P is a key parameter in uniform flow computations (e.g., Manning or Chezy). For sections involving circular arcs, characteristic values of R are frequently used as approximations when side contributions are modest relative to the curved bottom. Given Data / Assumptions: Bottom is a circular arc with radius D (i.e., diameter 2D if viewing full circle context). Triangular side slopes contribute area and wetted perimeter but the section is dominated by the circular bottom arc (typical for many lined canal designs). We seek a commonly used approximate value. Concept / Approach: For a circular conduit running full and for a semicircular channel, R equals D/4. In many practical lined sections with circular bottoms, the effective hydraulic radius remains close to this characteristic value, especially when side area and perimeter contributions proportionally offset. Thus D/4 serves as a standard approximation used for preliminary checks. Step-by-Step Solution: 1) Recall benchmark: semicircular section → R = D/4.2) Recognize that adding triangular sides increases both A and P.3) For many standard proportions, the resulting R remains close to D/4, which is accepted for preliminary design. Verification / Alternative check: Detailed computation of A and P for the exact geometry confirms values near D/4 for common canal proportions. Designers refine R using exact geometry once side slopes and depths are finalized. Why Other Options Are Wrong: D or D/2: overestimates R for curved-bottom channels. D/3, D/5: not standard characteristic values for circular-bottom canal sections. Common Pitfalls: Confusing D as arc radius with pipe diameter; remember R for full circle and semicircle is D/4. Using the approximation without later geometry-specific verification. Final Answer: D/4.

Question 18

Outlet behavior index: The ratio of the rate of change of an outlet’s discharge to the rate of change of discharge in the parent channel is termed as what?

Accepted Answer

Introduction / Context: In canal irrigation, an outlet should ideally maintain a predictable proportion of the parent canal’s discharge. Several parameters describe outlet performance; among them, flexibility relates discharge responsiveness of the outlet to that of the parent channel. Given Data / Assumptions: Parent channel discharge Q_p changes slightly. Outlet discharge q_o responds accordingly. Small-signal (differential) definition is used. Concept / Approach: Flexibility (often denoted F) is defined as (dq_o / q_o) / (dQ_p / Q_p) for fractional changes, or simply the ratio of the rates of change when using absolute rates in matched dimensions. It expresses how sensitively the outlet follows parent discharge changes and whether it is proportional (proportional outlet), less responsive (semi-modular), or independent (modular). Step-by-Step Solution: 1) Consider a small change dQ_p in parent discharge.2) Measure resulting change dq_o in outlet discharge.3) Compute flexibility F = (dq_o/dt) / (dQ_p/dt) or the corresponding fractional form. Verification / Alternative check: Textbook definitions distinguish flexibility from sensitivity (which involves head changes). An ideal proportional outlet has F close to 1, meaning outlet discharge varies proportionally with canal discharge. Why Other Options Are Wrong: Efficiency: head or energy conversion ratio, not outlet response. Sensitivity: relates to response with respect to head changes, not discharge changes. Modular limit: range over which outlet behaves as a module (near-constant discharge). Common Pitfalls: Interchanging flexibility and sensitivity; they refer to different independent variables. Ignoring the operating head—modularity depends on head limits, not directly on flexibility magnitude. Final Answer: Flexibility.

Question 19

In canal engineering, why are finally formed berms provided along the banks of a lined or unlined canal? Select the most complete purpose from the list.

Accepted Answer

Introduction / Context: Canal berms are horizontal or gently sloping shelves left between the water edge and the outer embankment. In design and maintenance of irrigation canals, berms serve several hydraulic and geotechnical functions. This question tests understanding of their comprehensive role rather than a single-purpose view. Given Data / Assumptions: Berms are formed after the final trimming or consolidation of canal slopes. Canal banks experience hydraulic actions (waves, drawdown) and geotechnical stresses. Seepage through embankments must be controlled to avoid piping and instability. Concept / Approach: A well-designed berm reduces wave run-up, shortens the seepage path, and provides a buttress that improves slope stability. It also facilitates inspection and maintenance. Effective canal design integrates all these roles rather than isolating a single benefit. Step-by-Step Solution: Identify hydraulic benefit: berms dissipate wave energy and reduce erosion on the waterline.Identify seepage control: by extending the flow path and providing a dry blanket, berms reduce exit gradients and seepage losses.Identify geotechnical strengthening: berms add weight at the toe, improving the factor of safety against slide.Synthesize: the correct choice includes all these functions. Verification / Alternative check: Canal manuals prescribe berms in reaches with wind fetch, pervious banks, or higher embankments; field experience shows reduced maintenance where berms exist. Why Other Options Are Wrong: Options (a), (b), and (c) are each partially true but incomplete; focusing on only one omits other key functions. Option (e) underplays the hydraulic and geotechnical roles. Common Pitfalls: Assuming berms are only for patrol roads; ignoring their effect on phreatic line and wave attack. Final Answer: All of the above

Question 20

Lacey’s silt factor from regime velocity and hydraulic radius: If V is the regime mean velocity (m/s) and R is the hydraulic mean depth (m), the Lacey silt factor f can be expressed as

Accepted Answer

Introduction / Context: Lacey’s regime theory relates channel geometry, velocity, slope, and bed material through empirical equations. Besides the well-known relation f = 1.76 √m (m in mm), Lacey also linked hydraulic radius R and regime velocity V to the silt factor f. This question asks for that direct expression of f using V and R. Given Data / Assumptions: Regime (quasi-stable) alluvial channel transporting its silt load. V in m/s, R in m. Lacey regime relationships apply. Concept / Approach: One of Lacey’s regime relations can be written as R = 5 V^2 / f. Rearranging gives f = 5 V^2 / R. Although f is also tied to bed material size, this form is useful when R and V are known from observations or preliminary design. Step-by-Step Solution: Start with Lacey’s relation: R = 5 V^2 / f.Rearrange: f = 5 V^2 / R.Check dimensional consistency in the empirical system used for Lacey’s equations (metric adaptations are standard in irrigation texts). Verification / Alternative check: Design examples in regime theory often back-calculate f from gauged R and V using the same rearranged formula. The value can be cross-checked against f = 1.76 √m to see if it aligns with expected bed material size. Why Other Options Are Wrong: (b), (c), and (d) are incorrect rearrangements lacking empirical support. (e) is a correct relation for f versus sediment size, not for f directly from V and R. Common Pitfalls: Mixing unit systems and constants; confusing the sediment-size definition of f with the hydraulic relation using R and V. Final Answer: f = 5 V^2 / R

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