Q: Compressible cakes: how does the specific cake resistance of a compressible sludge change as the pressure drop across the cake increases?

Introduction / Context: Filtration performance depends strongly on the structure of the cake. Many sludges are compressible: their pore structure compacts under higher pressure, changing permeability and thus the specific cake resistance. Given Data / Assumptions: Compressible cake (e.g., biological sludges, fine clays). Pressure drop across the cake is increased during operation or by control. Darcy-type laminar flow through porous media applies. Concept / Approach: For compressible cakes, the specific cake resistance α typically follows α = α0 * (ΔP)^s with a positive compressibility index s (often 0.1–1). As ΔP rises, particles pack more tightly; porosity falls; permeability decreases; α increases. Step-by-Step Solution: Recognize compressibility: porosity is pressure dependent.Higher ΔP → greater compaction → lower permeability.Therefore, specific cake resistance increases with ΔP. Verification / Alternative check: Filtration curves (time vs. filtrate volume) steepen under higher ΔP for compressible cakes, indicating rising resistance per unit mass captured. Why Other Options Are Wrong: Decreases/constant: valid only for rigid (incompressible) cakes.Increases linearly: the relationship is commonly non-linear and captured via an exponent s. Common Pitfalls: Blindly increasing pressure to speed filtration without considering cake compressibility can slow the process and worsen washing efficiency. Final Answer: increases

Q: Gravity settling chambers (dust catchers): in which particle-size range do these simple devices perform most effectively and efficiently?

Introduction / Context: Gravity settling chambers provide low-cost, low-pressure-drop particulate removal by allowing particles to fall out of a gas stream under gravity. Their efficiency depends on particle size, gas residence time, and chamber design. Given Data / Assumptions: Horizontal flow dust catcher with quiescent zone. Turbulence kept modest; Stokes/transition settling applies. Goal: identify the size range where efficiency is reasonable. Concept / Approach: Very fine particles ( ~100 microns) are easy to settle in almost any device. Gravity chambers are typically used for an intermediate size band where they remain economical and simple—commonly around 10–25 microns for industrial gases at moderate velocities. Step-by-Step Solution: Compare options with known performance bands.Select the intermediate band where settling velocity allows capture in practical chamber lengths.Hence, 10 to 25 microns is the effective range. Verification / Alternative check: Design charts show gravity chambers capturing a meaningful fraction of particles above roughly 10 microns, whereas sub-5 micron control requires cyclones, scrubbers, or ESPs. Why Other Options Are Wrong: 1000 microns: trivially settle; such oversized particles are rarely the design driver. Common Pitfalls: Overestimating efficiency for fines; gravity chambers are often used only as precleaners upstream of higher-efficiency devices. Final Answer: 10 to 25

Question 1

Ball mill practice: actual operating speed typically ranges from 65% to 80% of critical. In which duty is the mill usually run closest to the maximum percentage of critical speed?

Accepted Answer

Introduction / Context: Ball mill speed affects the charge motion (cascading, cataracting) and therefore the breakage environment. Operators choose a fraction of critical speed to balance energy efficiency, liner/media wear, and required impact intensity. Given Data / Assumptions: Typical operating band: 65–80% of critical speed. Larger feed needs more impact/cataracting to break efficiently. Unbaffled (smooth) mills provide less lift; higher speed is often needed to promote cataracting. Concept / Approach: Cataracting impacts dominate breakage of coarse, hard particles in dry grinding. In unbaffled mills, lifter action is limited; therefore, a higher fraction of critical speed helps raise media, increase impact frequency and energy, and avoid sluggish cascading that insufficiently breaks coarse lumps. Step-by-Step Solution: Identify duty needing strongest impacts → coarse, dry, unbaffled.Higher % of critical promotes cataracting → better coarse breakage.Therefore select: dry grinding of large particles in unbaffled mills. Verification / Alternative check: Plant practice often uses lower speeds for viscous wet slurries to limit power spikes and excessive heat, while coarse dry grinding benefits from faster rotation to generate impact. Why Other Options Are Wrong: Low-viscosity wet milling: typically mid-band speeds suffice.High-viscosity wet milling: speeds are often reduced to avoid overload and poor media mobility.Dry with large feed (baffled): lifters allow adequate cataracting at slightly lower speeds than a smooth shell. Common Pitfalls: Confusing critical speed (theoretical centrifuging point) with optimal operating speed; running too fast can still be inefficient if it causes centrifuging instead of controlled cataracting. Final Answer: Dry grinding of large particles in unbaffled mills.

Question 2

Packing geometry: the sphericity of a Raschig ring (length equal to its outside diameter) is expected to be

Accepted Answer

Introduction / Context: Sphericity is a shape factor widely used in packed-bed calculations and particle technology. It compares a real particle’s surface-to-volume characteristics with those of a perfect sphere of the same volume. Given Data / Assumptions: Sphericity, Φ = (surface area of sphere of equal volume) / (actual surface area of the particle). A perfect sphere has Φ = 1 by definition. A Raschig ring is a short, hollow cylinder whose length equals its outside diameter. Concept / Approach: Non-spherical particles expose more surface area per unit volume compared with a sphere. Since Φ uses the ratio of the smaller spherical area to the larger actual area, Φ for elongated, flaked, or hollow shapes is less than one. Random packings like Raschig rings therefore have Φ < 1. Step-by-Step Solution: Recognize definition: Φ = A_sphere / A_actual.For ring or cylinder segments, A_actual > A_sphere at same volume.Hence Φ < 1. Verification / Alternative check: Tabulated sphericities for cylinders, rings, and saddles are typically in the 0.3–0.9 range, always below unity. Why Other Options Are Wrong: Φ > 1 or Φ = 2 is impossible with this definition; no real particle has less actual area than the equal-volume sphere.Φ = 1 applies only to perfect spheres. Common Pitfalls: Confusing sphericity with roundness or aspect ratio; sphericity is a precise surface/volume-based metric, not a visual descriptor. Final Answer: < 1

Question 3

Compressible cakes: how does the specific cake resistance of a compressible sludge change as the pressure drop across the cake increases?

Accepted Answer

Introduction / Context: Filtration performance depends strongly on the structure of the cake. Many sludges are compressible: their pore structure compacts under higher pressure, changing permeability and thus the specific cake resistance. Given Data / Assumptions: Compressible cake (e.g., biological sludges, fine clays). Pressure drop across the cake is increased during operation or by control. Darcy-type laminar flow through porous media applies. Concept / Approach: For compressible cakes, the specific cake resistance α typically follows α = α0 * (ΔP)^s with a positive compressibility index s (often 0.1–1). As ΔP rises, particles pack more tightly; porosity falls; permeability decreases; α increases. Step-by-Step Solution: Recognize compressibility: porosity is pressure dependent.Higher ΔP → greater compaction → lower permeability.Therefore, specific cake resistance increases with ΔP. Verification / Alternative check: Filtration curves (time vs. filtrate volume) steepen under higher ΔP for compressible cakes, indicating rising resistance per unit mass captured. Why Other Options Are Wrong: Decreases/constant: valid only for rigid (incompressible) cakes.Increases linearly: the relationship is commonly non-linear and captured via an exponent s. Common Pitfalls: Blindly increasing pressure to speed filtration without considering cake compressibility can slow the process and worsen washing efficiency. Final Answer: increases

Question 4

Gravity settling chambers (dust catchers): in which particle-size range do these simple devices perform most effectively and efficiently?

Accepted Answer

Introduction / Context: Gravity settling chambers provide low-cost, low-pressure-drop particulate removal by allowing particles to fall out of a gas stream under gravity. Their efficiency depends on particle size, gas residence time, and chamber design. Given Data / Assumptions: Horizontal flow dust catcher with quiescent zone. Turbulence kept modest; Stokes/transition settling applies. Goal: identify the size range where efficiency is reasonable. Concept / Approach: Very fine particles (< ~5 microns) have tiny settling velocities and are poorly captured. Very coarse particles (> ~100 microns) are easy to settle in almost any device. Gravity chambers are typically used for an intermediate size band where they remain economical and simple—commonly around 10–25 microns for industrial gases at moderate velocities. Step-by-Step Solution: Compare options with known performance bands.Select the intermediate band where settling velocity allows capture in practical chamber lengths.Hence, 10 to 25 microns is the effective range. Verification / Alternative check: Design charts show gravity chambers capturing a meaningful fraction of particles above roughly 10 microns, whereas sub-5 micron control requires cyclones, scrubbers, or ESPs. Why Other Options Are Wrong: < 5 microns: too fine for economical gravity capture.< 74 microns: too broad and includes many fines; not specific.> 1000 microns: trivially settle; such oversized particles are rarely the design driver. Common Pitfalls: Overestimating efficiency for fines; gravity chambers are often used only as precleaners upstream of higher-efficiency devices. Final Answer: 10 to 25

Question 5

Sub-micronic dust control from blast-furnace gas: which device is the most efficient for removing particles in the sub-micron range?

Accepted Answer

Introduction / Context: Blast-furnace top gas contains a wide particle-size spectrum. Achieving very low particulate emissions, especially in the sub-micron regime, requires high-efficiency control equipment that does not rely solely on inertial effects. Given Data / Assumptions: Target: sub-micron particulate removal. Industrial-scale gas flows and temperatures. Device choices: ESP, cyclone, gravity chamber, venturi-type device (listed as atomiser). Concept / Approach: Cyclones and gravity chambers depend on inertia and gravity and are ineffective for sub-micron fines. Wet scrubbers (e.g., venturi scrubbers) can capture very fine particles but at high pressure drop; the listed option “venturi atomiser” is not the standard scrubber. Electrostatic precipitators (ESPs) impart charge to particles and drive them to collecting plates with an electric field, achieving very high efficiencies even for sub-micron particles at reasonable pressure drop. Step-by-Step Solution: Identify device physics: electrostatic force is effective for very small particles.Compare alternatives: inertia/gravity insufficient; unspecified atomiser is not the classic high-ΔP venturi scrubber.Choose ESP as the best available option. Verification / Alternative check: Steel plants commonly use cyclones or wet scrubbers as precleaners and ESPs for final polishing of blast-furnace gas to very low dust levels. Why Other Options Are Wrong: Gravity chamber: low efficiency for fines.Cyclone: good for > 5–10 micron particles; weak for sub-micron.Venturi atomiser: not the standard term for high-efficiency venturi scrubber; ESP remains superior in this list. Common Pitfalls: Confusing venturi scrubbers with ordinary spray devices; only high-ΔP venturi scrubbers approach ESP performance for sub-micron capture. Final Answer: electro-static precipitator

Question 6

Froth flotation reagents: xanthates are widely used as which type of reagent in sulfide ore flotation?

Accepted Answer

Introduction / Context: Froth flotation relies on selective attachment of certain minerals to air bubbles. Reagents are added to control surface chemistry: collectors, frothers, activators, depressants, and modifiers. Knowing each reagent’s role is fundamental to circuit design and troubleshooting. Given Data / Assumptions: Xanthates are organosulfur compounds, commonly sodium/potassium salts. Typical application: sulfide minerals (e.g., PbS, ZnS, CuFeS2). Concept / Approach: Collectors selectively render mineral surfaces hydrophobic. Xanthates chemisorb onto sulfide mineral surfaces forming metal–xanthate species, which strongly increase hydrophobicity and bubble attachment probability. Frothers (e.g., pine oil, MIBC) control bubble size and froth stability; activators (e.g., CuSO4) enhance collector adsorption on certain minerals; conditioners/modifiers adjust pH or ionic environment. Step-by-Step Solution: Identify xanthate function: hydrophobize sulfide minerals via chemisorption.Map to reagent class: "collector."Therefore, choose "collector." Verification / Alternative check: Plant reagent suites list xanthates (e.g., PEX, SEX) under collectors, often blended for selectivity and cost. Why Other Options Are Wrong: Frother: controls froth, not hydrophobicity.Activator: enhances adsorption by surface ion exchange, not primary hydrophobization.Conditioner: pH/ionic modifiers, not specific collectors. Common Pitfalls: Assuming pine oil is a collector; it is a classic frother. Collectors are typically thiol-based for sulfides. Final Answer: collector

Question 7

Filter press fundamentals: which description best characterizes a plate-and-frame filter press?

Accepted Answer

Introduction / Context: Plate-and-frame filter presses are ubiquitous for solid–liquid separation when high-solids cakes are desired. Understanding their operating mode, strengths, and limitations helps in selecting between press, vacuum drum, or continuous pressure filters. Given Data / Assumptions: Classical recessed or plate-and-frame press. Cycles include fill, filter, wash (optional), blow/dry (optional), and cake discharge. Concept / Approach: Filter presses operate in discrete cycles; therefore, they are batch filters. They can handle a wide range of slurries, especially those forming rigid cakes. Whether the liquid or the solid is the main product depends on economics and washing needs; presses can deliver clear filtrate as the main product if cycle time and labor are acceptable. Step-by-Step Solution: Identify mode: cycle-based → batch.Evaluate other claims: maintenance and applicability depend on design and duty; blanket statements are inaccurate.Therefore, the correct characterization is "a batch filter." Verification / Alternative check: Vendor literature presents cycle times and cake yields per batch; continuous duties typically use rotary drums, belt filters, or continuous pressure filters. Why Other Options Are Wrong: Not suitable if liquid is main product: incorrect; many plants use presses to obtain very clear filtrate.Prohibitively high maintenance: varies; not an inherent trait.Not suitable for wide ranges: presses are versatile with proper fabric and operating pressure. Common Pitfalls: Ignoring cycle time and labor in cost estimates; presses deliver quality but require batching logistics. Final Answer: a batch filter.

Question 8

Crusher sizing: compared at the same gape, handling the same feed and product size range, the capacity of a gyratory crusher is approximately how much relative to a jaw crusher?

Accepted Answer

Introduction / Context: Primary crushers include jaw and gyratory types. For comparable gape (largest feed opening dimension), their throughput capacities differ due to differences in continuous vs. intermittent crushing action and chamber geometry. Given Data / Assumptions: Same gape and similar feed and product size specifications. Normal operating conditions. Concept / Approach: The gyratory crusher provides continuous crushing over the whole of the receiving opening as the mantle gyrates within the concave. A jaw crusher crushes intermittently as the jaw closes and opens. Consequently, for the same gape, gyratories achieve higher capacity—commonly about 2.5 times—under comparable conditions. Step-by-Step Solution: Compare mechanisms: continuous (gyratory) vs. cyclic (jaw).Throughput scales with active crushing zone/time.Rule-of-thumb capacity ratio ≈ 2.5 → select "2.5 times." Verification / Alternative check: Design charts and handbooks provide capacity curves indicating gyratories outpace jaws for the same gape by roughly 2–3×, with 2.5× a typical quoted value. Why Other Options Are Wrong: Same as: ignores continuous action advantage.5× or 10×: overstated for same gape and duty. Common Pitfalls: Comparing specific models without normalizing gape and product size; capacities also depend on bulk density, moisture, and nip angle. Final Answer: 2.5 times

Question 9

Grinding aids in comminution: adding suitable aids during milling typically results in which outcome(s)?

Accepted Answer

Introduction / Context: Grinding aids (e.g., glycols, amines) are small-dose additives that alter particle–particle interactions, reduce agglomeration, and improve flow in mills. They are widely used in cement and mineral grinding. Given Data / Assumptions: Appropriate dosage and compatibility with the system. Milling equipment operating in a regime where coating and agglomeration occur. Concept / Approach: By reducing surface energy effects and preventing powder coating of media and liners, grinding aids maintain an efficient impact/attrition environment. This increases mill throughput (production rate) at a given fineness or enables finer product at the same throughput by suppressing agglomeration and improving classification efficiency. Step-by-Step Solution: Add aid → reduced agglomeration/coating → better media motion and classification.Result 1: more tons/hour at target fineness (higher production).Result 2: or, at constant rate, finer Blaine/residue (finer product). Verification / Alternative check: Plant trials typically show specific energy reductions or fineness improvements at equal energy, confirming both effects depending on control strategy. Why Other Options Are Wrong: Claiming only one benefit understates the dual impact; "neither" contradicts extensive practice. Common Pitfalls: Overdosing can cause foaming or separator instability; always optimize dosage by test. Final Answer: both (a) & (b).

Question 10

Line filtration in pipelines: the device that places a screen across a flow channel to remove rust, scale, and debris from a liquid stream is called a

Accepted Answer

Introduction / Context: Protecting pumps, valves, and heat exchangers from debris requires simple inline devices. While many separation units exist, the simplest is a screen that intercepts large particles from the flowing liquid. Given Data / Assumptions: Liquid service in a pipe or channel. Target removal: rust flakes, scale, fibers, and chips. Device uses a physical screen or perforated basket. Concept / Approach: A strainer installs a screen across the flow to trap debris while allowing liquid to pass. A thickener concentrates slurry solids by gravity; a classifier separates by size in a fluid; a clarifier settles fine particles to produce a clear overflow. Only a strainer fits the described inline, coarse screening function. Step-by-Step Solution: Map definition to device: screen across flow → strainer.Eliminate: thickener/clarifier (gravity settlers), classifier (hydraulic size separation). Verification / Alternative check: Common types include Y-strainers and basket strainers; both incorporate removable screens for cleaning. Why Other Options Are Wrong: Thickener/clarifier: tank-based, not inline.Classifier: uses fluid velocity differences; no fixed screen across a pipeline. Common Pitfalls: Using ultra-fine mesh strainers where pressure drop becomes excessive; fine clarification belongs to filters or membrane systems. Final Answer: strainer

Question 11

Tube mill versus ball mill: what is the principal differentiating design parameter between the two?

Accepted Answer

Introduction / Context: Both ball mills and tube mills are tumbling mills using grinding media. Their naming reflects geometry, which in turn affects residence time, classification arrangements, and typical duty in circuits. Given Data / Assumptions: Both mills use similar media types and run at similar fractions of critical speed. Design difference centers on shell proportions. Concept / Approach: A tube mill has a much larger length-to-diameter (L/D) ratio than a standard ball mill. The extended length allows multi-compartment liners and media gradation for staged grinding, often used in cement finish grinding. Ball mills are shorter (lower L/D), often single-compartment. Step-by-Step Solution: Identify the geometric distinction: L/D ratio.Associate function: long residence and compartmentation in tube mills.Hence, the principal differentiator is L/D ratio. Verification / Alternative check: Manufacturer catalogs specify L/D > 3 for tube mills versus ~1–2 for ball mills. Why Other Options Are Wrong: Media size, product size, and speed can overlap across designs; they are not the defining difference. Common Pitfalls: Assuming the name implies different mechanisms; both rely on impact/attrition of tumbling media. Final Answer: length to diameter ratio.

Question 12

Plate-and-frame filter press construction: the slurry is introduced through a port in each frame. What surface geometry does the mating plate typically have to provide drainage channels?

Accepted Answer

Introduction / Context: In plate-and-frame presses, frames form cavities to hold cake, while plates support the cloth and provide filtrate drainage paths. Surface geometry of plates is crucial to reduce cloth blinding and allow filtrate to exit uniformly. Given Data / Assumptions: Classical plate-and-frame construction. Slurry introduced via frame ports; filtrate flows along the plate. Concept / Approach: Plates are cast or machined with ribs or grooves. The ribbed pattern keeps the cloth off the solid surface locally, creating channels that collect filtrate and route it to corner ports. A plane plate would flatten the cloth and restrict flow; curving alone does not create uniform channels. Step-by-Step Solution: Identify design function: provide drainage under the cloth.Design feature: ribbed/grooved plate face.Answer: ribbed. Verification / Alternative check: Press manuals illustrate diamond or herringbone rib patterns to support cloth and promote drainage. Why Other Options Are Wrong: Plane/curved plates without ribs cannot maintain continuous drainage channels everywhere across the face. Common Pitfalls: Confusing recessed-chamber presses with true plate-and-frame; both use ribbed faces for drainage. Final Answer: ribbed

Question 13

Thickening vs. clarification: the separation of a slurry into a clear supernatant liquid and a thick sludge with high solids concentration is termed

Accepted Answer

Introduction / Context: Gravity settlers operate in several modes. Clarification emphasizes a clear overflow (low solids), while thickening emphasizes a concentrated underflow (high solids). The umbrella term for separation by settling under gravity is sedimentation. Given Data / Assumptions: A suspension (slurry) is allowed to settle. Two outputs: clear supernatant and thickened sludge. Concept / Approach: When settling separates phases by gravity without size-based hydraulic classification, it is sedimentation. Clarification is a subset of sedimentation focusing on overflow clarity; thickening is another subset focusing on dense underflow. The question’s wording covers both outcomes simultaneously, so the best general term is sedimentation. Step-by-Step Solution: Identify phenomenon: gravity settling of suspended solids.Map to general term: sedimentation.Select "sedimentation" accordingly. Verification / Alternative check: Thickeners are sometimes called sedimentation tanks, and clarifiers are clarifying sedimentation basins; both are unit operations of sedimentation. Why Other Options Are Wrong: Classification: hydraulic size separation with rising/overflow streams, not simple settling to two products.Clarification: stresses only the clear overflow, not the thick sludge.Decantation: the mechanical act of pouring off supernatant; not the separation mechanism itself. Common Pitfalls: Using "clarification" generically when the process objective is actually thickening; design criteria differ. Final Answer: sedimentation

Question 14

Moisture for comminution: the optimum moisture content in solids to be crushed or ground typically ranges within which percent band?

Accepted Answer

Introduction / Context: Moisture content has a strong influence on size reduction. Too little moisture can increase dust and reduce nip; too much moisture causes coating, chute plugging, and reduced screening efficiency. There is an "optimum" band that aids dust control without impairing breakage. Given Data / Assumptions: General-purpose crushing and dry grinding circuits. Moisture’s role limited to handling and nip—not slurry grinding. Concept / Approach: A small amount of moisture improves fines agglomeration enough to reduce airborne dust and can improve gripping (nip) in certain crushers. Beyond a few percent, materials begin to cake and adhere to liners and media, drastically reducing throughput. Standard practice cites a narrow optimum around a few percent for dry crushing/grinding. Step-by-Step Solution: Balance dust suppression vs. caking.Select the smallest band that represents typical optimum for dry comminution: 3–4%. Verification / Alternative check: Operating manuals and handbooks commonly warn that > 5–6% moisture in many ores impairs screening and promotes chute build-up; conversely < 1% can be too dusty. Why Other Options Are Wrong: 8–20%: suitable for wet grinding/slurrying, not for dry crushing-grinding circuits. Common Pitfalls: Confusing optimum moisture for dry circuits with the solids content used in slurry grinding (often 60–75% solids by mass). Final Answer: 3 to 4

Question 15

Screening performance: choose the correct statement about capacity versus effectiveness and the construction of a reel (revolving screen) used in flour mills.

Accepted Answer

Introduction / Context: Screen selection involves trade-offs between throughput (capacity) and separation quality (effectiveness). In addition, certain industries use specialized screen constructions tailored to their products, such as reels in flour milling. Given Data / Assumptions: Capacity means tons/hour passed; effectiveness means separation accuracy (sharpness of cut, undersize in oversize, etc.). Flour-mill reels are cylindrical, slowly rotating screens. Concept / Approach: As feed rate increases, bulk bed depth and blinding generally worsen, reducing screening effectiveness. Thus capacity and effectiveness oppose each other beyond a certain point. In flour mills, "bolting cloth" (silk or synthetic) is stretched over supporting wire mesh to form the reel’s screening surface, providing fine apertures with structural support. Step-by-Step Solution: Acknowledge the trade-off: higher capacity often reduces effectiveness.Recall construction: silk bolting cloth over wire mesh in reels.Therefore, statements (b) and (c) are correct. Verification / Alternative check: Performance curves for screens show decline in efficiency with excessive loading; flour milling texts detail reel construction with bolting cloth. Why Other Options Are Wrong: (a) Equating capacity to effectiveness is incorrect; they are distinct and often competing objectives. Common Pitfalls: Attempting to maximize both simultaneously without considering bed depth limits and screen blinding control. Final Answer: both (b) and (c).

Question 16

In mechanical classification, particles are called equal-settling when their terminal settling velocities are identical. Under what conditions is this definition applied?

Accepted Answer

Introduction / Context: Equal-settling concepts are central to the design and operation of classifiers (hydrocyclones, hydraulic classifiers, and settling tanks). The idea is used to predict how particles of different sizes and densities behave in a given fluid under a specified driving force, so that cut sizes and sharpness of separation can be estimated. Given Data / Assumptions: The term “terminal settling velocity” means the steady velocity reached by a particle when gravitational (or centrifugal) forces balance drag. We are comparing particles in a specific, unchanged environment. “Field of force” refers to the driving force regime (usually gravitational settling; sometimes centrifugal fields). Concept / Approach: Particles are said to be equal-settling when they have the same terminal velocity in the same fluid and under the same field of force. This ensures that differences in viscosity, density of the fluid, or magnitude of the driving acceleration are not confusing the comparison. Under this definition, particles of different size–density combinations may follow the same trajectory and report to the same product stream in a classifier. Step-by-Step Solution: Fix the fluid: choose one fluid (e.g., water at given temperature) so its density and viscosity are defined.Fix the field: define gravity settling (g) or a specific centrifugal acceleration.Compare particles: identify pairs that have the same terminal velocity under those fixed conditions.Conclusion: equal-settling requires both same fluid and same field of force. Verification / Alternative check: Settling velocity charts (log–log plots) or Stokes/Allen–Oseen relations show iso-velocity lines. Particles lying on one iso-velocity line in a given fluid and field are equal-settling and will separate similarly in hydraulic classifiers. Why Other Options Are Wrong: Different fluids: viscosity and density change, so equal velocity in different fluids does not define equal-settling for classifier design.Same fluid only: incomplete; the driving acceleration must also be the same.Same field only: incomplete; the fluid properties must also be the same. Common Pitfalls: Confusing same-size particles with equal-settling particles; density differences can compensate for size differences. Also, forgetting temperature effects on viscosity leads to wrong equal-settling assumptions. Final Answer: both (b) and (c)

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