Q: Filter aids in cake filtration Which material is most commonly used as a filter aid to form porous, permeable precoat layers and prevent blinding?

Introduction / Context: Filter aids are used to increase permeability, reduce cake resistance, and protect the septum in pressure and vacuum filtration. Selecting the right aid improves throughput and clarifies challenging slurries. Given Data / Assumptions: Objective: build a porous precoat or body-feed network. Slurry tends to blind or forms compressible cakes. Compatibility with process fluid is assumed. Concept / Approach: Diatomaceous earth (kieselguhr) consists of fossilized diatom skeletons with high porosity and intricate microstructure. This produces a rigid, permeable lattice that captures fines without excessive pressure drop. It is therefore the industry standard for clarification and polishing steps. Step-by-Step Solution: Identify need: reduce cake resistance and prevent blinding.Select a highly porous, inert, and inexpensive material.Diatomaceous earth meets these criteria and is widely adopted. Verification / Alternative check: Beer, wine, sweetener, and pharmaceutical filtrations commonly specify diatomaceous earth for precoating or body feed, confirming broad acceptance. Why Other Options Are Wrong: Fuller’s earth and clays are sorbents for decolorization, not optimized as filter aids for permeability. Vermiculite can be used in specialty cases but is not the predominant industrial choice. Common Pitfalls: Poor precoat application leads to channeling; always establish a uniform layer before introducing the slurry. Ensure safe handling as dust can be hazardous. Final Answer: Diatomaceous earth

Question 1

Roll crushers: Pick the WRONG statement about operating characteristics and design.

Accepted Answer

Introduction / Context: Roll crushers nip and compress particles between two counter-rotating rolls. Their design parameters include roll diameter, speed, surface pattern, and the possibility of differential speeds to improve nipping and throughput. Given Data / Assumptions: Conventional two-roll crusher with adjustable gap. Hard/brittle feeds impose limits on reduction ratios. Feed size relative to roll diameter governs nipping feasibility. Concept / Approach: To draw particles into the nip, a sufficient angle of nip and friction are needed. Roll diameter scales with maximum feed size. Differential roll speeds are often used to improve nipping, minimize slippage, and tailor product size; equal speeds are not mandatory and not universal. Step-by-Step Solution: Check statements (a), (b), (d) against standard practice → all true.Evaluate (c): “Both rolls must run at same speed.” → false; many designs intentionally use different speeds.Thus, (c) is the wrong statement. Verification / Alternative check: Design texts and manufacturers describe differential speed rolls to reduce slippage and increase shearing action, especially for tough or moist feeds. Why Other Options Are Wrong: They are accurate statements concerning dependence on feed size, prudent reduction ratios for hard materials, and the influence of speed and ratio on performance. Common Pitfalls: Assuming symmetry implies identical speeds; overlooking the role of friction and nip angle in design. Final Answer: Both rolls must necessarily run at the same peripheral speed.

Question 2

For roll crushers, the typical value of the angle of nip (the angle between roll tangents at the points of contact with the particle being nipped) is approximately

Accepted Answer

Introduction / Context: The angle of nip determines whether a particle will be successfully drawn into the rolls for crushing. It depends on friction and geometry and is central to sizing and performance predictions of roll crushers. Given Data / Assumptions: Smooth or lightly corrugated rolls handling typical ores/rocks. Reasonable surface friction coefficient. Classical geometric nip criterion applies. Concept / Approach: The maximum practical angle of nip for most industrial roll crushers lies in the mid-teens to about 24 degrees. Values near 16 degrees are commonly cited for smooth rolls; higher angles risk slippage instead of nipping, especially for hard, smooth particles. Step-by-Step Solution: Use the empirical range for common materials: ~16°–24°.Select the closest standard figure widely quoted in design problems → 16°. Verification / Alternative check: Reference examples and solved problems typically use 16° as a representative nip angle for smooth rolls with ordinary friction levels. Why Other Options Are Wrong: 32°, 52°, 64°: Too large for stable nipping; particles would slip rather than be drawn into the gap unless extreme roughness or special conditions exist. Common Pitfalls: Confusing half-angle versus full included angle; using unrealistic friction coefficients for smooth, hard particles. Final Answer: 16°

Question 3

Sizing of fine materials: Which screening device is generally most suitable for fine particle separations in industrial practice?

Accepted Answer

Introduction / Context: Screening separates particles based on size using a perforated surface. The mechanical excitation method determines efficiency, capacity, and the fineness attainable without blinding. Given Data / Assumptions: Fine sizing (sub-millimeter to a few millimeters). Industrial throughputs and continuous operation. Typical screen media and anti-blinding aids are available. Concept / Approach: Vibrating screens deliver high frequency, controlled amplitude motion that stratifies the bed and clears apertures, making them ideal for fine separations. Trommels are better for coarse, sticky feeds; grizzlies for very coarse scalping; shaking screens are older technology with lower capacity and efficiency for very fine cuts. Step-by-Step Solution: List devices and typical cut sizes.Match fine separations with high-frequency vibration → vibrating screens.Exclude coarse-feed devices (grizzly, trommel) and lower-efficiency shaking screens for very fine cuts. Verification / Alternative check: Plant experience confirms multi-deck vibrating screens dominate fine screening in minerals and chemicals processing. Why Other Options Are Wrong: Trommel/Grizzly: Coarse scalping; poor for fines. Shaking screen: Lower capacity/efficiency at very fine apertures compared to modern vibratory designs. Common Pitfalls: Using trommels for fines when moisture and stickiness cause blinding; not installing vibratory aids or proper media for small apertures. Final Answer: Vibrating screen

Question 4

Separation using forces greater than gravity: What is the process called when solids and fluids of different densities are separated by applying a centrifugal field?

Accepted Answer

Introduction / Context: Many suspensions settle too slowly under gravity for practical throughput. By imposing high centrifugal acceleration, separation times can be reduced by orders of magnitude compared with simple sedimentation tanks. Given Data / Assumptions: Mixture contains a denser dispersed solid (or a denser liquid phase) and a lighter continuous phase. Equipment such as disc-stack, decanter, or tubular-bowl centrifuges is considered. Goal is rapid clarification, thickening, or phase splitting. Concept / Approach: Centrifugation replaces gravitational acceleration g with an effective field N*g, where N can be hundreds to tens of thousands in high-speed centrifuges. Terminal velocities scale accordingly, yielding fast separations governed by Stokes-type relationships adapted to centrifugal fields. Step-by-Step Solution: Identify driving force → centrifugal rather than gravitational.Name the operation → centrifugation.Differentiate from sedimentation (gravity), flocculation (agglomeration chemistry), dispersion (breaking into smaller entities). Verification / Alternative check: Industrial practice uses centrifugation for biomass harvesting, lube oil purification, and cream separation—classic applications of high “g” separation. Why Other Options Are Wrong: Sedimentation: Gravity only. Flocculation: Chemistry to enlarge particles. Dispersion: Opposite of separation; creates small droplets/particles. Common Pitfalls: Confusing centrifugation with filtration centrifuges; both use rotation, but the former relies on density differences rather than porous media flow resistance. Final Answer: Centrifugation

Question 5

Mixed facts in mechanical operations: Pick out the WRONG statement from the list below (assume ordinary industrial practice).

Accepted Answer

Introduction / Context: Mechanical operations span crushing, grinding, classification, dust collection, and size enlargement. Understanding what is and is not true in common plant practice helps avoid design and operating errors. Given Data / Assumptions: Comparison of wet versus dry crushing conditions for similar materials and machines. Standard terminology for circulating load and dust catcher geometry. Size enlargement is recognized as a mechanical unit operation. Concept / Approach: Water in wet crushing lubricates and cushions contacts, often reducing liner and media wear compared with dry crushing, where abrasion is more severe and dust is generated. Circulating load and dust catcher definitions are standard. Size enlargement uses mechanical force to form larger agglomerates and is indeed a mechanical operation. Step-by-Step Solution: Evaluate each statement against practice and textbooks.(a) Correct: circulating load is the coarse fraction looped back.(b) Incorrect: wet crushing typically reduces wear relative to dry service.(c) Correct: agglomeration/pelletizing/briquetting are mechanical operations.(d) Correct: dust catchers slow gas to let particles settle by gravity. Verification / Alternative check: Mining/mineral processing references consistently note lower wear and dust in wet grinding/crushing versus dry conditions, other factors equal. Why Other Options Are Wrong: They are accurate descriptions of standard terminology and unit operation categories. Common Pitfalls: Overgeneralizing: special slurries can be corrosive, but the typical wear comparison still favors wet crushing for abrasion reduction. Final Answer: Wear and tear in wet crushing is more than in dry crushing of similar materials.

Question 6

Hydraulic classification vocabulary: Separation of solid particles based on differences in their settling/flow velocities through a fluid is called

Accepted Answer

Introduction / Context: When particles move through a fluid, their terminal velocities differ according to size, density, and shape. Industrial equipment exploits these differences to split feeds into fine and coarse fractions for closed-circuit grinding and sizing. Given Data / Assumptions: Hindered settling or free settling regimes may apply depending on solids concentration. Fluid can be water or air in hydraulic or pneumatic classifiers. Goal is to obtain products of different size/density ranges based on velocity differences. Concept / Approach: Classification is the general term for separating solids according to settling/flow velocities in a fluid (e.g., hydrocyclones, rake/spiral classifiers). Elutriation is a specific upward-flow method that preferentially removes fines. Clarification removes suspended solids to produce a clear overflow; sedimentation refers to the broad settling phenomenon, not necessarily the selective sizing split aimed in classifiers. Step-by-Step Solution: Map definitions to operations: classification = velocity-based split.Recognize elutriation as a subtype; clarification as liquid cleanup; sedimentation as general settling.Select the broad, correct term → classification. Verification / Alternative check: Mineral processing texts describe hydrocyclones and classifiers as velocity-based separators producing overflow/underflow cuts characterized by size distributions. Why Other Options Are Wrong: Elutriation: Specific counter-current upflow technique; not the generic term. Clarification: Produces clear liquid rather than a precise size split. Sedimentation: General settling without classification intent. Common Pitfalls: Using “sedimentation” interchangeably with “classification”; forgetting that classification aims for controlled cut size (d50). Final Answer: Classification

Question 7

Bulk material handling – belt conveyors The rated capacity of a belt conveyor depends primarily on two factors. If one is the effective cross-sectional area of the material on the belt, the other governing factor is the __________ of the belt.

Accepted Answer

Introduction / Context: Belt conveyors are widely used in mining, cement, food, and packaging industries. Their rated capacity is a basic design parameter that determines how much bulk solid can be transported per unit time. Understanding which variables truly control capacity helps in sizing drives, belts, and transfer points. Given Data / Assumptions: Belt is troughed; loading cross-section is well defined by troughing idlers and surcharge angle. Material is free-flowing and the belt is operated within allowable troughing and speed limits. No spillage; steady continuous operation. Concept / Approach: Conveyor capacity (mass flow rate) is the product of the bulk density ρ_b, the effective cross-sectional area A of the load on the belt, and the belt linear velocity v. Thus, capacity depends directly on A and v. While thickness and length are important for strength and layout, they do not directly set the instantaneous capacity. Step-by-Step Solution: Define capacity: M_dot = ρ_b * A * vRecognize that A is fixed by troughing geometry and surcharge angle for a given belt width.Hence the other independent factor controlling M_dot is the belt speed v. Verification / Alternative check: Design handbooks provide capacity tables in terms of belt width (which sets area) and belt speed. For the same width and loading, doubling belt speed approximately doubles capacity, confirming the relationship. Why Other Options Are Wrong: Thickness: relates to tensile strength, impact resistance, and life; it does not directly change the loaded cross-section or velocity. Length: affects total power and tension distribution but not the instantaneous mass flow rate at a given section. None of these: incorrect because speed is the co-determining factor with cross-sectional area. Common Pitfalls: Assuming belt width alone fixes capacity; if the speed is too low, capacity falls short. Conversely, excessively increasing speed can cause dusting, belt wear, and spillage, reducing effective capacity. Final Answer: speed

Question 8

Filtration of compressible cakes What is the typical range of the compressibility coefficient (s) for commercial compressible cakes encountered in industrial filtration?

Accepted Answer

Introduction / Context: In solid–liquid separation, cake compressibility strongly influences filtrate throughput and energy requirements. The compressibility coefficient s (sometimes denoted n) characterizes how cake resistance changes with applied pressure, a key concept in chemical engineering operations. Given Data / Assumptions: Commercial cakes formed from fine, deformable particles (e.g., biological sludges, pigments) Constant-pressure or constant-rate filtration models Definition: specific cake resistance α ∝ (ΔP)^s, where s indicates compressibility (s = 0 for incompressible) Concept / Approach: For industrial, compressible cakes, s typically lies well above zero. Experience shows values in the broad range 0.2–0.8 depending on structure, particle size, and binding. This explains why increasing pressure often yields diminishing returns in flow rate when dealing with soft cakes. Step-by-Step Solution: Recall relation: α = α_0 * (ΔP)^sFor incompressible cakes, s ≈ 0 (rare in practice).Commercial compressible cakes usually exhibit s within 0.2–0.8, reflecting significant structural collapse under pressure. Verification / Alternative check: Operational data from filter presses, rotary vacuum filters, and leaf filters show that doubling pressure seldom doubles flow for compressible slurries, consistent with s in the 0.2–0.8 band. Why Other Options Are Wrong: 0.01–0.1 and 0.1–0.3: Too low for most commercial compressible cakes; closer to mildly compressible or near-incompressible behavior. 0.2–0.4: Possible for some systems but too narrow; does not cover many highly compressible cakes encountered in practice. Common Pitfalls: Over-pressurizing in hopes of linear gains; for compressible cakes, dewatering aids (flocculants), precoat or filter aids, and conditioning can be more effective than just raising pressure. Final Answer: 0.2 to 0.8

Question 9

Comminution mechanism – cage mills In a cage mill, one or more concentric rows of alloy steel bars rotate in opposite directions to crush mineral particles. This type of mill primarily operates on which grinding mechanism?

Accepted Answer

Introduction / Context: Choosing a size-reduction device depends on matching material characteristics with the dominant breakage mechanism: impact, compression, shear, or attrition. Cage mills are common in fertilizer, chemical, and mineral processing for medium-fine reduction. Given Data / Assumptions: Cage mill has rotating cages with bars; feed is accelerated and struck repeatedly. Target is brittle to moderately tough solids (e.g., limestone, gypsum, salts). Product size typically in the coarse to medium-fine range. Concept / Approach: In cage mills, particles are flung by centrifugal force and collide at high relative velocities with bars and other particles. The dominant energy transfer is through impact, causing crack initiation and propagation in brittle solids. Step-by-Step Solution: Identify force type: high-speed collisions → impact.Compression/roll mechanism is characteristic of roll crushers, not cage mills.Vibratory mills rely on high-frequency vibration (attrition), unlike the bar impact of cages. Verification / Alternative check: Operating curves show throughput increasing with tip speed (impact intensity), and wear patterns on bars indicate repeated striking, confirming impact dominance. Why Other Options Are Wrong: Roll: Requires opposing cylindrical rolls; not the geometry of a cage mill. Vibratory: Uses oscillation and attrition; different mechanism and equipment class. None of these: Incorrect because impact clearly applies. Common Pitfalls: Feeding excessively damp or gummy materials can lead to build-up and reduced impact effectiveness; pre-drying or conditioning may be necessary. Final Answer: impact

Question 10

Gas cleaning of fine acidic mist Which type of wet scrubber is particularly effective for arresting very fine sulphuric acid mist aerosols?

Accepted Answer

Introduction / Context: Removing submicron acidic mists (e.g., H2SO4) from process exhaust is critical for environmental compliance and corrosion control. Selection of a scrubber depends on the target particle size and pressure drop one is willing to accept. Given Data / Assumptions: Mist droplets are very fine (often < 2 μm). Acceptable pressure drop is higher for better capture efficiency. Liquid is compatible with sulphuric acid. Concept / Approach: Venturi scrubbers accelerate gas through a throat to very high velocities, atomizing the scrubbing liquid into extremely fine droplets and producing intense turbulence. Collection of fine particles occurs by inertial impaction and diffusion, making venturis ideal for mists and fumes that defeat conventional packed beds. Step-by-Step Solution: Recognize target: submicron to a few micron H2SO4 mist.Select device with high energy dissipation and fine droplet generation.Venturi scrubber offers highest fine-particle capture among listed choices. Verification / Alternative check: Performance correlations show increased collection efficiency with gas velocity and liquid-to-gas ratio in venturis, matching field practice for acid mist control. Why Other Options Are Wrong: Packed wet and hollow wet scrubbers are suitable for gas absorption and larger droplets; capture of fine mist is limited at moderate pressure drops. Co-current describes flow orientation, not a specific high-efficiency mist control device. Common Pitfalls: Neglecting demisters downstream; venturi-generated fine droplets must be separated to prevent carryover. Also ensure materials of construction resist acidic environments. Final Answer: venturi

Question 11

Filter aids in cake filtration Which material is most commonly used as a filter aid to form porous, permeable precoat layers and prevent blinding?

Accepted Answer

Introduction / Context: Filter aids are used to increase permeability, reduce cake resistance, and protect the septum in pressure and vacuum filtration. Selecting the right aid improves throughput and clarifies challenging slurries. Given Data / Assumptions: Objective: build a porous precoat or body-feed network. Slurry tends to blind or forms compressible cakes. Compatibility with process fluid is assumed. Concept / Approach: Diatomaceous earth (kieselguhr) consists of fossilized diatom skeletons with high porosity and intricate microstructure. This produces a rigid, permeable lattice that captures fines without excessive pressure drop. It is therefore the industry standard for clarification and polishing steps. Step-by-Step Solution: Identify need: reduce cake resistance and prevent blinding.Select a highly porous, inert, and inexpensive material.Diatomaceous earth meets these criteria and is widely adopted. Verification / Alternative check: Beer, wine, sweetener, and pharmaceutical filtrations commonly specify diatomaceous earth for precoating or body feed, confirming broad acceptance. Why Other Options Are Wrong: Fuller’s earth and clays are sorbents for decolorization, not optimized as filter aids for permeability. Vermiculite can be used in specialty cases but is not the predominant industrial choice. Common Pitfalls: Poor precoat application leads to channeling; always establish a uniform layer before introducing the slurry. Ensure safe handling as dust can be hazardous. Final Answer: Diatomaceous earth

Question 12

Jaw crusher components – Blake type Identify the item that is not a component of a Blake jaw crusher assembly.

Accepted Answer

Introduction / Context: Jaw crushers (Blake type) are common primary crushers. Knowing their parts helps in maintenance, inspection, and troubleshooting mechanical failures such as toggle breakage or jaw wear. Given Data / Assumptions: Blake jaw crusher includes fixed and movable jaws. Drive mechanism converts rotary motion to reciprocating jaw motion. Typical parts: pitman, toggles, cheek/check plates, flywheels. Concept / Approach: The pitman connects to the eccentric shaft, transmitting motion to the movable jaw via toggles which provide the crushing action and overload protection. Check (cheek) plates protect the side frames. A “hanger” is not a standard component of the Blake jaw crusher mechanism. Step-by-Step Solution: List recognized components: pitman, toggles, cheek plates, jaws, flywheel, frame.Cross-check each option against standard nomenclature.Conclude that “Hanger” does not belong to the Blake jaw crusher assembly. Verification / Alternative check: Manufacturer drawings and maintenance manuals confirm the presence of pitman, toggle(s), cheek plates; “hanger” is not listed as a part. Why Other Options Are Wrong: Check plates (cheek plates): Wear plates protecting side walls. Toggles: Linkage transmitting motion and providing a safety relief. Pitman: Main moving member attached to eccentric shaft. Common Pitfalls: Confusing “cheek plates” with “jaw plates”; both are wear parts but serve different locations (sides vs crushing faces). Final Answer: Hanger

Question 13

Choosing comminution equipment Size reduction of which of the following is well suited to ball mills, crushing rolls, and rod mills?

Accepted Answer

Introduction / Context: Comminution equipment is chosen based on material brittleness, toughness, and structure. Ball mills, rod mills, and crushing rolls rely on impact, compression, and attrition—most efficient with brittle, crystalline solids such as metallic ores. Given Data / Assumptions: Standard wet/dry grinding practice in mineral processing. Product sizes from coarse to fine depending on circuit. Comparison includes fibrous vs brittle materials. Concept / Approach: Metalliferrous ores (e.g., iron, copper) fracture along grain boundaries and are amenable to impact and abrasion. Fibrous materials like asbestos and mica tend to flatten or split into sheets and are poorly handled by these mills; they require special delamination equipment. Basic slags and certain non-metallics may be treated, but the classic and most typical fit for ball/rod mills and rolls is metalliferrous ores. Step-by-Step Solution: Match breakage mechanism to material: impact/attrition → brittle crystalline ores.Metalliferrous ores fulfill this, yielding predictable grindability.Hence, these mills are appropriate choices for metalliferrous ore circuits. Verification / Alternative check: Standard mineral processing flowsheets (crushing → rod/ball milling) for copper, gold, iron ore validate the selection. Why Other Options Are Wrong: Asbestos & mica: Fibrous/lamellar; require delamination or special equipment, not conventional ball/rod milling for size control. Basic slags/non-metallic ores: Some can be milled, but the question asks the best suited among the listed; metalliferrous ores are archetypal for these machines. Common Pitfalls: Assuming one mill type fits all materials; always check work index, friability, and desired product shape. Final Answer: metalliferrous ores

Question 14

Coal preparation – cleaning very fine coal For cleaning fine coal dust smaller than 0.5 mm in size, which unit operation is most suitable?

Accepted Answer

Introduction / Context: Coal beneficiation separates valuable coal from mineral matter. The choice of separator depends strongly on particle size. Fine particles become difficult to treat by gravity alone due to low settling velocities. Given Data / Assumptions: Particle size < 0.5 mm (500 microns). Clean coal must be separated from ash-forming minerals. Water-based processes considered. Concept / Approach: Froth flotation exploits differences in surface hydrophobicity. Fine coal is naturally hydrophobic (or can be made so with collectors) and attaches to air bubbles, rising to the froth, while hydrophilic mineral matter stays in the slurry. This makes flotation ideal for ultrafines where gravity methods fail. Step-by-Step Solution: Identify particle size regime: fine to ultrafine.Choose a surface-based separation (flotation) rather than density-based jigs or spirals.Apply flotation reagents and air dispersion to recover clean coal in froth. Verification / Alternative check: Plant practices commonly route −0.5 mm fraction to flotation cells or columns; coarser fractions go to jigs, spirals, or dense medium cyclones. Why Other Options Are Wrong: Trough washers and Baum jigs rely on hindered settling—inefficient for ultrafines. Spiral separators handle moderately fine sizes (typically 0.15–3 mm), not the finest fractions as effectively as flotation. Common Pitfalls: Insufficient reagent conditioning or poor air dispersion reduces recovery; thick froths may entrap ash unless froth washing or column flotation is used. Final Answer: Froth floatation

Question 15

Separations by inertia vs gravity In which of the following units is gravity settling not the operative separation mechanism?

Accepted Answer

Introduction / Context: Particle–fluid separators rely on different forces: gravity, centrifugal, and sometimes interfacial forces. Correctly identifying the dominant mechanism helps select and size equipment for slurry classification and thickening. Given Data / Assumptions: Hydrocyclone imposes strong swirling flow field. Classifiers and thickeners operate under Earth gravity. Feed is a solid–liquid slurry. Concept / Approach: Hydrocyclones separate based on centrifugal acceleration (often tens to hundreds of g), vastly exceeding normal gravity and enabling sharp classification at small sizes. Dorr-thickeners, sedimentation tanks, and many classifiers rely on gravitational settling and hindered settling behavior. Step-by-Step Solution: Identify force field: hydrocyclone → centrifugal (inertial) separation.Classifiers/thickeners → gravity settling and rake compaction (for thickeners).Therefore, gravity is not the primary mechanism in a hydrocyclone. Verification / Alternative check: Cut size correlations in hydrocyclones use swirl intensity and pressure drop (centrifugal field), unlike settling basin design using Stoke’s law under 1 g. Why Other Options Are Wrong: Classifier, Dorr-thickener, Sedimentation tank: All depend on gravity-driven settling and clarification. Common Pitfalls: Assuming hydrocyclones can handle very high solids without roping; stable operation requires proper pressure and underflow/overflow control. Final Answer: hydrocyclone

Question 16

Powder technology – converting mass to particle count For a crushed solid sample, the total number of particles N can be expressed in terms of the total sample mass m, the volume of one particle Vp, and the particle density ρ. Which expression is co…

Accepted Answer

Introduction / Context: In particle technology and size-reduction analysis, it is often necessary to relate bulk measurements (like total mass) to microscopic counts (number of particles). This conversion is foundational for population balance modeling, breakage kinetics, and estimating specific surface area from size distributions. Given Data / Assumptions: Total mass of all particles in the sample: m. Volume of a single representative particle: Vp. True (material) density of the particles: ρ. Particles are compositionally identical (same ρ) and Vp represents the volume per particle used in the expression. Concept / Approach: The mass of one particle mp equals its density multiplied by its volume. The number of particles N is then the ratio of the total sample mass to the mass per particle. No special geometry is required for this mass–count relationship; only density and per-particle volume are needed. Step-by-Step Solution: Define single-particle mass: mp = ρ * VpNumber of particles: N = m / mpSubstitute mp: N = m / (ρ * Vp) Verification / Alternative check: Check dimensional consistency. Units: m in kg, ρ in kg/m^3, Vp in m^3. Then ρ * Vp has units kg, so m/(ρ * Vp) is dimensionless, as expected for a count. The other options either put ρ and Vp in the numerator incorrectly or invert the relationship, yielding wrong dimensions. Why Other Options Are Wrong: m * ρ / Vp: Has units kg * kg/m^3 / m^3 = kg^2/m^6, not dimensionless. m * Vp / ρ: Reduces to m^4/kg when using SI base units; physically meaningless for a count. Vp/(m * ρ): Inverts the ratio; would decrease as mass increases, contradicting physics. Common Pitfalls: Confusing bulk (apparent) density with true density, and interpreting Vp as geometric volume without accounting for porosity. For porous particles, use skeletal density for ρ or redefine Vp accordingly. Final Answer: m/(ρ * Vp)

Question 17

In mineral processing and metallurgical operations, which unit operation is referred to as “comminution” (i.e., the deliberate size reduction of ore into finer particles prior to separation)?

Accepted Answer

Introduction: “Comminution” is the fundamental first step in most mineral dressing flowsheets. It refers to reducing run-of-mine rock to smaller, more liberatable sizes so that valuable minerals can be economically separated from gangue in later stages. This question checks whether you can distinguish comminution from downstream concentration methods such as panning, spiralling, and tabling. Given Data / Assumptions: Context is mineral dressing (mineral processing). Comminution means mechanical size reduction. Panning, spiralling, and tabling are gravity separation methods, not size reduction steps. Concept / Approach: Comminution is carried out by crushing (jaw, gyratory, cone crushers) and grinding (rod, ball, SAG, and AG mills). Its goals include liberation of valuable minerals, preparing feed for classification, and controlling surface area for subsequent leaching or flotation. Gravity devices (pans, spirals, tables) classify or separate particles by density/shape after comminution and classification, not before. Step-by-Step Solution: Identify what comminution means: deliberate size reduction.List examples: crushing and grinding equipment.Recognize each option: panning, spiralling, tabling are gravity concentration methods.Therefore none of the listed devices performs comminution. Verification / Alternative check: Standard flowsheets show crushing and grinding before gravity concentration or flotation. No reputable text classifies panning/spiralling/tabling as comminution operations. Why Other Options Are Wrong: Panning: density-based gold recovery; no size reduction. Spiralling: separates by density and hydrodynamics; no breakage. Tabling: uses differential motion on a riffled deck; again, separation not size reduction. Common Pitfalls: Assuming any early-stage unit is “comminution.” Only machines that break particles (crushers, mills) qualify. Gravity tools handle already ground material. Final Answer: None of these

Question 18

Roll crusher nip condition: which inequality correctly relates the coefficient of friction (μ) between rock and roll and the half-angle of nip (α) required to draw particles into the rolls?

Accepted Answer

Introduction: For a roll crusher to “nip” a particle and pull it into the crushing zone, friction must be sufficient to overcome the particle’s tendency to slide. This basic force balance produces a design inequality relating friction to the nip angle. Recognizing the correct form helps in selecting roll diameter, surface, and operating conditions. Given Data / Assumptions: Two smooth rolls; half-angle of nip is α. Coefficient of friction between particle and roll is μ. Quasi-static force balance at the point of contact. Concept / Approach: Resolving normal and tangential components on the particle shows that the tangential friction force must at least equal the component of normal force trying to eject the particle. The well-known criterion is μ ≥ tan α (strictly μ must not be less than tan α). If μ is lower, the particle will slip instead of being nipped. Step-by-Step Solution: At contact, let N be normal force; friction available = μN.Tangential component of the geometry at angle α is N sin α; normal component is N cos α.Condition to avoid slip: μN ≥ N tan α ⇒ μ ≥ tan α.Hence the correct inequality is μ ≥ tan α. Verification / Alternative check: Textbook derivations for smooth rolls produce the same inequality and relate maximum nip angle to friction (larger μ allows larger nip angles). Surface roughening effectively increases the usable μ. Why Other Options Are Wrong: μ > tan α: sometimes stated, but the minimal requirement includes equality; ≥ is the more correct design condition. μ > tan 2α: dimensionally wrong; angle should not be doubled. μ ≤ tan α: would predict slipping at or above nip condition. μ = cot α: unrelated to the nip balance. Common Pitfalls: Confusing α (half-angle) with the full nip angle, or forgetting that surface texturing changes effective friction. Final Answer: μ ≥ tan α

Question 19

Equal-settling particles in a classifier: two particles are called “equal settling” when they have the same what (in the same fluid and field of force)?

Accepted Answer

Introduction: Separators and classifiers often sort particles by their settling behavior rather than by diameter alone. The term “equal-settling” formalizes this idea: particles that fall at the same rate behave similarly in the separator even if their sizes or densities differ. Given Data / Assumptions: Same continuous fluid and same gravitational (or centrifugal) field. Particles may differ in size, density, and shape. Concept / Approach: Terminal settling velocity depends on particle size, density difference, fluid viscosity, and drag regime. Two particles are equal-settling if their terminal velocities match under identical fluid and field conditions. This is the basis of “equal-settling ratios” used in sizing classifiers and hydrocyclones for mixed-density ores. Step-by-Step Solution: Define v_t as the terminal settling velocity.Equal-settling condition: v_t1 = v_t2 in the same fluid and field.This does not require equal diameter or equal density; combinations can compensate.Thus, classification behavior groups such particles together. Verification / Alternative check: In Stokes or Newton regimes, explicit v_t expressions show that a smaller but denser particle may equal-settle with a larger but lighter particle when v_t values coincide. Why Other Options Are Wrong: Size or specific gravity alone does not guarantee equal settling. “None of these” is incorrect because the precise definition is given in option (c). Sphericity influences drag but is not the defining equality. Common Pitfalls: Assuming screens and classifiers separate on the same metric. Screens sort by size; classifiers respond to settling velocity. Final Answer: Terminal settling velocities in the same fluid and field of force

Question 20

Ball and tube mills charged with flint or porcelain media are typically selected for size reduction of which materials, to avoid iron contamination and achieve fine grinding?

Accepted Answer

Introduction: Media choice in tumbling mills affects contamination, product purity, and wear. Flint or porcelain (ceramic) balls are used when iron pickup must be minimized, such as in ceramics and certain non-metallic mineral applications. Given Data / Assumptions: Ball/tube mills with non-metallic media (flint/porcelain). Goal: fine grinding with minimal iron contamination. Concept / Approach: Grinding media can shed material into the product. For whitewares, glass, feldspar, quartz, and other non-metallics, iron contamination is detrimental (color/chemistry). Hence, non-metallic media are chosen. Asbestos is fibrous and not efficiently ground this way; rubber is not normally size-reduced in such mills; limestone grinding for cement typically uses steel media due to throughput and cost. Step-by-Step Solution: Identify applications needing low iron: ceramics, glass batch, non-metallic ores.Match to media: flint/porcelain provide low contamination.Conclude correct selection is non-metallic ores and ceramic raw materials. Verification / Alternative check: Industrial practice and handbooks list porcelain-lined mills with flint pebbles for feldspar, silica, kaolin, and glaze preparation to preserve whiteness and purity. Why Other Options Are Wrong: Asbestos: fibrous; milling behavior and health concerns make it unsuitable. Rubber: elastomeric; typically not comminuted this way. Limestone for cement: steel media is standard for economy and throughput. Metallic concentrates: steel media acceptable; minor iron pickup is usually not critical. Common Pitfalls: Assuming “any” ball mill uses any media; the chemistry of the product dictates media selection to control contamination. Final Answer: Non-metallic ores and ceramic raw materials

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