Q: Special handling materials: Size reduction of soft, fusible solids is often done on steam-heated rolls and roll crushers. Which of the following is typically processed this way to avoid gumming or smearing?

Introduction / Context: Some materials soften, smear, or gum up conventional grinders. For such thermoplastic or fusible materials, controlled heating (or cooling) plus specific milling arrangements are used to obtain a manageable fracture behavior and avoid clogging screens. Given Data / Assumptions: Steam-heated rolls provide a controlled temperature surface. Goal is to nip and flatten brittle–plastic solids without smearing. Target material is soft and fusible. Concept / Approach: Waxes and certain resins soften and smear at modest temperatures. Using heated rolls or roll crushers allows forming thin, cooled flakes or controlled-size particles after pressing. Waxes are classic examples: heating maintains a workable consistency and prevents clogging; subsequent cooling and flaking give a granular product. Step-by-Step Solution: Identify fusible candidates: waxes and some thermoplastic resins.Heated rolls mitigate smearing and allow controlled thickness sheeting then breaking.Among options, waxes are the textbook case for steam-heated roll processing. Verification / Alternative check: Process handbooks cite roll/crusher handling of waxes, bitumen-like materials, and certain resins with heat control to avoid agglomeration. Why Other Options Are Wrong: Resins: some are handled similarly, but waxes are the clearer canonical example. Gums: typically handled in solution; dry grinding is problematic. Hard rubber and quartz: require different, more robust comminution methods. Common Pitfalls: Attempting to grind waxes in high-energy mills at room temperature, leading to dangerous heat build-up and smeared screens. Final Answer: Waxes

Q: Shape factor in particle technology: For a non-spherical particle, how is “sphericity” (ψ) correctly defined?

Introduction / Context: Sphericity quantifies how closely a particle’s shape approximates a sphere. It is widely used in correlations for drag, heat transfer, and packed-bed pressure drop (e.g., Ergun equation). A correct definition is essential for consistent calculations. Given Data / Assumptions: Compare an arbitrary particle with a sphere that has the same volume. Use surface areas to construct a dimensionless ratio. Particles are rigid and nonporous for the definition. Concept / Approach: Sphericity ψ is defined as ψ = A_sphere,eq / A_particle, where A_sphere,eq is the surface area of a sphere having the same volume as the particle. Because the sphere has the minimum surface area for a given volume, ψ ≤ 1, with ψ = 1 for a perfect sphere. Step-by-Step Solution: Let V_p be the particle volume.Define sphere of equal volume: diameter d_v so that (pi/6) d_v^3 = V_p.Compute A_sphere,eq = pi * d_v^2, compare to actual surface area A_p.Therefore ψ = A_sphere,eq / A_p (dimensionless). Verification / Alternative check: Textbook definitions and Perry’s handbook align with this expression and note that ψ approaches 1 as shapes near spherical. Why Other Options Are Wrong: Dimension of length: ψ is dimensionless. “Always less than 1”: incorrect because spheres have ψ = 1 exactly. Volume-based inversion (Option D) is not the standard definition. Option E is not a recognized sphericity form. Common Pitfalls: Mixing sphericity with aspect ratio, or confusing equal-volume vs equal-surface reference spheres. Final Answer: ψ = surface area of a sphere having the same volume as the particle divided by the actual particle surface area

Question 1

Particle sizing — what distribution does microscopic analysis yield? When particle size is determined by direct microscopic counting and measurement, which type of size distribution is obtained?

Accepted Answer

Introduction / Context: Different sizing methods yield different statistical weightings (number-, length-, area-, or volume-weighted). Understanding which distribution a method produces is crucial for comparing datasets and interpreting results in powder technology. Given Data / Assumptions: Microscopic analysis counts and sizes individual particles on a field. All particles observed have equal “voting weight” as counts unless corrected. Concept / Approach: Direct microscopy produces a number-weighted distribution by default because each particle contributes one count regardless of its size. Other methods (e.g., sieving or sedimentation) often correlate more closely with mass/volume-weighted distributions. Step-by-Step Solution: Identify that counting at the microscope increments a tally per particle.Therefore the underlying weighting is by number of particles.Select “number” distribution. Verification / Alternative check: Standard texts classify: microscopy → number distribution; laser diffraction → volume distribution; sieving → mass (weight) distribution. Why Other Options Are Wrong: Length/area/volume: these weight larger particles more heavily; not the default outcome of simple counting without special weighting corrections. Common Pitfalls: Comparing number-based D50 with volume-based D50; they are not directly interchangeable. Final Answer: number

Question 2

Particle shape — sphericity using equivalent diameter, volume, and surface area If dp is the volume-equivalent diameter of a non-spherical particle, Vp its actual volume, and Sp its actual surface area, what is the correct expression for sphericity …

Accepted Answer

Introduction / Context: Sphericity Φs quantifies how closely a particle's shape approaches a sphere. It is essential in calculating drag, settling velocity, and permeability in packed beds, where deviations from sphericity strongly affect hydrodynamics. Given Data / Assumptions: dp is the diameter of a sphere that has the same volume as the particle (volume-equivalent). Vp is the particle volume; Sp is the particle surface area. By definition, Φs = (surface area of volume-equivalent sphere) / (actual particle surface area). Concept / Approach: Volume-equivalent sphere volume = (π/6) dp^3; its surface area = π dp^2. Therefore Φs = (π dp^2)/Sp. Rearranging using Vp and dp yields an equivalent expression not requiring π explicitly: 6 Vp/dp = π dp^2 for a volume-equivalent sphere, hence Φs = (6 Vp/dp)/Sp. Step-by-Step Solution: Start with Φs = (surface area of sphere with volume Vp) / Sp.For volume-equivalent dp: Vp = (π/6) dp^3 ⇒ 6 Vp/dp = π dp^2.Thus Φs = (6 Vp/dp)/Sp. Verification / Alternative check: Dimensional check: 6Vp/dp has dimensions of area; dividing by Sp yields a dimensionless Φs (0 < Φs ≤ 1). Why Other Options Are Wrong: Options (b), (c), (d) are not dimensionally consistent or invert the relation, giving Φs > 1 for many shapes, which is impossible. Common Pitfalls: Confusing dp as surface-area equivalent diameter instead of volume-equivalent; that changes formulas. Final Answer: Φs = 6 Vp/(dp Sp)

Question 3

Comminution & classification — identify the incorrect statement Which of the following statements about grinding circuits, additives, classifiers, and size enlargement is incorrect?

Accepted Answer

Introduction / Context: Particle processing spans size reduction, separation, and size enlargement. Many terms sound similar (classifier vs. clarifier), leading to common exam traps. This question checks precise terminology and unit operations knowledge. Given Data / Assumptions: Closed vs. open circuit grinding practices. Use of grinding aids in cement milling. Definition of classifier vs. clarifier/filter. Examples of size enlargement. Concept / Approach: Classifiers separate particles by size (or settling velocity) in suspensions or pneumatic streams. Removing traces of solids from liquids is the role of clarifiers and filters. Grinding aids reduce agglomeration and energy consumption. Tablet pressing is a classic size enlargement (agglomeration) example. Step-by-Step Solution: (a) Closed circuit grinding recycles coarse fraction → generally more energy efficient → true.(b) Lubricious additives like animal/vegetable oils and stearates are used as grinding aids → true.(c) Calling a trace-solids remover a “classifier” is wrong; that is a clarifier/filter → incorrect statement.(d) Compressing powders into tablets increases effective particle size → true. Verification / Alternative check: Unit operations texts list gravity/hydraulic/pneumatic classifiers for sizing; clarifiers and filters for liquid-solid clarification. Why Other Options Are Wrong: (a), (b), (d) align with industrial practice and standard references. Common Pitfalls: Mixing “classifier” and “clarifier” due to similar spelling. Final Answer: The equipment used for the removal of traces of solids from a liquid is called a classifier.

Question 4

Filtration equipment — selecting a pressure filter Which one of the following is (classically) operated as a pressure filter in process industries?

Accepted Answer

Introduction / Context: Filtration units are broadly classified by driving force (vacuum vs. pressure) and configuration (presses, leaf/tank, rotary, granular media). Correct identification affects sizing, cake washing strategy, and maintenance planning. Given Data / Assumptions: Typical industrial configurations are implied. We seek the canonical example of a pressure filter. Concept / Approach: The plate and frame filter press is the archetypal pressure filter: slurry is pumped under pressure, solids form a cake between plates, and filtrate exits through channels. Rotary drum filters are most commonly vacuum-driven. Moore-type leaf units are classically vacuum leaf filters (tank leaf), although pressure leaf variants exist; the “Moore” name is strongly associated with vacuum operation in many texts. Sand filters are typically gravity or modest-pressure granular media filters used in water treatment, not cake pressure filters. Step-by-Step Solution: Identify the canonical pressure cake filter → plate and frame.Eliminate rotary drum (usually vacuum) and sand filter (granular media).Moore leaf commonly categorized under vacuum leaf configurations. Verification / Alternative check: Handbooks list plate and frame presses under pressure filtration; rotary drums under vacuum filtration. Why Other Options Are Wrong: Leaf (Moore): commonly vacuum operation in classical descriptions. Rotary drum: standard vacuum filter. Sand filter: gravity/pressure granular filter, not a pressure cake filter press. Common Pitfalls: Assuming all “leaf” filters are pressure devices; variants exist but the Moore design is widely taught as vacuum. Final Answer: Plate and frame filter

Question 5

Ultrafine grinding — dominant breakage mechanism In ultrafine grinders (e.g., fluid energy mills, stirred media mills), the main size-reduction mechanism is:

Accepted Answer

Introduction / Context: Ultrafine grinding targets sub-10 μm (often sub-5 μm) sizes for pigments, fillers, and pharmaceuticals. Different mills rely on different breakage modes; matching mechanism to material saves energy and preserves product quality. Given Data / Assumptions: Ultrafine grinders include jet mills and stirred media mills. Particles experience high-frequency, low-amplitude interactions. Concept / Approach: At ultrafine scales, attrition (surface abrasion and shear between particles or between particles and media) dominates, producing smooth, very fine particles. While impact contributes (e.g., in jets), attrition is the principal, especially in stirred media milling where shear fields are intense and continuous. Step-by-Step Solution: Identify the class of mills → ultrafine grinders.Recall primary mechanism → attrition (shear/abrasion).Select “attrition.” Verification / Alternative check: Process texts describe stirred media mills as attritors; the name itself highlights the attrition mechanism. Why Other Options Are Wrong: Cutting: typical of knife mills for coarse sizing. Compression: primary in roll crushers. Impact: key for hammer mills but less dominant in ultrafine attritors. Common Pitfalls: Assuming “jet mill” implies pure impact; interparticle attrition in high-velocity jets is substantial. Final Answer: attrition

Question 6

Bulk solids handling — short-distance conveying of granular materials For short-distance transport of grain, gravel, sand, ash, or asphalt, which conveyor type is most commonly used?

Accepted Answer

Introduction / Context: Choosing a conveyor depends on material properties, distance, incline, and containment needs. For short runs inside plants, a compact, enclosed, and versatile unit is preferred for granular or powdery materials. Given Data / Assumptions: Materials: grain, gravel, sand, ash, asphalt (granular to fine, sometimes hot). Short-distance conveying within a facility. Desire for enclosed transport to limit dust and spillage. Concept / Approach: Screw conveyors are ubiquitous for short distances. They are simple, enclosed, tolerant of a range of bulk densities, allow controlled feeding, and can be inclined modestly. Alternatives like drag (slat) or flight conveyors serve niche layouts but are bulkier or more maintenance-prone for general short-run duties. Step-by-Step Solution: Match requirements (short, enclosed, versatile) → screw conveyor.Check material compatibility: screws routinely handle grain, sand, ash, and even warm asphalt with proper materials of construction.Select “screw.” Verification / Alternative check: Vendor catalogs list screw conveyors for metering and transfer over spans typically up to 30–40 m per section, ideal for “short distance.” Why Other Options Are Wrong: Flight and slat/drag: workable but often chosen for abrasive, long, or vertical lifts; more complex casing and chain wear. Ribbon: a screw variant used to mix/handle sticky materials; not the generic transfer solution. Common Pitfalls: Assuming belt conveyors are always preferred; belts excel at longer distances and higher capacities but are not listed among the options here. Final Answer: screw

Question 7

Particle sizing in process engineering: The “equivalent diameter” of an irregular particle is defined as the diameter of a perfect sphere that has the same physical measure as the particle. Which measure is being equated in the usual volume-equivale…

Accepted Answer

Introduction / Context: In particle technology, engineers compare irregular particles to “equivalent” spheres to simplify calculations in settling, filtration, and heat/mass transfer. Several equivalent diameters exist (volume-equivalent, surface-equivalent, sieve-equivalent). Knowing which physical measure is matched in each definition avoids confusion in design correlations. Given Data / Assumptions: We are discussing the most common “equivalent diameter” used in many correlations for sedimentation and fluidization. The alternative measures include surface area and various ratios; however, the standard volume-equivalent diameter equates particle volume to that of a sphere. Particle shape is irregular but nonporous for the purpose of definition. Concept / Approach: The volume-equivalent diameter d_v is defined by equating the volume of the irregular particle to that of a sphere: (pi/6) * d_v^3 = V_particle. This makes d_v useful in mass-based and buoyancy-driven relations, because both mass and buoyancy depend directly on volume. Step-by-Step Solution: Let V_p be the actual particle volume.Define d_v such that sphere volume equals V_p.Hence (pi/6) * d_v^3 = V_p ⇒ d_v = (6 * V_p / pi)^(1/3).Therefore, the correct “measure” being equated is volume, not a ratio like surface/volume. Verification / Alternative check: Compare with sphericity-based definitions: sphericity uses surface-area equivalence for the comparison but still relies on an independent diameter definition such as d_v. Handbooks consistently define equivalent diameter (unless otherwise specified) as the sphere of equal volume. Why Other Options Are Wrong: Ratio of surface/volume or volume/surface: these are not the standard equivalence criteria for d_v. Surface area equal to that of the particle describes a different measure (surface-equivalent diameter), not the usual equivalent diameter asked here. “None of these” is incorrect because the correct choice is explicitly listed. Common Pitfalls: Confusing volume-equivalent diameter with sieve diameter (from screen analysis) or surface-equivalent diameter (used with sphericity). Always check the intended definition in a given correlation. Final Answer: Volume equal to that of the particle

Question 8

Industrial filtration practice: What is the principal purpose of adding a filter aid (e.g., diatomaceous earth, perlite) during cake filtration?

Accepted Answer

Introduction / Context: Filter aids such as diatomaceous earth and perlite are widely used in beverage, pharmaceutical, and chemical industries. They are pre-coated onto the filter medium or dosed into the slurry to prevent blinding, create a porous initial layer, and maintain permeability throughout cake build-up. Given Data / Assumptions: Cake filtration at near-constant pressure is considered. Filter medium tends to blind quickly when fine particles deposit directly on it. A small fraction of filter aid is either pre-coated or body-fed during the run. Concept / Approach: Filtration rate under a given pressure depends on total resistance (medium + cake). A highly porous, permeable precoat reduces initial resistance and slows blinding. As cake grows with embedded filter aid, average permeability increases, sustaining higher filtrate flow rates over time. Step-by-Step Solution: Without filter aid: fine particles plug pores of the septum → rapid rise in resistance → low flow.With filter aid: a porous “skeleton” layer forms → effective permeability k increases.For constant pressure filtration: dV/dt ∝ k/μ / (R_medium + R_cake), so higher k directly raises dV/dt.Net effect: a higher and more stable filtration rate. Verification / Alternative check: Precoat/body-feed operating manuals show flatter dV/dt decline curves with filter aids, confirming improved throughput and longer cycles at the same pressure differential. Why Other Options Are Wrong: Decrease pressure drop by reducing viscosity: filter aids do not change liquid viscosity; they change cake permeability. Increase porosity/permeability (Option C) describes the mechanism, but the principal purpose asked for is the performance outcome: higher rate. Act as the septum: the septum is a fixed support (cloth, screen, cartridge), not the filter aid. Reduce feed solids concentration: dosing filter aid slightly raises, not lowers, solids in the slurry. Common Pitfalls: Confusing mechanism (more porous cake) with the performance metric (higher rate). Also, overdosing filter aid can waste material and add unnecessary solids load. Final Answer: Increase the rate of filtration

Question 9

Sugar industry centrifugation: Which centrifuge type is most commonly used in sugar mills for separating massecuite (sugar crystals and mother liquor)?

Accepted Answer

Introduction / Context: Raw and refined sugar production requires separation of sugar crystals from the mother liquor (molasses). The mixture, called massecuite, is highly viscous and contains relatively large crystals. Centrifugation is the standard unit operation to achieve effective separation. Given Data / Assumptions: Massecuite contains sizable crystalline solids with sticky mother liquor. Robust mechanical handling and washing of crystals within the basket is required. Industry practice guides equipment choice more than “laboratory” centrifuge types. Concept / Approach: Suspended batch basket centrifuges (also called batch sugar centrifugals) feature a perforated rotating basket lined with a screen. The massecuite is charged, liquor is forced out by centrifugal action, and the sugar crystals are retained as a cake. Water or steam washing may be applied before discharging the crystals. Step-by-Step Solution: Identify the physical characteristics: large crystal size, viscous liquor → suitable for basket centrifuge.Batch processing matches crystallizer output cycles and washing needs.Therefore, the standard choice is the suspended batch basket centrifuge. Verification / Alternative check: Industry texts and equipment suppliers list “batch sugar centrifugals” as the workhorses in sugar mills, capable of high g-forces and effective washing. Why Other Options Are Wrong: Tubular/Disc-bowl: used for fine, low-solids applications (e.g., polishing bio-broths), not for large crystal cakes. Perforated horizontal basket continuous: found in some continuous duties, but traditional sugar massecuite separation is typically batch. Vacuum filters: not the principal equipment for crystal–liquor separation in sugar centrifugation step. Common Pitfalls: Assuming high-speed clarifier centrifuges suitable for all slurries; crystal size and cake washing needs dictate basket centrifuges in sugar mills. Final Answer: Suspended batch basket centrifuge

Question 10

Ultrafine grinding vs. crushers: Which machine is NOT classified as an ultrafine grinder (colloid mill) for producing sub-100 μm material?

Accepted Answer

Introduction / Context: Comminution equipment is categorized by the fineness it can achieve. Ultrafine grinders (colloid and jet mills) reach very small particle sizes suitable for pigments, pharmaceuticals, and specialty chemicals. Crushers and coarse grinders serve much larger size ranges. Given Data / Assumptions: Ultrafine range commonly targets sub-100 μm, often down to a few micrometers. Fluid energy (jet) mills and agitated media mills are classic ultrafine machines. Crushers like toothed roll units typically produce millimeter-scale product. Concept / Approach: Toothed roll crushers operate by nipping and shearing; they are best for friable, medium-hard solids, producing coarse to intermediate sizes, not colloidal or ultrafine powders. In contrast, micronizers exploit high-velocity gas jets and particle–particle collisions to break particles to micrometer sizes. Step-by-Step Solution: List ultrafine equipment: jet mills, agitated media mills, classifier mills.Identify non-ultrafine: toothed roll crusher (coarse grinder/crusher).Hence, select toothed roll crusher as NOT an ultrafine grinder. Verification / Alternative check: Manufacturer catalogs confirm product size ranges: crushers seldom below a few hundred micrometers; jet mills routinely achieve <10 μm. Why Other Options Are Wrong: Micronizer/fluid energy mill: core ultrafine machines. Agitated mills: use small media for sub-100 μm grinding. Hammer/classifier and pin/classifier mills: with internal classification, can reach fine to ultrafine cuts. Common Pitfalls: Assuming higher rotor speed alone makes a mill “ultrafine”; mechanism and classification are key. Final Answer: Toothed roll crusher

Question 11

Special handling materials: Size reduction of soft, fusible solids is often done on steam-heated rolls and roll crushers. Which of the following is typically processed this way to avoid gumming or smearing?

Accepted Answer

Introduction / Context: Some materials soften, smear, or gum up conventional grinders. For such thermoplastic or fusible materials, controlled heating (or cooling) plus specific milling arrangements are used to obtain a manageable fracture behavior and avoid clogging screens. Given Data / Assumptions: Steam-heated rolls provide a controlled temperature surface. Goal is to nip and flatten brittle–plastic solids without smearing. Target material is soft and fusible. Concept / Approach: Waxes and certain resins soften and smear at modest temperatures. Using heated rolls or roll crushers allows forming thin, cooled flakes or controlled-size particles after pressing. Waxes are classic examples: heating maintains a workable consistency and prevents clogging; subsequent cooling and flaking give a granular product. Step-by-Step Solution: Identify fusible candidates: waxes and some thermoplastic resins.Heated rolls mitigate smearing and allow controlled thickness sheeting then breaking.Among options, waxes are the textbook case for steam-heated roll processing. Verification / Alternative check: Process handbooks cite roll/crusher handling of waxes, bitumen-like materials, and certain resins with heat control to avoid agglomeration. Why Other Options Are Wrong: Resins: some are handled similarly, but waxes are the clearer canonical example. Gums: typically handled in solution; dry grinding is problematic. Hard rubber and quartz: require different, more robust comminution methods. Common Pitfalls: Attempting to grind waxes in high-energy mills at room temperature, leading to dangerous heat build-up and smeared screens. Final Answer: Waxes

Question 12

Shape factor in particle technology: For a non-spherical particle, how is “sphericity” (ψ) correctly defined?

Accepted Answer

Introduction / Context: Sphericity quantifies how closely a particle’s shape approximates a sphere. It is widely used in correlations for drag, heat transfer, and packed-bed pressure drop (e.g., Ergun equation). A correct definition is essential for consistent calculations. Given Data / Assumptions: Compare an arbitrary particle with a sphere that has the same volume. Use surface areas to construct a dimensionless ratio. Particles are rigid and nonporous for the definition. Concept / Approach: Sphericity ψ is defined as ψ = A_sphere,eq / A_particle, where A_sphere,eq is the surface area of a sphere having the same volume as the particle. Because the sphere has the minimum surface area for a given volume, ψ ≤ 1, with ψ = 1 for a perfect sphere. Step-by-Step Solution: Let V_p be the particle volume.Define sphere of equal volume: diameter d_v so that (pi/6) d_v^3 = V_p.Compute A_sphere,eq = pi * d_v^2, compare to actual surface area A_p.Therefore ψ = A_sphere,eq / A_p (dimensionless). Verification / Alternative check: Textbook definitions and Perry’s handbook align with this expression and note that ψ approaches 1 as shapes near spherical. Why Other Options Are Wrong: Dimension of length: ψ is dimensionless. “Always less than 1”: incorrect because spheres have ψ = 1 exactly. Volume-based inversion (Option D) is not the standard definition. Option E is not a recognized sphericity form. Common Pitfalls: Mixing sphericity with aspect ratio, or confusing equal-volume vs equal-surface reference spheres. Final Answer: ψ = surface area of a sphere having the same volume as the particle divided by the actual particle surface area

Question 13

Contamination-sensitive milling: In pebble mills used for paints, pigments, and cosmetics (where iron contamination must be avoided), what are the pebbles typically made of?

Accepted Answer

Introduction / Context: When grinding color-sensitive or purity-critical products, iron contamination from grinding media must be minimized. Pebble mills use nonmetallic media to prevent discoloration and unwanted catalytic effects in paints, pigments, and cosmetics. Given Data / Assumptions: Tumbling (ball/pebble) mill configuration. Product sensitive to metallic contamination. Desire for chemically inert, hard, and wear-resistant media. Concept / Approach: Flint pebbles and porcelain (alumina-based ceramics) are traditional nonmetallic media. They are hard, relatively dense, and chemically inert, reducing contamination while still providing effective grinding. Stainless steel or steel shot is avoided when iron-free product is required. Step-by-Step Solution: Define requirement: nonmetallic, inert media → ceramic or natural stone.Compare options: bronze/stainless/concrete introduce metals or impurities.Select flint or porcelain as the standard choice. Verification / Alternative check: Materials handbooks list flint pebbles and high-alumina porcelain balls for contamination-sensitive grinding applications. Why Other Options Are Wrong: Bronze/stainless/mild steel: risk metallic contamination. Concrete: not wear-resistant or clean enough for high-purity pigments. Common Pitfalls: Using mixed media that introduces tramp metals; always align media choice with purity specifications. Final Answer: Flint or porcelain

Question 14

Constant-pressure cake filtration: For filtration operated at a constant pressure drop, how does the instantaneous filtrate flow rate vary with time (t)?

Accepted Answer

Introduction / Context: In incompressible-cake filtration at constant pressure, resistance increases as cake thickness grows. Understanding how filtrate flow rate declines with time is fundamental for cycle time estimates and area sizing in process filtration. Given Data / Assumptions: Constant pressure drop across the filter and cake. Incompressible cake; viscosity and temperature constant. Filter medium resistance is small or absorbed into constants. Concept / Approach: For constant-pressure cake filtration, the classical equation gives t = α * V^2 + β * V (α relates to specific cake resistance and solids concentration, β to medium resistance). Differentiating with respect to time gives the instantaneous flow rate dV/dt, which is inversely proportional to a linear function of V. Since V ∝ √t (for large t when cake resistance dominates), dV/dt ∝ 1/√t. Step-by-Step Solution: Start with t = a V^2 + b V.Differentiate: dt/dV = 2 a V + b ⇒ dV/dt = 1 / (2 a V + b).For cake-dominated regime (b negligible): dV/dt ≈ 1 / (2 a V).But V ≈ k √t ⇒ dV/dt ∝ 1 / √t. Verification / Alternative check: Plotting V versus √t typically yields a straight line under constant-pressure filtration; slope relates to cake parameters. This confirms the √t dependence and the 1/√t decay in rate. Why Other Options Are Wrong: 1/t: too steep a decay and not supported by the filtration equation. Constant with time or increasing: contradicts the growing resistance of the cake. Zero after a few seconds: unrealistic; flow declines gradually, not abruptly. Common Pitfalls: Ignoring medium resistance at early times (b term) or cake compressibility, which can further modify the time dependence. Always check regime validity. Final Answer: Varies inversely with the square root of time, i.e., dV/dt ∝ 1/√t

Question 15

Screens and crushers: Identify the correct statement regarding mineral processing operations and equipment selection.

Accepted Answer

Introduction / Context: Mineral processing involves crushing, screening, and separation steps. Equipment choice impacts product quality, energy use, and downstream performance. Understanding which assertions are accurate helps avoid common plant design mistakes. Given Data / Assumptions: Typical ceramics require high whiteness and purity. Screens can be vibrating or shaking (reciprocating) with different costs and efficiencies. Crusher selection depends on material hardness, stickiness, and abrasiveness. Concept / Approach: Iron contamination (from tramp iron or iron-bearing minerals) causes ceramic discoloration upon firing. Magnetic separation removes iron-bearing particles, protecting product whiteness. Vibrating screens generally offer higher capacity and lower maintenance than shaking screens. Screen capacity is affected by bulk density/specific gravity. Toothed roll crushers are better for friable, moderately soft materials (e.g., coal, salt) rather than sticky asphalt. Step-by-Step Solution: Evaluate Option A: Correct—magnetic separation removes iron that would stain ceramics.Option B: Incorrect—shaking screens tend to have higher operating cost than vibrating screens.Option C: Incorrect—capacity depends on material properties including bulk density.Option D: Dubious—sticky asphalt tends to smear; toothed rolls are not ideal. Verification / Alternative check: Ceramics processing references specify magnetic removal to achieve white bodies. Screen manufacturer data show capacity and cost advantages of vibrating designs. Why Other Options Are Wrong: B: Reverses the usual cost relation. C: Ignores role of bulk density on bed depth and screening rate. D & E: Mis-match crusher type to sticky feeds; asphalt requires specialized handling. Common Pitfalls: Assuming one crusher fits all; not accounting for stickiness leading to plugging and smearing. Final Answer: Removing iron from ceramic feed by magnetic separation prevents discoloration of ceramic products

Question 16

Ore beneficiation methods: Froth flotation is most suitable for the separation and upgrading of which type of ores?

Accepted Answer

Introduction / Context: Froth flotation is a selective separation technique based on differences in surface hydrophobicity. It revolutionized mineral processing by enabling efficient concentration of low-grade ores, especially sulfides, at relatively fine particle sizes. Given Data / Assumptions: Appropriate reagents (collectors, frothers, modifiers) are available. Ores are ground to liberate valuable minerals from gangue. Pulp chemistry (pH, ionic strength) can be adjusted to achieve selectivity. Concept / Approach: Sulfide minerals bond well with xanthates and related collectors, rendering them hydrophobic. Air bubbles attach to hydrophobic particles, which rise to form a froth concentrate. Gangue (e.g., silicates) remains hydrophilic and sinks as tailings. This makes sulfide ores ideal candidates for flotation. Step-by-Step Solution: Identify ore type with strong collector response: sulfides.Apply grinding and reagent scheme to selectively float the valuable sulfide minerals.Collect froth concentrate; depress unwanted minerals as needed (e.g., Zn vs Pb selectivity). Verification / Alternative check: Historical and modern concentrators for Pb–Zn–Cu rely primarily on froth flotation; iron ores more commonly use magnetic or gravity separation (though reverse flotation is used in some hematite systems after desliming and reagentization). Why Other Options Are Wrong: Iron ores/quartzite: not typically floated as primary step without significant conditioning; magnetic/gravity often dominate. Bauxite: processed mainly by digestion (Bayer process), not by simple flotation at mine scale. None of these: incorrect because sulfide ores are the classic flotation feeds. Common Pitfalls: Overlooking liberation: insufficient grinding yields poor flotation performance regardless of reagents. Final Answer: Sulphide ores (e.g., galena, sphalerite, chalcopyrite)

Question 17

In industrial comminution: Balls used in ball mills are commonly made from hard, wear-resistant materials. Which of the following materials is NOT used for manufacturing mill balls for routine grinding service?

Accepted Answer

Introduction / Context: Ball mills rely on hard, wear-resistant grinding media to crush and grind ores, pigments, and ceramic raw materials. The choice of ball material affects contamination, wear rate, energy efficiency, and product purity. Given Data / Assumptions: The question concerns standard industrial duty (not specialty laboratory use). Typical ball materials include forged/cast steels, high-Cr white irons, and sometimes ceramics or flint pebbles for low contamination. Media must withstand high impact and abrasion without deforming excessively. Concept / Approach: Grinding media must be hard, tough, and dimensionally stable. Ductile or very soft metals deform, smear, and shed, causing contamination and poor grinding. Toxicity and low melting point can also disqualify a material for routine milling. Step-by-Step Solution: Identify common media: forged steel, cast steel, high-Cr iron → widely used due to high hardness and toughness.Check lead: very soft (Brinell hardness ~5–22 HB), easily deforms and cold-flows under impact.Conclude lead is unsuitable for standard ball mill duty → not used as balls. Verification / Alternative check: Handbooks and supplier catalogs list forged/cast steel and cast irons; lead appears only as a milling additive or as a component in lead-lined mills for specialty corrosion service, not as grinding media. Why Other Options Are Wrong: Alloy steel / Forged steel / Cast iron: All are conventional grinding media materials with proven wear resistance and service life. Common Pitfalls: Confusing “lining” or process additives with grinding media; assuming any metal sphere can serve as a mill ball. Final Answer: Lead

Question 18

Unit operations overview: Which of the following is NOT categorized as a mechanical operation in chemical engineering?

Accepted Answer

Introduction / Context: Chemical engineering groups practical steps into unit operations such as mechanical handling (crushing, screening), fluid flow, heat transfer, and mass transfer. Knowing which category a process belongs to helps in choosing the right design equations and scale-up rules. Given Data / Assumptions: Mechanical operations manipulate size, shape, and phase dispersion using mechanical energy. Mass transfer operations involve species transfer across phases driven by concentration differences. Heat/momentum transfer may accompany either category but do not define it. Concept / Approach: Filtration, agitation, and size enlargement rely primarily on mechanical work and equipment geometry. Humidification is a gas–vapor mass transfer operation where moisture content changes by diffusion and interfacial transfer, typically analyzed with psychrometrics and HTU/NTU methods rather than purely mechanical balances. Step-by-Step Solution: List operations by dominant mechanism.Mechanical: filtration (pressure/drag), agitation (impeller power), size enlargement (pressing/rolling/granulation).Mass transfer: humidification (evaporation/absorption of water into gas).Select the non-mechanical item → humidification. Verification / Alternative check: Textbook classifications place humidification in gas–vapor contacting, alongside dehumidification and drying (with mass transfer cores), not in mechanical operations. Why Other Options Are Wrong: Size enlargement / Filtration / Agitation: Classic mechanical operations driven by equipment-imparted mechanical energy and force balances. Common Pitfalls: Equating “moving equipment” with “mechanical operation.” Some mass transfer equipment also moves, but the governing mechanism is species transfer. Final Answer: Humidification (gas–vapor mass transfer)

Question 19

Plate-and-frame filter press (washing type): What is the typical ratio of washing rate to the final filtrate rate when arranged for efficient cake washing?

Accepted Answer

Introduction / Context: In washing-type plate and frame presses, once the cake reaches the terminal thickness, wash liquid is passed to displace mother liquor. The relative rates of wash and final filtrate influence washing efficiency and cycle time. Given Data / Assumptions: Washing is performed at similar pressure drop and flow paths as the final filtration step. Final filtrate rate refers to the terminal (end) filtration rate just before switching to wash. Hydraulics of channels, cloth, and cake do not change abruptly at switchover. Concept / Approach: Because the driving conditions and resistances are comparable at switchover, the practical design target is to maintain a wash rate close to the final filtrate rate. Matching rates avoids channeling and ensures efficient displacement of mother liquor without over-pressuring or under-washing the cake. Step-by-Step Solution: Consider Darcy’s law: Q ∝ ΔP / R_total.At end of filtration, R_total is at maximum; during washing, the same cake and cloth resistances dominate.With similar ΔP, the washing flow approximates the final filtrate flow → ratio ≈ 1. Verification / Alternative check: Operational guidelines for washing plate-and-frame presses recommend keeping wash flow near the terminal filtrate flow to maintain uniform displacement front and washing efficiency. Why Other Options Are Wrong: 1/2 or 1/4: Too low and prone to channeling/inefficient displacement. 4: Unrealistically high relative to the same resistance and pressure limits; risks cloth damage and bypassing. Common Pitfalls: Confusing average filtrate rate over the cycle with the terminal rate; neglecting cake compressibility effects which may require modest adjustments, not orders of magnitude changes. Final Answer: 1

Question 20

Hammer crusher fundamentals: Which statement set best characterizes hammer crushers used for primary or secondary size reduction?

Accepted Answer

Introduction / Context: Hammer crushers (or hammer mills) are widely used for brittle materials (limestone, shale, gypsum). Understanding their operating principle, feed limitations, and methods to control product size is a core mechanical operations topic. Given Data / Assumptions: Brittle feed materials, moderate hardness. Industrial machines with breaker plates/cages and adjustable settings. Typical feed size in coarse service can be several tens of centimeters. Concept / Approach: Hammers rotating at high tip speed impart impact forces that fracture particles. Product size is controlled by grate bars, cage settings, or breaker plate clearances. Feed size limits depend on rotor diameter and design but often approach ~300 mm for primary units. Step-by-Step Solution: Identify dominant breakage → impact (not compression).Recognize typical feed size capability → around 30 cm for robust designs.Note control variable → clearance to breaker/cage affects residence time and top size → adjustable reduction ratio.Therefore, all listed statements are valid. Verification / Alternative check: Manufacturer data sheets show impact breakage, adjustable grate/clearance, and feed size ranges compatible with the values cited. Why Other Options Are Wrong: Choosing any single statement ignores the others which are also correct; the comprehensive answer is that all apply. Common Pitfalls: Confusing hammer crushers with roll or jaw crushers (compression-dominant); overlooking that exact feed size depends on equipment scale. Final Answer: All of the above

Mechanical Operations Questions