Q: Conveying ultrafine powders (e.g., <75 μm): which conveyor type is generally preferred for reliable transport over distance?

Introduction / Context: Very fine powders fluidize easily and can dust or segregate on belts and in screws. Pneumatic conveying suspends particles in air, enabling controlled, enclosed transport. Concept / Approach: Pneumatic systems (dilute or dense phase) provide high enclosure, minimal spillage, and low mechanical degradation for ultrafines. Belts suffer from windage and dust; screws may compact or smear fine powders and have higher leakage/dusting at clearances. Final Answer: Pneumatic conveyor

Q: Selecting equipment to transport particles around 200-mesh size (~74 μm): which conveying method is most suitable?

Introduction / Context: At ~74 μm, particles behave like dust, requiring enclosed handling to prevent losses and environmental exposure. Concept / Approach: Pneumatic conveying excels for fines, providing sealed transport and good control of bends and elevation changes. Bucket elevators and belts are more suitable for granules; screws can handle fines but may leak dust and degrade flow consistency. Final Answer: Pneumatic conveyor

Q: Beneficiation of iron ore: among the listed choices, which method is most commonly applied at industrial scale?

Introduction / Context: Iron ore beneficiation flowsheets vary by ore type, liberation size, and impurities. Gravity, magnetic separation, and sometimes flotation are used. Concept / Approach: From the options provided, jigging and tabling are classical, widely used gravity methods for coarse hematite/goethite ores after crushing and screening. While magnetic separation is prevalent in many circuits, it is not listed among the options. Flotation is used mainly for fine slimes and specific gangue removal; flocculation is an auxiliary chemical aid, not a primary beneficiation step. Final Answer: Jigging and tabling (gravity concentration)

Question 1

Rotary drum vacuum filter (Rm ≪ Rc): the instantaneous filtrate flow rate is proportional to which viscosity term and to the available filtration segment of cycle time?

Accepted Answer

Introduction / Context: Rotary drum vacuum filters (RDVFs) operate with a rotating sectoral cycle: submergence (cake formation), drainage, drying, and discharge. When the filter medium resistance Rm is negligible compared to cake resistance Rc, the classical cake filtration model governs the flow. Given Data / Assumptions: Rm ≪ Rc, incompressible cake approximation during a short instant. Constant vacuum (approximately constant pressure drop during a sector). Filtrate viscosity μ is the dominant fluid property. Concept / Approach: Darcy’s law for cake filtration gives flux J ∝ ΔP / (μ Rc). Holding ΔP and Rc fixed in the short term, J ∝ 1/μ. Over a cycle, the total filtrate volume per revolution scales with the fraction of time the sector spends under vacuum; hence it is also proportional to the effective filtration segment of the cycle time. Step-by-Step Solution: Write J = ΔP / (μ (Rm + Rc)).With Rm ≪ Rc, J ≈ ΔP / (μ Rc) → J ∝ 1/μ.Total flow per cycle ∝ J * (time under vacuum) → proportional to the filtration time segment. Verification / Alternative check: Vendor performance curves show inverse proportionality to μ and near-linear increase with longer submergence or vacuum exposure. Why Other Options Are Wrong: μ or 1/μ^2: incorrect dependence; the law is first power inverse in μ. Common Pitfalls: Confusing filtrate volume per cycle (time dependent) with instantaneous flux; both scale with 1/μ but only the former reflects cycle fraction. Final Answer: 1/μ (and proportional to the filtration time segment)

Question 2

Identify the mill that is NOT a revolving (tumbling) mill used for grinding by cascading media.

Accepted Answer

Introduction / Context: Revolving or tumbling mills (ball, pebble, rod, tube, compartment) grind by cascading and cataracting media in a rotating cylindrical shell. Impact mills such as cage mills operate on a different principle. Given Data / Assumptions: Pebble, tube, and compartment mills are ball/pebble variants. Cage mill consists of counter-rotating cages; the shell itself does not tumble media. Concept / Approach: Distinguish media-tumbling action from high-speed impact within stationary housings. Tumbling mills rotate a cylinder partially filled with media; cage mills accelerate particles through bars for impact and shattering, not tumbling. Step-by-Step Solution: Classify each option by grinding mechanism.Identify the outlier (impact-type, not tumbling): cage mill. Final Answer: Cage mill

Question 3

Tyler (Taylor) standard screen scale: what is the ratio of the actual mesh opening (aperture) of a screen to that of the next smaller screen in the series?

Accepted Answer

Introduction / Context: The Tyler (often called Taylor) standard screen scale uses a geometric progression for sieve apertures. Recognizing the fixed ratio between successive openings helps interpolate sizes and relate mesh counts to actual openings. Given Data / Assumptions: Standard Tyler scale based on a geometric series. Successive opening ratio is constant. Concept / Approach: The aperture size in the Tyler scale decreases by a constant factor between adjacent sieves. The factor is the square root of 2 (≈1.414) for one step. Hence the opening of a given sieve is √2 times the opening of the next smaller sieve. Step-by-Step Solution: Aperture progression: a_n = a_0 / (√2)^n.Therefore, a_n / a_{n+1} = √2 ≈ 1.414. Why Other Options Are Wrong: 2.0 and 3.0: far larger than the accepted ratio; would create overly coarse steps.1.50: close, but not the standardized √2. Final Answer: √2 ≈ 1.414

Question 4

Plate-and-frame filter press hydraulics: the filtrate flow through the cake predominantly follows which flow regime?

Accepted Answer

Introduction / Context: In pressure filtration of slurries using plate-and-frame presses, flow through the porous cake is typically slow and highly resistive. Identifying the flow regime informs the correct use of Darcy’s law. Concept / Approach: Darcy’s law assumes creeping (laminar) flow through a porous medium. Filtration velocities are small and pore Reynolds numbers are well below the transition threshold, so inertial effects are negligible and turbulence does not occur inside the cake. Step-by-Step Solution: Model cake as porous medium.Apply Darcy’s law: ΔP = μ * (α M/A) * v.Conclude laminar regime dominates inside the cake. Why Other Options Are Wrong: Turbulent: pore scales and velocities are too small.Plug flow: refers to reactor axial profiles, not porous-medium microflow. Final Answer: Laminar flow

Question 5

Gas–liquid contacting: which device is used to disperse a gas into fine bubbles within a liquid for mass transfer operations?

Accepted Answer

Introduction / Context: Mass transfer operations like aeration, stripping, and oxidation require efficient dispersion of a gas into a liquid phase. Equipment selection targets small bubble size and uniform distribution. Concept / Approach: A sparger (porous plate, drilled pipe, ring, or nozzle) injects gas below the liquid surface, creating bubbles. Smaller bubbles yield higher interfacial area per volume and improve transfer rates. Kneaders and masticators are solids/paste mixers; they do not disperse gas into liquids. Final Answer: Sparger

Question 6

Cohesive versus free-flowing bulk solids: identify the cohesive material among the following common bulk solids.

Accepted Answer

Introduction / Context: Flow behavior of bulk solids dictates hopper design and conveyor selection. Cohesive materials exhibit interparticle attraction (moisture, plasticity), tending to arch, rat-hole, or smear. Concept / Approach: Wet clay has strong cohesion due to moisture and plate-like particles; it deforms plastically and tends to stick. Wheat (granular) and dry sand (rounded angular grains) are comparatively free-flowing, exhibiting low cohesion in properly conditioned moisture ranges. Final Answer: Wet clay

Question 7

Screening performance: to first order, the mass capacity of a screen is proportional to which function of the characteristic aperture size S?

Accepted Answer

Introduction / Context: Screen capacity depends on open area, aperture size, material properties, and motion. A common heuristic is proportionality to the aperture dimension for similar conditions and media. Concept / Approach: For geometrically similar screens and wire diameters scaled with aperture, the open area and passage probability scale roughly with S, leading to a near-linear relation with capacity for the same duty. Strong departures occur with pegging, near-size blinding, and moisture. Final Answer: S (linear proportionality)

Question 8

Conveying ultrafine powders (e.g., <75 μm): which conveyor type is generally preferred for reliable transport over distance?

Accepted Answer

Introduction / Context: Very fine powders fluidize easily and can dust or segregate on belts and in screws. Pneumatic conveying suspends particles in air, enabling controlled, enclosed transport. Concept / Approach: Pneumatic systems (dilute or dense phase) provide high enclosure, minimal spillage, and low mechanical degradation for ultrafines. Belts suffer from windage and dust; screws may compact or smear fine powders and have higher leakage/dusting at clearances. Final Answer: Pneumatic conveyor

Question 9

Selecting equipment to transport particles around 200-mesh size (~74 μm): which conveying method is most suitable?

Accepted Answer

Introduction / Context: At ~74 μm, particles behave like dust, requiring enclosed handling to prevent losses and environmental exposure. Concept / Approach: Pneumatic conveying excels for fines, providing sealed transport and good control of bends and elevation changes. Bucket elevators and belts are more suitable for granules; screws can handle fines but may leak dust and degrade flow consistency. Final Answer: Pneumatic conveyor

Question 10

Beneficiation of iron ore: among the listed choices, which method is most commonly applied at industrial scale?

Accepted Answer

Introduction / Context: Iron ore beneficiation flowsheets vary by ore type, liberation size, and impurities. Gravity, magnetic separation, and sometimes flotation are used. Concept / Approach: From the options provided, jigging and tabling are classical, widely used gravity methods for coarse hematite/goethite ores after crushing and screening. While magnetic separation is prevalent in many circuits, it is not listed among the options. Flotation is used mainly for fine slimes and specific gangue removal; flocculation is an auxiliary chemical aid, not a primary beneficiation step. Final Answer: Jigging and tabling (gravity concentration)

Question 11

Grinding target definition: the limiting particle size for a grinding operation corresponds to which particle in the feed/sample?

Accepted Answer

Introduction / Context: Comminution objectives are often specified as “all material below X μm”. Achieving that specification requires consideration of the coarsest particles present. Concept / Approach: The limiting size to which the entire sample must be ground is governed by the largest particle; you must supply enough energy and residence time for these coarsest pieces to reach the target size. Finer particles are already below specification and need no further breakage. Final Answer: Largest particle

Question 12

“Chance process” (dense medium/coal washing): it is industrially used for which application among the following?

Accepted Answer

Introduction / Context: The Chance process is a dense medium (suspension) separation historically used in coal preparation plants to separate coal from shale/stone based on density differences. Concept / Approach: Coal (lower density) floats in a magnetite-water (or sand-water) slurry while denser impurities sink. This improves coal quality by reducing ash and sulfur carriers. The method is distinct from ore concentration like magnetic separation for iron or flotation for sulfides. Final Answer: Cleaning of coal

Question 13

Sphericity φ for a non-spherical particle: choose the correct expression in terms of particle volume V, particle surface area S, and the diameter of a sphere with the same volume.

Accepted Answer

Introduction / Context: Sphericity is a shape factor widely used in fluid-particle systems to correct drag, settling velocity, and packed-bed correlations. It normalizes any particle against a sphere of the same volume. Concept / Approach: By definition, φ = (surface area of the volume-equivalent sphere) / (actual particle surface area). For a sphere of diameter D_eq having the same volume V as the particle, D_eq = (6V/π)^(1/3). The sphere’s surface area is A_sph = π D_eq^2. Therefore φ = A_sph / S = π D_eq^2 / S. Substituting for D_eq yields φ = π * [(6V/π)^(2/3)] / S = (π^(1/3) * (6V)^(2/3)) / S. Step-by-Step Solution: Compute D_eq from V: D_eq = (6V/π)^(1/3).Compute sphere area: A_sph = π D_eq^2.Form ratio: φ = A_sph / S. Why Other Options Are Wrong: S / (π D_eq^2): this is the reciprocal (shape factor >= 1).V / S: wrong dimensions; not bounded by 1.(6V/π) / S: incorrect exponent on V; ignores square power for area. Common Pitfalls: Confusing φ with its reciprocal (often termed shape factor). Remember φ ≤ 1 and equals 1 only for a sphere. Final Answer: φ = (surface area of equal-volume sphere) / S = π · D_eq^2 / S, where D_eq = (6V/π)^(1/3)

Question 14

For soft, friable, and crystalline materials such as ice or gypsum, which crusher type is most suitable to achieve size reduction with minimal fines?

Accepted Answer

Introduction / Context: Material properties govern crusher choice. Soft, friable, and moderately moist materials like gypsum and ice are best handled with shearing/tearing actions rather than high compressive forces that create excessive fines. Concept / Approach: Toothed roll crushers grip and shear material using intermeshing teeth, delivering controlled top size with relatively low fines production for soft minerals. Jaw and gyratory crushers apply strong compression, which is ideal for hard, abrasive rocks but tends to over-crush soft materials. Final Answer: Toothed roll crusher

Question 15

Terminology: the reciprocal of sphericity (i.e., actual particle surface area divided by surface area of the equal-volume sphere) is commonly called the ________.

Accepted Answer

Introduction / Context: Shape descriptors appear in correlations for drag, pressure drop, and heat/mass transfer. Two complementary terms are sphericity (≤1) and its reciprocal (≥1). Concept / Approach: Shape factor is often defined as actual particle surface area divided by the surface area of a sphere having the same volume, i.e., the reciprocal of sphericity. This usage distinguishes it from other “specific surface” or “Sauter diameter” terms, which relate size and area but not shape relative to a sphere. Final Answer: Shape factor

Question 16

Traditional stamp mills historically found widest use in crushing which type of ore?

Accepted Answer

Introduction / Context: Stamp mills are gravity-driven impact crushers that repeatedly drop heavy stamps onto ore. They were iconic in early mining. Concept / Approach: Historically, stamp mills were widely used in gold mining districts to crush auriferous quartz, liberating gold for amalgamation or later cyanidation. They were less common for iron ore (which is harder and processed differently) and not suited to very soft minerals like talc or gemstones like diamond. Final Answer: Gold ores

Question 17

Pan mixer operation: which mixing mechanism best describes the action in a pan (muller) mixer used for foundry sand and similar materials?

Accepted Answer

Introduction / Context: Pan (muller) mixers are used to prepare cohesive mixes like foundry molding sand by combining sand, clay binders, and water to achieve uniform plasticity. Concept / Approach: Mulling involves rolling, smearing, and compressive shearing under heavy wheels and scrapers, thoroughly coating particles with binder. This differs from simple kneading (typical of dough mixers) and from high-shear dispersion used for liquids or slurries. Final Answer: Mulling

Question 18

Screening statements: choose the single incorrect statement after normalization of facts.

Accepted Answer

Introduction / Context: Screen terminology often causes confusion. Standard laboratory sieves (ASTM/ISO) use woven wire cloth with square apertures and specify mesh as openings per linear inch. Given Data / Assumptions (Repaired): Mesh refers to count per linear inch, not per cm. Standard woven wire test sieves have square openings. Impact crushers (hammer mills) break by impact. Why the Correct Option Is Wrong: Statement “Standard test screens are manufactured with circular openings” is incorrect; standard test sieves use square openings produced by orthogonal wire warp and weft. Circular perforated plates exist but are not the standard for test sieving nomenclature. Why Other Options Are Right: Hammer crushers: impact is the principal mechanism.Mesh number vs opening: as mesh count increases, aperture decreases.200-mesh: indeed 200 openings per linear inch. Common Pitfalls: Confusing “mesh per cm” with the standard US “per inch”, and assuming all industrial screens are identical to laboratory test sieves. Final Answer: Standard test screens are manufactured with circular openings.

Question 19

Constant-pressure cake filtration behavior: how does the filtrate flow rate change with time during a run, assuming increasing cake thickness?

Accepted Answer

Introduction / Context: In constant-pressure filtration of a cake-forming slurry, the pressure drop is held constant while cake thickness grows. This increases resistance over time. Concept / Approach: Darcy’s law: filtrate flux J = ΔP / (μ (Rm + Rc)). As the cake builds, Rc increases with time, so J decreases. Thus the instantaneous flow rate declines monotonically during the run. Step-by-Step Solution: Hold ΔP constant.Rc(t) ↑ as cake thickens.Therefore J(t) ∝ 1/(Rm + Rc(t)) ↓ with time. Common Pitfalls: Confusing initial surge (wetting/priming) with sustained behavior; after the initial transient, the trend is decreasing due to added resistance. Final Answer: It continuously decreases.

Question 20

In industrial filtration operations, the flowing filtrate must overcome multiple resistances. Which of the following resistances are encountered during normal cake filtration on a porous medium?

Accepted Answer

Introduction / Context: Industrial liquid–solid separation by cake filtration is governed by the hydraulic resistances that oppose flow. Understanding where these pressure losses occur helps engineers diagnose slow filtration, choose filter aids or precoats, and size equipment correctly. Given Data / Assumptions: A porous septum (cloth, screen, leaf) supports the cake. A cake builds on the medium as filtration proceeds. Piping/porting delivers slurry to the filter and removes filtrate. Concept / Approach: The total pressure drop (ΔP_total) equals the sum of the pressure drops across the cake (ΔP_cake), the clean or partially blinded medium (ΔP_medium), and ancillary hydraulic losses in manifolds, channels, and nozzles (ΔP_channel). Engineers often model cake and medium using Darcy’s law, then add estimated minor losses. Step-by-Step Solution: Recognize contributions: cake resistance, medium resistance, and channel losses.State relation: ΔP_total = ΔP_cake + ΔP_medium + ΔP_channel.Therefore, all three listed resistances are encountered. Verification / Alternative check: Plotting reciprocal filtration rate versus filtrate volume usually shows an intercept (medium + channel resistance at zero cake) and a slope term (cake resistance growth), confirming multiple contributions. Why Other Options Are Wrong: Filter medium only: ignores the dominant growing cake layer.Cake only: neglects initial resistance and hydraulic losses.Channels only: these are typically smaller but non-zero contributors. Common Pitfalls: Underestimating channel losses in small lab filters, and overfocusing on cake while a blinded cloth or plugged outlet governs flow. Final Answer: all (a), (b) and (c)

Mechanical Operations Questions