Question 1

Cake washing in filtration — behavior of resistances: During the washing step of a formed filter cake, how do the hydraulic resistances generally behave as washing proceeds under constant conditions?

Accepted Answer

Introduction / Context:After cake formation in filtration, a washing step is often applied to displace mother liquor and soluble impurities. Engineers must understand how hydraulic resistance evolves, because it governs wash time, pressure drop, and pump energy. Although detailed behavior depends on cake compressibility and wash chemistry, a common trend is that resistance does not fall; instead, it tends to increase or at best remain steady as washing proceeds.Given Data / Assumptions:Cake has already been formed on the medium.Washing is performed at roughly constant pressure difference and steady temperature.No cake removal between wash passes, and no drastic dissolution of the solid matrix.Concept / Approach:Total resistance is the sum of medium resistance and cake resistance. As washing continues, the cake structure may compact due to continued hydraulic loading, reducing porosity and increasing specific resistance. Fines migration can also block pores near the medium. While displaced liquor composition improves, the hydraulic pathway rarely becomes easier. Therefore, the most common textbook expectation is an increase in overall resistance during washing, particularly for compressible cakes.Step-by-Step Solution:Recognise components: R_total = R_medium + R_cake.During wash, mechanical consolidation and fines relocation occur.Infer trend: R_cake typically rises; select “Increase.”Verification / Alternative check:Pilot tests of compressible cakes (e.g., precipitates, biological sludges) show rising pressure drop with wash throughput, requiring longer times or higher driving force to achieve target wash ratios.Why Other Options Are Wrong:Decrease/constant: possible only with unusual cake dissolution or rigid incompressible cakes; not the general rule.Oscillation: lacks a physical basis under steady conditions.“None of these”: unnecessary; “Increase” matches practice.Common Pitfalls:Assuming improved liquor purity implies lower resistance; purity rises while permeability can fall.Final Answer:Increase

Question 2

Colloid stability — preventing flocculation: To prevent flocculation (agglomeration of fine particles into flocs), which dispersing agents are most commonly used in aqueous suspensions?

Accepted Answer

Introduction / Context:In mineral processing, ceramics, and paint formulations, fines tend to agglomerate due to van der Waals forces or charge neutralisation. Dispersants (deflocculants) keep particles apart by enhancing electrostatic repulsion or steric hindrance, thereby stabilising suspensions and improving downstream steps like classification, filtration, or casting. Identifying typical chemical families used as dispersants is essential for troubleshooting slurry behavior.Given Data / Assumptions:Aqueous system of inorganic solids.Common, low-cost industrial additives are intended.Concept / Approach:Alkali silicates (e.g., sodium silicate) and condensed phosphates (e.g., sodium hexametaphosphate, sodium tripolyphosphate) are classic deflocculants. They adsorb on particle surfaces, increase negative surface charge, and raise zeta potential, producing electrostatic repulsion. They also can complex cations that otherwise compress the electrical double layer. Carbonates/bicarbonates are weak pH buffers rather than strong dispersants, while sulphates/chlorides often screen charges and promote coagulation rather than dispersion.Step-by-Step Solution:Recognise the goal: increase interparticle repulsion.Identify families that adsorb and raise zeta potential: silicates and phosphates.Select “Silicates and phosphates.”Verification / Alternative check:Ceramic slip preparation and ore pulping practices routinely specify sodium silicate or sodium hexametaphosphate dosages to minimise viscosity rise from flocculation.Why Other Options Are Wrong:Carbonates/bicarbonates: mild pH modifiers; limited dispersing power.Sulphates/chlorides: electrolytes that can compress the double layer and induce flocculation.Common Pitfalls:Overdosing dispersants can reverse benefits by salting-out or altering ionic strength; optimisation by jar testing is recommended.Final Answer:Silicates and phosphates

Question 3

Ultrafine grinding thermals: As ultrafine grinding proceeds in high-energy mills, how does the product temperature typically change?

Accepted Answer

Introduction / Context:Producing ultrafine powders requires substantial specific energy input. Most mills convert only a fraction of input power into creating new surface area; the remainder is dissipated as heat via friction and inelastic impacts. Understanding the thermal consequences is crucial for heat-sensitive products (polymers, pharmaceuticals, organics) where softening or degradation can occur during milling.Given Data / Assumptions:Dry milling under standard plant conditions.No cryogenic assistance or external cooling coils considered unless specified.Concept / Approach:As particle size falls, energy required per unit mass rises sharply (Rittinger/Bond regimes). The inefficiency of breakage converts most power to heat within the mill charge and shell. Consequently, the product temperature typically rises above ambient, sometimes significantly. Engineers mitigate this by using intermittent milling, cooling jackets, nitrogen purges, or cryogenic milling when necessary. A temperature decrease during routine ultrafine grinding is atypical without deliberate cooling measures.Step-by-Step Solution:Relate energy input to heat generation in the charge.Note poor conversion efficiency from power to new surface.Conclude product temperature generally increases.Verification / Alternative check:Operational logs from jet mills, pin mills, and stirred media mills commonly record outlet or product temperatures elevated above feed and ambient, necessitating cooling strategies for heat-sensitive feeds.Why Other Options Are Wrong:Decreases/constant: would require strong external cooling or cryogenic processes.“Depends on the material only”: material matters, but heat rise is a generic outcome of energy dissipation.Adiabatic expansion cooling: not the dominant phenomenon in mechanical milling.Common Pitfalls:Ignoring softening points; once softened, materials smear and agglomerate, slowing comminution and raising heat further.Final Answer:Increases

Question 4

Impact grinding equipment: Which mills are commonly referred to as “impactors” in size reduction practice?

Accepted Answer

Introduction / Context:Size-reduction mechanisms include compression, impact, attrition, and cutting. Equipment is often grouped by its dominant breakage mode. “Impactors” rely primarily on high-velocity impacts between particles and moving elements or breaker plates to shatter the feed. Correctly identifying impactors aids in selecting machines for brittle materials and in predicting product top size and fines content.Given Data / Assumptions:Standard industrial definitions are assumed.Multiple answers could apply; select the option that captures the commonly accepted set.Concept / Approach:Hammer mills use rapidly rotating hammers to impart impact energy to particles, which then collide with breaker plates/screens. Cage mills employ counter-rotating cages to throw particles at high speed for multiple impacts. Both are classic impactors. Rolling-compression devices (smooth/ toothed rolls) rely on nipping and compressive crushing rather than impact and therefore are not classed as impactors.Step-by-Step Solution:List machines dominated by impact: hammer and cage mills.Exclude compression-dominated machines: roll crushers.Pick the combined option covering both impactor types.Verification / Alternative check:Equipment catalogs and unit-ops texts group hammer and cage mills together under impact mills, distinct from compression and attrition devices.Why Other Options Are Wrong:Choosing only one (hammer or cage) is incomplete.Rolling-compression: not an impactor.“None”: incorrect given the above.Common Pitfalls:Confusing toothed rolls (which do impart some local impact) with true impactor action; the dominant mechanism remains compression/cleaving in rolls.Final Answer:Both hammer and cage mills

Question 5

Screen standards and mesh numbering: The rule “higher mesh number → smaller aperture” applies to which screen standards?

Accepted Answer

Introduction / Context:“Mesh” denotes the number of openings per linear inch in a screen. Across common standards, a larger mesh number indicates more openings per inch and therefore smaller apertures. While the exact aperture for a given mesh can vary slightly among standards (due to different wire diameters and series), the inverse relationship between mesh number and opening size remains consistent.Given Data / Assumptions:Comparison among British, German (DIN), and American (ASTM/Tyler) standards.General trend, not the exact numeric aperture values, is under discussion.Concept / Approach:With more openings counted per inch, each opening must be smaller to fit within the same linear measure. Therefore, a 200-mesh screen has much smaller openings than a 20-mesh screen regardless of standard. Differences among standards affect the precise mapping of mesh number to aperture size (and whether the series is based on rational or square-root-of-two progressions), but not the qualitative trend.Step-by-Step Solution:Define mesh: openings per inch.Infer inverse relation between count and opening size.Recognise that all listed standards follow this rule.Verification / Alternative check:Published tables for ASTM E11, Tyler equivalent, BS, and DIN show decreasing opening sizes as the mesh count increases.Why Other Options Are Wrong:Selecting only one standard ignores that the relationship is universal across the listed systems.“None”: contradicts basic definition.Common Pitfalls:Confusing “mesh” with “micron grade”; always consult the specific standard for exact conversion, especially when wire diameter matters.Final Answer:All of the above standards

Question 6

Characterising ultrafine particles: For ultrafine powders, which measure best expresses their size in a way that relates to process behavior?

Accepted Answer

Introduction / Context:Ultrafine powders exhibit behavior (reactivity, dissolution rate, rheology) that correlates more with total surface area than with a single length dimension. Traditional sieve analysis fails below about 38 µm, so alternative metrics become useful. Specific surface area is therefore the preferred descriptor for very fine powders in catalysis, pharmaceuticals, and ceramics.Given Data / Assumptions:Ultrafine range where sieving is impractical.Surface-driven phenomena are of interest (e.g., reaction or sintering rates).Concept / Approach:While micrometre-scale sizing (laser diffraction, DLS) provides number- or volume-based distributions, these still reduce complex polydispersity to a few moments. Specific surface area (e.g., via BET nitrogen adsorption) captures the cumulative surface of all particles, directly impacting adsorption, catalytic activity, and cohesive forces. Thus, for ultrafines, reporting m^2/g is often more informative than a nominal “size.”Step-by-Step Solution:Note sieving is not suitable for ultrafines → mesh size not applicable.Connect process behavior to surface-controlled kinetics.Select specific surface area as the best expression.Verification / Alternative check:Materials data sheets for fumed silica, nano-oxides, and micronised APIs prominently list BET surface area instead of sieve size.Why Other Options Are Wrong:Centimetre/micron alone: single length scales miss surface-driven effects.Screen size: not measurable for ultrafines.Particle count: difficult to determine accurately and not directly linked to surface phenomena.Common Pitfalls:Comparing powders only by “average size” can be misleading; different distributions can share the same mean yet have very different surface areas.Final Answer:Specific surface area (surface area per unit mass)

Question 7

Secondary crushing of hard, tough stone: Which machine is most commonly selected as a secondary crusher for hard and tough rock?

Accepted Answer

Introduction / Context:Crushing circuits are staged: primary crushers accept run-of-mine rock, while secondary units reduce product to sizes suitable for tertiary crushing or milling. Matching crusher type to material hardness and abrasiveness is crucial for capacity, product shape, and liner wear economics.Given Data / Assumptions:Material: hard and tough stone (e.g., granite, basalt).Duty: secondary stage after primary reduction.Concept / Approach:Jaw crushers serve as robust primaries for hard rock. For secondary duty on hard, abrasive material, cone crushers (gyratory derivatives) provide high reduction with good cubicity and handle abrasive wear better than many impactors. Impact crushers excel on softer, less abrasive rock where shattering dominates. Toothed rolls are suited to friable materials and sized coal, not hard stone.Step-by-Step Solution:Identify stage: secondary.Match hardness to crusher type: cones favor hard, abrasive rock.Select “Cone crusher.”Verification / Alternative check:Typical quarry flowsheets: primary jaw → secondary cone → tertiary cone/VSIs for shape, confirming the widespread use of cones for tough stone.Why Other Options Are Wrong:Jaw crusher: primarily a primary crusher in hard-rock service.Impact crusher: wear-heavy on hard, abrasive feeds.Toothed roll/hammer: not preferred for very hard, tough rock.Common Pitfalls:Selecting impactors for abrasive rock leads to excessive blow-bar wear and downtime.Final Answer:Cone crusher

Question 8

Impeller placement in tall agitated tanks: When multiple impellers are used on one shaft in a tall tank, what should be the clearance between the tank bottom and the lowest impeller? (D = impeller diameter)

Accepted Answer

Introduction / Context:In mixing design, axial spacing and clearances strongly affect circulation loops, dead zones, and power draw. For tall tanks requiring multiple impellers, proper bottom clearance ensures good sweeping of the floor region without excessive shear against the wall or risk of solids deposition (in slurries).Given Data / Assumptions:Cylindrical tank with typical baffle configuration.Multiple impellers mounted vertically on one shaft.Impeller type is standard (e.g., 45° pitched blade or Rushton), not specialty close-clearance types.Concept / Approach:Rules of thumb: bottom impeller clearance ≈ 0.5 D provides adequate floor sweeping and promotes a lower circulation loop. Larger clearances risk stagnant bottom regions and solids settling; much smaller clearances increase hydraulic losses and mechanical risk. Vertical spacing between successive impellers is often 1.0–1.5 D depending on flow patterns sought (axial vs radial).Step-by-Step Solution:Identify design heuristic: C_bottom ≈ 0.5 D.Eliminate larger spacings that under-sweep the floor.Select “0.5 D.”Verification / Alternative check:Mixing handbooks specify 0.3–0.6 D as workable; 0.5 D is the most-quoted nominal clearance for general service.Why Other Options Are Wrong:≥ 1.0 D: too high; can leave a dead zone below the impeller.0.25 D: overly close, risking mechanical issues and inefficient circulation.Common Pitfalls:Not adjusting clearance for bottom dish geometry; dished or conical bottoms may warrant modest adjustments.Final Answer:0.5 D

Question 9

Mixers taxonomy — resemblance to ball mills: Which mixer most closely resembles a ball mill without the grinding media (balls)?

Accepted Answer

Introduction / Context:Tumbling mixers and ball mills share a cylindrical shell that rotates about its axis. In a ball mill, grinding media fill a fraction of the volume to effect comminution; in a tumbling mixer, the shell is partially filled with solids (or solids plus small liquid additions) and rotated to promote intermixing without intentional grinding media. Recognising these geometric and kinematic similarities helps in understanding mixing limits and scale-up correlations.Given Data / Assumptions:Cylindrical, rotating vessel considered.No grinding media present in the mixer.Concept / Approach:Tumbling mixers (a.k.a. drum mixers) rely on cascading of particles as the vessel rotates below critical speed. Banbury (internal) mixers are intensive shear kneaders for polymers; pug mills comprise twin mulling paddles; pan mixers use rotating paddles in a stationary pan; sigma-blade kneaders deliver high-viscosity shear. Only the tumbling mixer mirrors the rotating cylinder of a ball mill minus the balls.Step-by-Step Solution:Compare geometries and motion to a ball mill.Identify the device with a rotating cylindrical shell only.Select “Tumbling mixer.”Verification / Alternative check:Photographs and P&IDs show close physical resemblance between laboratory drum mixers and small ball mills sans media.Why Other Options Are Wrong:Banbury/pug/pan/sigma-blade: different geometries and shear-dominated mechanisms.Common Pitfalls:Confusing “tumbling” with “planetary” mixers; planetary mixers have rotating tools and revolution motion, not a rotating vessel shell.Final Answer:Tumbling mixer

Question 10

Nutsch (tank) filters — typical usage: A Nutsch (tank) filter is best described as which of the following in industrial filtration practice?

Accepted Answer

Introduction / Context:Nutsch (tank) filters are widely used in fine chemicals and pharmaceuticals where contained, batch solid–liquid separation is required. They consist of a perforated plate supporting a filter medium inside a tank, with options for vacuum or pressure assist and features like heel removal and cake washing.Given Data / Assumptions:Focus is on operational mode (batch vs continuous) and typical scale of use.Generic Nutsch configuration (not agitated Nutsch dryer) is intended.Concept / Approach:Classic Nutsch filters operate in batch mode: charge slurry, drain/pressurise or apply vacuum, optionally wash the cake, then discharge. They are chosen for contained handling, product purity, and flexibility at small to moderate batch sizes—not for continuous, high-throughput service. Leaf filters and rotary drums/discs serve continuous duties, while high-pressure plate-and-frame or candle filters are different classes altogether.Step-by-Step Solution:Identify Nutsch as a tank-type batch unit.Recognise flexibility for washing and contained operation.Select the description matching batch small/medium-scale usage.Verification / Alternative check:Equipment brochures describe Nutsch filters as batch vessels with options for pressure or vacuum, CIP, and GMP finishes—ideal for campaign production.Why Other Options Are Wrong:Continuous high-pressure/rotary vacuum: different equipment classes.Leaf filter: a separate manifold type.“Only for > 60% solids”: incorrect; workable over a range of slurry solids.Common Pitfalls:Assuming “tank filter” implies gravity only; many operate with vacuum/pressure assist.Final Answer:A batch filter commonly used for small to moderate scale work

Question 11

Primary function of cyclones: Industrial cyclones are used primarily for the separation of which phases?

Accepted Answer

Introduction / Context:Hydrocyclones and gas cyclones exploit centrifugal fields to effect density-based separation. Recognising what phases they best separate is foundational for selecting them in dust collection, product recovery, dewatering, and classification circuits.Given Data / Assumptions:“Cyclone” includes gas cyclones (for dust) and hydrocyclones (for slurries).Operation involves swirling flow producing radial acceleration.Concept / Approach:In both gas and liquid service, cyclones separate dispersed solid particles from a continuous fluid phase by imparting centripetal acceleration, forcing denser solids to migrate outward for collection while clean fluid exits centrally. They are not commonly used to separate liquid–liquid pairs (though specialty designs exist), nor to sort gas species of nearly equal density. Solid–solid separation is indirect—via classification in a suspending fluid—not by directly processing two solid streams.Step-by-Step Solution:Identify continuous phase: gas or liquid.Recognise target phase: dispersed solids.Select “Solids from fluids.”Verification / Alternative check:Plant P&IDs show gas cyclones upstream of baghouses and hydrocyclones in grinding circuits to classify solids from slurry—both aligning with solids-from-fluids duty.Why Other Options Are Wrong:“Solids” alone is incomplete.Liquids only/gases from gases: not typical cyclone duty.Solids from solids: requires a fluidising medium; the cyclone acts on a slurry or gas-solid stream, not two solid feeds.Common Pitfalls:Expecting submicron capture with gas cyclones; their efficiency drops for very fine particles without preconditioning or multicyclones.Final Answer:Solids from fluids (gas or liquid)

Question 12

Fertiliser mixing operation: In ammonium nitrate fertiliser production, molten ammonium nitrate is mixed with ground limestone (or dolomite) using which mixer?

Accepted Answer

Introduction / Context:Neutralising or conditioning molten ammonium nitrate with finely ground mineral additives produces fertiliser grades with improved handling and reduced caking. The operation demands robust mixing of a paste-like mass at moderate temperatures and high throughput, making selection of the mixer critical for product quality and safety.Given Data / Assumptions:Molten ammonium nitrate is blended with ground limestone.Continuous, intensive mixing of a viscous/pasty mixture is needed.Concept / Approach:Pug mills feature twin contra-rotating shafts with paddles that fold and knead the mass while conveying it forward, ideal for sticky or pasty mixtures such as fertiliser conditioning, clay tempering, or moist agglomerates. Banbury mixers are batch kneaders for polymers; muller mixers (pan with heavy wheels) are used in foundry sand preparation; mixer-extruders suit some plastics but are less common for fertilisers in this specific service.Step-by-Step Solution:Identify rheology: pasty/viscous blend.Match to equipment providing continuous kneading and transport.Select “Pug mill.”Verification / Alternative check:Fertiliser process descriptions routinely show pug mills for conditioning ammonium nitrate with fillers/limestone before prilling or granulation.Why Other Options Are Wrong:Banbury/planetary: batch, high-shear lab or polymer service.Muller: suited to foundry sands; different mechanics.Mixer-extruder: not the standard for this fertiliser step.Common Pitfalls:Insufficient mixing time or poor residence control in the pug mill can lead to segregation or hot spots; residence time distribution tuning is essential.Final Answer:Pug mill

Question 13

Ball charge level (static): When a ball mill is stopped, approximately what percentage of the mill volume is occupied by the grinding media (balls)?

Accepted Answer

Introduction / Context:Ball charge level influences power draw, grinding efficiency, and liner wear. In most conventional mills, the ball load is set to balance cataracting/cascading motions while leaving sufficient voidage for slurry or air flow. Knowing the typical static fill helps sanity-check data sheets and commissioning reports.Given Data / Assumptions:Conventional tumbling ball mill (not SAG/AG).Static (mill stopped) volumetric occupancy referenced.Concept / Approach:Common ball charge levels range from about 30% to 40% of the mill volume for secondary/tertiary grinding duties. Higher values can lead to power inefficiency and poor toe trajectory; lower values reduce throughput. Hence, a widely quoted nominal value is 35% of the mill volume when stationary (dynamic shoulder appears lower due to motion during operation).Step-by-Step Solution:Recall standard ball charges: ~30–40% v/v.Select the mid-range nominal value: 35%.Confirm that much larger fills (70–85%) are unrealistic for grinding performance.Verification / Alternative check:OEM recommendations and plant audits commonly report 33–36% for closed-circuit cement and mineral grinding mills.Why Other Options Are Wrong:50–85%: excessive; leaves inadequate voidage and hampers media motion.15%: too low for efficient throughput.Common Pitfalls:Confusing volumetric ball charge at rest with “filling degree” that may include slurry holdup; ensure consistent definitions.Final Answer:35%

Question 14

Reciprocating screens — suitability limits: Reciprocating screens (gyratory at feed end, reciprocating at discharge) are generally NOT suitable for screening which material/service?

Accepted Answer

Introduction / Context:Screen types differ in motion, stroke, and robustness. Reciprocating/gyratory screens provide gentle, accurate sizing with low vertical acceleration—excellent for fragile or light materials. For heavy, abrasive rock at large tonnage, more rugged vibrating or inclined screens are preferred to withstand impact and high throughput.Given Data / Assumptions:Reciprocating screens combine gentle gyratory feed action and reciprocating discharge motion.Material choices span light powders to heavy rock.Concept / Approach:The low-intensity motion of reciprocating/gyratory screens promotes stratification and precise cuts with minimal degradation but lacks the dynamic capacity to process very heavy, coarse rock at high rates. Vibrating screens (linear or circular) give higher accelerations and capacities, making them standard in aggregates and mining for large tonnage rock screening.Step-by-Step Solution:Match screen motion to material duty.Eliminate light/fragile materials, which suit reciprocating screens.Identify heavy rocks/gravel at high tonnage as unsuitable.Verification / Alternative check:Aggregate plant flowsheets almost exclusively use heavy-duty vibrating screens for primary/secondary scalping and sizing, not reciprocating types.Why Other Options Are Wrong:Light powders, chemicals, foods, pellets: commonly processed on gyratory/reciprocating screens.Common Pitfalls:Attempting to scale reciprocating screens into high-impact services leads to rapid wear and blinding.Final Answer:Heavy tonnages of rocks or gravel

Question 15

Particle size analysis — pick the wrong statement: Identify the incorrect statement regarding surface-area estimation, crusher capacity under choke feed, and mill charge motion terminology.

Accepted Answer

Introduction / Context:Size analysis and comminution terminology can be confusing. Two common data presentations are cumulative and differential size distributions, each with strengths and limitations. Separately, choke feeding and mill charge motion concepts are frequent exam topics. This question asks you to spot the one incorrect or misleading statement among several commonly cited facts.Given Data / Assumptions:Cumulative and differential analyses refer to the same underlying sieve or laser data.Crusher is operated in choke feed (chamber filled to ensure inter-particle crushing).Standard tumbling-mill motion terms apply.Concept / Approach:Differential analysis reports the mass in each size interval and is the standard basis for surface-area estimation, but it requires assuming a representative size within each interval (often the geometric mean). Cumulative analysis sums undersize and is excellent for visualising cut points, but deriving surface from a cumulative curve still implies an assumed size distribution within bins; it does not “avoid” the representative-size assumption. Thus, claiming cumulative analysis is preferred because it avoids that assumption is incorrect. The Gates–Gaudin–Schuhmann (GGS) cumulative plot against 1/d permits area-based surface estimates, choke feeding generally raises capacity (and fines) for suitable crushers, and “cascading”/“cataracting” definitions are standard.Step-by-Step Solution:Evaluate each statement against accepted practice.Note that surface estimation from any binned data implies a representative size per bin.Conclude (a) is the incorrect justification.Verification / Alternative check:Texts derive specific surface from differential distributions by summing over size classes using class midpoints; cumulative plots are a reexpression and do not eliminate that need.Why Other Options Are Wrong:(b): GGS plot relation to surface is standard.(c): Choke feeding can increase throughput for certain crusher types.(d): Motion terms are correctly defined.Common Pitfalls:Assuming a change of plotting style (cumulative vs differential) changes the underlying assumptions; it does not.Final Answer:Cumulative analysis is preferred over differential for surface area estimation because it avoids assuming “all particles in a size fraction are equal”, which differential analysis requires.

Question 16

Energy–fineness relationship: As the target product becomes finer in grinding, how does the specific energy requirement generally change?

Accepted Answer

Introduction / Context:Grinding energy is a dominant operating cost in mineral processing and cement. All classical comminution laws predict higher energy demand as product size decreases, with the severity depending on the theory and the fineness regime. Recognising the monotonic increase is crucial for realistic feasibility studies and energy budgeting.Given Data / Assumptions:Normal brittle materials; dry or wet grinding.Comparable feed size; only product fineness changes.Concept / Approach:Rittinger’s law (E ∝ new surface) dominates at fine sizes and grows rapidly as size decreases. Bond’s law (E ∝ 1/√P − 1/√F) applies widely to ball milling and also increases as P gets smaller. Even Kick’s law (log ratio) rises with greater overall reduction. Hence, finer targets require more energy per ton than coarser ones, often nonlinearly so.Step-by-Step Solution:Hold feed size constant; decrease product size.Apply any comminution law; E increases with fineness.Select “Increases.”Verification / Alternative check:Plant data show specific energy climbing steeply as Blaine fineness (cement) or P80 (minerals) is pushed lower.Why Other Options Are Wrong:Decrease/same/negligible: contradict empirical laws and experience.Fixed multiplier (1.5×): energy rise depends on the actual fineness, not a constant factor.Common Pitfalls:Underestimating the energy penalty when tightening product specs; consider circuit upgrades (HPGR, classification) to manage energy.Final Answer:Increases

Question 17

Principle of jigging: Ore concentration by jigging primarily exploits differences in which particle property?

Accepted Answer

Introduction / Context:Jigging is a gravity separation technique in which a pulsating fluid (often water) stratifies particles based on density. Heavier particles migrate downward and concentrate, while lighter gangue rises. Understanding the property that drives separation allows engineers to evaluate whether jigging is appropriate for a given ore.Given Data / Assumptions:Mixed feed of valuable mineral and gangue with different densities.Pulsating fluid flow provided by the jig action.Concept / Approach:Under alternating acceleration and deceleration, particles experience differential settling velocities (per Stokes/allen regimes), which depend strongly on density and size. With suitable sizing (narrow size range), density differences dominate, enabling effective separation. Wettability differences are exploited in flotation, not jigging; magnetic/electrostatic properties are for specialized separators; shape effects are secondary and controlled by screening before jigging.Step-by-Step Solution:Identify jigging as a gravity method.Focus on density contrast between species.Select “Specific gravity (density).”Verification / Alternative check:Flowsheets for iron ore and coal beneficiation use jigs where density contrasts are sufficiently large, confirming the principle.Why Other Options Are Wrong:Wettability: flotation domain.Shape: managed via screening; not the primary mechanism.Magnetic/electrostatic: used in respective specialty separators.Common Pitfalls:Feeding wide size distributions reduces jig efficiency; size classification upstream is important.Final Answer:Specific gravity (density)

Question 18

Definition of crusher reduction ratio: In crusher terminology, the reduction ratio is best defined as which of the following?

Accepted Answer

Introduction / Context:“Reduction ratio” provides a compact descriptor of how much a crusher reduces the size of the feed. It supports quick equipment comparisons and preliminary sizing. While exact definitions can use characteristic sizes (e.g., 80% passing F80/P80), the qualitative meaning remains the ratio of typical feed size to typical product size.Given Data / Assumptions:Single crusher stage under steady operation.Characteristic sizes represent opening or 80% passing sizes.Concept / Approach:Reduction ratio R is commonly expressed as R = F/P, with F a characteristic feed dimension and P the corresponding product dimension. Primary crushers often have ratios around 3–8; secondary/tertiary units can be higher. The ratio is not a universal constant and does not by itself set absolute feed/product sizes; rather, it scales them.Step-by-Step Solution:State definition: R = characteristic feed size / characteristic product size.Map “feed opening to discharge opening” to that definition.Choose the option reflecting this ratio directly.Verification / Alternative check:Equipment data sheets and design examples compute reduction ratio using 80% passing sizes or nominal openings, consistent with option (a).Why Other Options Are Wrong:(b) Inverts the definition.(c) Mischaracterises R as a constant; R varies by machine and duty.(d) Contradicts the definition tied to feed/product sizes.(e) Invents an unrelated index.Common Pitfalls:Mixing “openings” with “P80/F80” values; be consistent about which characteristic sizes are used.Final Answer:Ratio of feed opening (or feed size) to discharge opening (or product size)

Question 19

Comminution laws — identify Rittinger’s law: Which expression represents Rittinger’s crushing (grinding) law for specific energy in terms of characteristic feed and product sizes?

Accepted Answer

Introduction / Context:Three classical energy–size relations guide comminution analysis: Kick’s, Bond’s, and Rittinger’s laws. Each associates specific energy with a different function of the feed and product sizes and applies best in a particular size range. Rittinger’s law emphasises surface creation and is most applicable at fine sizes where new surface area dominates the energy requirement.Given Data / Assumptions:P/m is specific power (energy per mass rate).Df and Dp denote characteristic feed and product sizes, respectively.Concept / Approach:Rittinger’s law states that specific energy is proportional to new surface area produced, which for similar particle shapes scales with (1/Dp − 1/Df). Kick’s law relates energy to the natural logarithm of the size ratio ln(Df/Dp), suitable for coarse crushing. Bond’s law uses the inverse square-root term (1/√Dp − 1/√Df), widely applied in grinding mill design. Therefore, the correct expression for Rittinger is P/m = K * (1/Dp − 1/Df).Step-by-Step Solution:Recall surface-based dependence → inverse of size.Match to expression with 1/D terms.Select the option with (1/Dp − 1/Df).Verification / Alternative check:Textbook derivations equate energy to surface created with proportionality K, yielding the 1/D form; Bond’s and Kick’s distinct forms help cross-check.Why Other Options Are Wrong:ln(Df/Dp): Kick’s law (coarse range).(1/√Dp − 1/√Df): Bond’s law (intermediate range).Independence from size ratio: contradicts all three laws.Common Pitfalls:Forgetting which exponent belongs to which law; use the mnemonic Rittinger (1/D), Bond (1/√D), Kick (ln D).Final Answer:P/m = K * (1/Dp − 1/Df)

Question 20

In particle-size reduction, what is the general dominant mechanism in intermediate and fine grinders used in chemical and mineral processing (consider mills such as ball, hammer, and pin mills operating beyond coarse crushing)?

Accepted Answer

Introduction / Context:Industrial comminution equipment for intermediate and fine grinding—such as ball mills, hammer mills, and pin mills—rely primarily on impact and attrition to reduce particle size. Recognizing the dominant mechanism guides equipment selection and operating parameter optimization.Given Data / Assumptions:Equipment considered: common intermediate/fine grinders.Feed is already below coarse-crushing range.Objective is to identify the main breakage mode.Concept / Approach:In tumbling and impact mills, particles are broken when grinding media or hammers strike (impact) and when particles rub or slide against media/surfaces (attrition). Compression and cutting dominate in crushers and knife mills used for coarse reduction or fibrous materials, not for general fine grinding of minerals and chemicals.Step-by-Step Solution:List typical fine grinders and their actions.Identify impact from falls/strikes and attrition from inter-particle/media rubbing.Conclude the combined mechanism rules performance.Verification / Alternative check:Design texts describe selection charts linking fine product sizes with impact–attrition mills, confirming the mechanism pairing.Why Other Options Are Wrong:Cutting: suits fibrous materials.Compression/tearing: characteristic of crushers, not fine grinders.Common Pitfalls:Assuming one mechanism only; real mills combine actions, but impact + attrition dominate.Final Answer:Impact and attrition

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