A plant handles angular lumps, rubbery pieces, free-flowing granules, and sticky compounds. Propose a strategy to standardize handling with minimal downtime across these materials. State two coordinated actions that make this feasible.

Fill in the blank with a precise term: A relatively small, discrete subdivision of matter used in mechanical operations is called a (a)   .

Specify the practical size range that usually defines particles in mechanical operations, and justify why this range matters for equipment choice.

A team proposes treating a rope-like pellet and a thin film identically in design calculations because both have one negligible dimension. Critique this plan and state the correct primary size parameters for each case.

A particle’s projected image shows two outermost points 2.4 mm apart along a given direction. Identify the size metric being measured and justify why this metric captures the maximum span rather than a central tendency.

An elongated flake is rotated so its thickness changes relative to the viewing direction, but its projected area stays constant. Predict how Feret and Martin diameters respond and explain the limitation revealed.

Fill in the blank: For a rectangular solid, size can be uniquely defined by (a)   .

You must report a single size for highly irregular grains used in a process model. Propose a defensible plan to measure and summarize size using Feret and Martin diameters from images, noting how to mitigate orientation bias.

A lab needs to predict the residence time in a gravity settler for a batch of irregular sand grains. They can measure only one equivalent diameter. Which choice will most directly support the settling-rate prediction, and why?

An irregular particle passes through a square mesh only when oriented favorably. The smallest square opening that allows passage is 1.4 mm. Name the specific equivalent diameter this measurement represents.

(a)  

A technician claims that one universal equivalent diameter can characterize any irregular particle for all unit operations. Evaluate this claim and provide a counterexample that cites two different operations requiring different diameters.

A process engineer must minimize pressure drop while maintaining flow through a packed bed of irregular sand. Which equivalent diameter is most appropriate to represent particles in the Ergun equation and why?

In a thickener design, particles settle in water. Select the most appropriate equivalent diameter to size the tank and justify your choice using fluid–particle interaction reasoning.

An engineer mistakenly uses volume diameter to predict adsorption capacity of a catalyst pellet bed. Predict the most likely consequence and explain.

Fill in the blank with the most appropriate term: For filtration and packed bed flow calculations, the (a)   diameter, derived from the volume-to-surface ratio, should be used.

Select the most defensible plan for choosing an equivalent spherical diameter for a porous, irregular catalyst pellet used in pressure drop calculations across a packed bed. Justify the key steps in one or two sentences.

Fill in the blank with the precise term: The property that a sphere’s measured size or hydrodynamic behavior does not change when rotated in space is called (a)   .

An engineer uses the same equivalent spherical diameter for both drying-time estimates and terminal settling calculations of flaky particles. Critique this decision and propose a better strategy that still uses spherical models.

Two particles have identical surface area Sp but different roughness. Predict which has the larger surface diameter ds and justify the reasoning briefly.

An irregular particle has volume Vp = $$6.0\times10^{-12} m^{3}$$ . Determine its volume diameter dv for an equivalent sphere.

(a)  

Explain why circularity is useful as a shape descriptor for engineering particles and describe one industrial decision it can inform.

Fill in the blank: For a perfect circle of area A and perimeter P, the circularity value equals (a)   .

An engineer must enhance surface-dependent reaction intensity without changing particle volume. Reason using circularity: which morphology adjustment is most consistent with the goal and why?

A particle’s projected image has area A = 25π mm² and perimeter P = 40 mm. Compute its circularity using 4πA/P² and interpret the shape class that best fits.

A crushed sand sample shows sharp corners and protrusions. Predict its circularity trend and one practical implication for hopper flow.

Explain how convexity influences abrasion in processing equipment and justify the mechanism using surface interaction reasoning.

Given two composites: Mix A uses high-convexity fillers; Mix B uses low-convexity fillers. Predict differences in mechanical interlocking and bonding, and justify.

A particle has maximum length L = 2.5 mm and maximum width W = 0.5 mm. Calculate elongation and classify the particle’s shape.

(a)  

Design a quick image-analysis screening rule using circularity and elongation thresholds to segregate acicular particles from rounded granules. State thresholds and explain trade-offs.

Fill in the blank: Sphericity Φ is defined as the ratio of the surface-to-volume ratio of a sphere with the same volume as the particle to the (a)   of the actual particle.

A powder processor wants faster combustion in a dust collector. Should they select particles with higher or lower specific surface ratio? Justify your choice in one or two sentences.

Derive the surface-to-volume ratio of a sphere with the same volume as a particle, in terms of its volume diameter dv. Show the key steps and final expression.

A quality engineer reports Sp/Vp = $$12 mm^{-1}$$ for an irregular particle. For a sphere of equal volume, dv = $$0.4 mm$$ . Compute the specific surface ratio and interpret its meaning in one sentence.

A cube has edge length a. Derive the ratio ds/dv for the cube using equivalent sphere diameters, and then compute Φ. Show the chain of reasoning and any simplifying exponents.

Fill in the blank: For a cube, numerical evaluation gives Φ_cube = (a)   .

You are comparing two cylinders made of the same material. Cylinder A has L = D, and Cylinder B has L ≪ D (a very flat disc). Without calculation, reason which has higher sphericity and justify why using volume–surface efficiency arguments.

A regular hexagonal prism is observed to have sphericity between 0.85 and 0.90 when equidimensional. Which design change would most likely decrease its Φ and why?

A porous alumina particle has a mass of 0.8 g. Helium pycnometry finds the true density of alumina is 3.97 g/cm³. When immersed in a liquid that enters open pores, the displaced volume is 0.30 cm³. Estimate the particle’s apparent density and justify whether it must be less than, equal to, or greater than the true density.

You measure a catalyst grain: mass = 1.2 g. Displacement in a wetting liquid that accesses open pores gives 0.40 cm³. Gas pycnometer (helium) gives solid volume of 0.28 cm³. Compute porosity as the fraction of open pore volume within the particle.

Fill in the blank: The preferred method to determine true particle density for unknown materials with closed pores is (a)   .

A researcher reports a particle’s density measured by immersion in water that penetrates open pores. They call this value the true density. Evaluate the claim and briefly correct the terminology and reasoning.

Given a porous particle with mass 1 g, total external volume including open pores 0.50 cm³, and true density of its solid material 2.5 g/cm³, estimate the fraction of open pore volume within the particle and explain the steps.

Two powders A and B have identical apparent density, but A packs with ε = 0.35 while B packs with ε = 0.50. Which powder yields higher bulk density, and why?

Fill the blank: Bulk density is mass of particles per unit (a)   of the particle bed, including all particle volume and all void space between particles.

Design a step sequence to minimize systematic error when measuring apparent density by liquid pycnometry for a hygroscopic powder. Explain your choices.

Explain how bulk density influences pressure drop in a packed-bed reactor, and outline a reasoning chain linking void fraction to Ergun-equation terms.

Design a gravity settling tank for a suspension with 5% by mass fines below 10 µm and the remainder near 200 µm. Explain what constraint the fines impose on tank sizing and why.

Choose the best filter medium for a PSD ranging from 1 µm to 200 µm if product retention of fines is critical. Justify your choice.

A plant claims average particle size alone is enough for reactor design. Evaluate this claim with PSD reasoning.

On a PSD plot with logarithmic x-axis (size) and y-axis as mass percentage, the curve has a broad peak and a right-skewed tail toward small sizes. What key metrics should you read off to specify this powder to a vendor?

A powder with the same median size as another shows a much wider spread. Predict two processing impacts and justify them using PSD.

Fill in the blank: In PSD terminology, the size at which 50% of particles by mass are smaller is called the (a)   .

A pigment batch has slightly higher d10 and unchanged d90 compared with last week. Infer the most likely visual or performance change and explain.

On a cumulative undersize curve, Sample A has d10=5 µm, d50=40 µm, d90=200 µm; Sample B has d10=20 µm, d50=40 µm, d90=80 µm. Which would you choose for fast sedimentation with acceptable clarity and why?

A catalyst manufacturer can either grind further to narrow PSD or accept a wide log-normal PSD. If grinding cost rises steeply, propose a decision rationale that balances reaction rate and cost.

Design a lab method to estimate sphericity for irregular pellets using only mass, calipers, and a pycnometer. Outline steps, key equations, and error sources.

Fill in the blank: For a packed bed with apparent particle density ρapp and void fraction ε, a simple estimate for bulk density is ρbulk ≈ ρapp × (a)   for randomly packed spheres.