Question 1

Shell-and-tube heat exchanger layout rules: which combined statement best reflects common preliminary design practices (cleaning lane on square pitch, tubesheet minimum thickness versus tube OD, and standard tube ODs/lengths used)?

Accepted Answer

Introduction / Context: Early-stage shell-and-tube heat exchanger design uses rules-of-thumb before detailed thermal and mechanical rating. Common choices include tube pitch patterns, cleaning access lanes, tubesheet thicknesses, and preferred tube sizes/lengths—each affecting manufacturability, maintenance, and cost. Given Data / Assumptions: Conventional exchanger (not special high-pressure or exotic alloy design). Square pitch layouts permit through-rod cleaning lanes; triangular pitch favors higher area density but poorer mechanical cleaning. “Minimum tubesheet thickness” refers to preliminary guidance, not a code calculation replacement. Concept / Approach: Design practices often specify a narrow cleaning lane between tubes on square pitch (about 6.5 mm) to allow brushes/rods. Tubesheet thickness is initially tied to tube outside diameter (OD), recognizing code checks will refine it later. Tube OD and standard stock lengths are chosen to balance heat transfer area, pressure drop, and availability. Step-by-Step Solution: Square pitch → provide a small cleaning lane (≈ 6.5 mm) to enable mechanical cleaning.Tubesheet thickness → preliminarily comparable to tube OD up to small sizes; adjustments occur with larger ODs per mechanical design.Tube sizes → OD commonly 6–40 mm; lengths often selected from 0.5 to 6 m stock. Verification / Alternative check: Vendor catalogues and plant standards list these practice ranges; final selection is validated by TEMA/API and pressure design codes after thermal rating. Why Other Options Are Wrong: Picking only one of (a), (b), or (c) ignores the broader set of accepted practices. Common Pitfalls: Assuming triangular pitch can be rod-cleaned; ignoring fouling when choosing very small tube ODs; treating preliminary thickness guidance as a substitute for full code calculation. Final Answer: All (a), (b) & (c)

Question 2

Gas–liquid contacting design: commercial packed scrubbers are typically sized for what pressure-drop range per metre of packed height (expressed in mm of water column)?

Accepted Answer

Introduction / Context: Packed scrubbers (absorption columns) remove gaseous pollutants using liquid contact over random or structured packings. A key hydraulic choice is allowable pressure drop per metre of packing, which trades off blower power against mass-transfer performance and flooding margin. Given Data / Assumptions: Steady operation with clean service or modest fouling. Random packings or moderate-resistance structured packings. Design below the flooding point with a reasonable turndown. Concept / Approach: Pressure drop increases as gas rate rises toward flooding. Designers therefore select a moderate range that provides good liquid distribution and film renewal without penalizing operating power. Practical experience places typical design ΔP values in a few tens of millimetres of water per metre of packing for many air pollution and absorption duties. Step-by-Step Solution: Define target ΔP across packing per metre of height.Choose range balancing fan/blower energy and mass-transfer efficiency.Adopt about 17–34 mm H2O per metre as a widely used design window for many scrubbers. Verification / Alternative check: Pilot tests and vendor rating programs show curves with typical operation well below flooding, often giving per-metre drops in the 20–30 mm H2O region for common packings and loads. Why Other Options Are Wrong: 4–8 mm H2O: too low for reliable contacting; risks maldistribution/inefficient transfer. 52–68 or 88–105 mm H2O: unnecessarily high for most services; increases blower power and may reduce turndown margin. Common Pitfalls: Ignoring liquid distribution quality; designing too close to flooding; not accounting for fouling which elevates pressure drop over time. Final Answer: 17–34 mm H2O per m

Question 3

Azeotropes and Raoult’s law: a binary azeotrope that boils at a temperature higher than either pure component shows which kind of deviation from Raoult’s law?

Accepted Answer

Introduction / Context: Understanding deviations from Raoult’s law is essential to predict vapor–liquid equilibria, design distillation columns, and anticipate azeotrope formation. Maximum-boiling and minimum-boiling azeotropes exhibit characteristic deviations that influence separation feasibility. Given Data / Assumptions: Binary liquid mixture at atmospheric pressure. Azeotrope has a boiling point higher than that of both pure components (maximum-boiling azeotrope). Concept / Approach: Raoult’s law assumes ideal solutions where each component’s partial pressure equals its mole fraction times its pure-component vapor pressure. Real mixtures may deviate because of intermolecular interactions. Stronger unlike-molecule attractions reduce escaping tendency, lowering total vapor pressure at a given temperature. This produces a higher boiling point than either component and constitutes negative deviation from Raoult’s law. Step-by-Step Solution: Identify azeotrope type: “higher boiling than either component” → maximum-boiling.Relate to total pressure: stronger attractions → lower total vapor pressure at composition → higher boiling temperature.Conclude deviation sign: interactions stronger than ideal → negative deviation. Verification / Alternative check: Systems like hydrochloric acid–water at certain compositions display maximum-boiling behavior consistent with negative deviations (enhanced attractions). Why Other Options Are Wrong: Positive deviation: corresponds to weaker unlike interactions, lower boiling, and minimum-boiling azeotropes. No deviation: would be ideal behavior, no azeotrope. None of these: not applicable because negative deviation is correct. Common Pitfalls: Confusing sign of deviation with direction of boiling point; assuming all azeotropes are minimum-boiling; ignoring pressure dependence of azeotrope behavior. Final Answer: Negative deviation

Question 4

Condensers in distillation service: from an operations viewpoint, when is a vertical condenser preferred over a horizontal condenser?

Accepted Answer

Introduction / Context: Overhead condensers on distillation columns can be mounted vertically or horizontally. The choice affects hydraulics, available net positive suction head, and reflux arrangements. A practical advantage of vertical orientation is the gravity head available for reflux return. Given Data / Assumptions: Overhead condensing duty with reflux returned to the column. No dedicated reflux pump desired (thermosyphon/total condenser arrangement). Normal pressure drop and condensate lines sized correctly. Concept / Approach: In a vertical condenser mounted above the reflux drum/column head, condensed liquid can return by gravity. The static head helps overcome line friction and tray weir heights, enabling stable reflux without a pump. Horizontal condensers offer large surface in compact footprints but do not inherently deliver extra hydrostatic head. Step-by-Step Solution: Identify need: provide reflux to the column reliably without a pump.Use elevation: vertical condenser gives gravitational head to drive condensate flow.Confirm suitability: arrangement is common in total condensers with overhead receivers above the column. Verification / Alternative check: P&IDs and plant standards frequently place vertical condensers and receivers to secure adequate NPSH and gravity reflux in light-end services. Why Other Options Are Wrong: Only condensation / deep subcooling claims do not inherently favor vertical over horizontal; either orientation can be designed for these duties. Combining duties is a design choice, not the principal reason for choosing vertical orientation. Common Pitfalls: Ignoring elevation constraints; undersizing condensate lines so gravity head is insufficient; overlooking vacuum service requirements that alter hydraulics. Final Answer: When hydrostatic head is required to provide reflux without a pump

Question 5

Bubble-cap tray hydraulics: in common practice, how are the riser annulus area and the slot area sized relative to each other to balance vapor traffic and pressure drop?

Accepted Answer

Introduction / Context: Bubble-cap trays use risers and caps with slots to distribute vapor into the liquid layer. Relative sizing of the riser annulus and cap slot areas determines the local pressure drop and the uniformity of vapor distribution across the tray. Given Data / Assumptions: Aa denotes the annular cross-sectional area between riser and cap skirt. Sa denotes the total slot flow area on the cap. Normal turndown ratios and hydrostatic submergence are assumed. Concept / Approach: For steady operation, designers seek comparable flow restrictions in the annulus and through the slots so neither feature chokes the vapor. Making these areas approximately equal helps keep the pressure drop contributions balanced and reduces sensitivity to fouling or minor fabrication tolerances. Step-by-Step Solution: Define control sections: annular gap under the cap and slotted discharge into the liquid.Set areas: choose Aa ≈ Sa so local velocities remain moderate in both sections.Check hydraulics: verify total tray ΔP at design and turndown conditions. Verification / Alternative check: Tray design guides commonly present relations where Aa and Sa are of similar magnitude, followed by final tuning with vendor correlations. Why Other Options Are Wrong: Large mismatches (1.5× either way) unnecessarily shift pressure drop to one element, increasing sensitivity and risking maldistribution. Scaling statement “1.2 Aa = 1.2 Sa” adds no information beyond equality and is not a standard guideline. Common Pitfalls: Oversizing slots leading to weeping at low vapor rates; too small annulus causing excessive ΔP and entrainment. Final Answer: Aa = Sa (annular passage area approximately equals slot area)

Question 6

Siting of large hazardous-chemical storage tanks: what is a commonly cited safe spacing range between two adjacent tanks, expressed as multiples of tank diameter?

Accepted Answer

Introduction / Context: Spacing between large above-ground tanks storing hazardous chemicals is a fundamental layout decision. Adequate separation limits fire escalation, allows firefighting access, and provides room for maintenance and inspection. Given Data / Assumptions: Vertical cylindrical atmospheric tanks in a tank farm. Flammable or otherwise hazardous contents. Generic spacing guidance; actual projects must check local codes/standards and risk assessments. Concept / Approach: Many plant standards express minimum tank-to-tank spacing as a fraction or multiple of tank diameter. A shell-to-shell distance around one tank diameter, sometimes up to 1.5D, offers fire separation and access while keeping plot area reasonable. Tighter spacing risks domino effects; much wider spacing consumes land and piping unnecessarily. Step-by-Step Solution: Define spacing metric as a multiple of tank diameter D.Select a practical range that balances safety and land use.Adopt about 1 to 1.5 times D as a commonly used design range for hazardous services, subject to code and radiation/overpressure studies. Verification / Alternative check: Company engineering practices and risk-based standards often quote minimum spacing near 1D, with increased distances in congested or high-inventory services. Why Other Options Are Wrong: 2.5–3.5D, 4–5D, 6–8D: these are far larger than typical baseline requirements and are rarely used except in special risk scenarios or where land is abundant. Common Pitfalls: Ignoring dike/containment requirements; forgetting foam-monitor access; not adjusting spacing for relief load interaction or vapor cloud hazards. Final Answer: 1 to 1.5 times the tank diameter

Question 7

Continuous rectification hydraulics: from theoretical sizing, how does the required column diameter of the stripping section compare to that of the enriching (rectifying) section?

Accepted Answer

Introduction / Context: In binary distillation, the column above the feed tray is called the enriching (rectifying) section and the part below is the stripping section. Required diameter depends on vapor and liquid traffic (factors like reflux ratio, boilup, and feed condition) that determine flooding limits and allowable vapor velocity. Given Data / Assumptions: Steady continuous operation with ideal mechanical design (same internals type in both sections). Similar tray/packing efficiency and allowable vapor velocity criteria in both sections. Typical feed conditions (not extreme cold/hot side streams). Concept / Approach: For many conventional designs, vapor rate is higher in the enriching section because overhead product plus reflux create larger upward traffic than boilup alone below the feed. Since allowable vapor velocity is set by entrainment/flooding limits, the higher vapor load usually dictates a larger diameter in the enriching section. Thus, the stripping section often requires a smaller diameter. Step-by-Step Solution: Estimate vapor/liquid flow profiles using material balances around the feed and products.Compute flooding velocities and choose design fractions (e.g., 70–85% of flooding).Compare cross-sectional areas required; enriching section typically governs, making the stripping section diameter less. Verification / Alternative check: Column rating tools commonly return a larger diameter above the feed tray for moderate reflux ratios; revamp case studies confirm this trend. Why Other Options Are Wrong: More than / same as: contrary to the usual vapor traffic distribution for typical designs. “Either more or less depending only on relative volatility”: diameter depends on actual hydraulic loads, not solely on relative volatility. Common Pitfalls: Ignoring the impact of subcooled or superheated feed (which can shift loads); mixing different internals across sections without adjusting allowable velocities; neglecting pressure drop limits. Final Answer: Less than the enriching section

Question 8

Pressure vessel classification: a cylindrical shell is classed as a “thick” shell when the ratio of its internal diameter to wall thickness (D/t) is approximately below which value?

Accepted Answer

Introduction / Context: Pressure vessel analysis distinguishes between thin and thick cylinders because stress distributions differ significantly. Thin-shell formulas assume negligible radial stress variation, while thick-shell theory (e.g., Lame’s equations) accounts for radial gradients and is needed when walls are relatively thick. Given Data / Assumptions: Internal pressure service with cylindrical geometry. D denotes internal diameter; t denotes wall thickness. Standard engineering thresholds used for preliminary classification. Concept / Approach: A common rule places thin-shell validity when t ≤ D/20 (i.e., D/t ≥ 20). As the wall becomes thicker (smaller D/t), thin-shell assumptions break down and thick-shell analysis is required. Some practices use a stricter threshold near D/t ≈ 10 for conservative classification of “thick” shells. Step-by-Step Solution: Relate thickness to diameter via D/t.If D/t is small (wall relatively thick), radial stress variation is appreciable.Adopt thick-shell treatment for D/t roughly below 10; use thin-shell formulas for D/t around 20 or higher. Verification / Alternative check: Design texts show thin-shell hoop stress σ_h = P D /(2 t) applies well when t ≤ D/20; for thicker walls, Lame’s solution is recommended. Why Other Options Are Wrong: “D/t greater than 10 or 20” indicate thin walls; thick-shell classification applies to smaller D/t, not larger. “D/t less than about 20” is broader and includes some thin-shell range; the more accepted “thick” cutoff is nearer 10. Common Pitfalls: Using thin-shell equations outside their range; forgetting joint efficiency and corrosion allowance implications; ignoring external pressure buckling checks. Final Answer: D/t less than about 10

Question 9

Filtration fundamentals: for constant-pressure cake filtration, the instantaneous rate of filtrate delivery (dV/dt) varies inversely with which factor most directly?

Accepted Answer

Introduction / Context: In cake filtration, engineers estimate cycle times and equipment sizes using relationships that tie filtrate flow rate to driving force, fluid properties, and resistances. Recognizing which variables increase or decrease the rate is essential for debottlenecking and scale-up. Given Data / Assumptions: Constant-pressure filtration of a compressible or incompressible cake. Darcy-type flow through porous media applies. Filtrate viscosity and cake/medium resistances are the dominant resistive terms. Concept / Approach: The basic form is dV/dt = (ΔP * A) / (μ * (R_c + R_m)), where ΔP is pressure drop, A is filtering area, μ is filtrate viscosity, R_c is cake resistance, and R_m is medium resistance. Thus, the rate is directly proportional to ΔP and A, and inversely proportional to μ and the total resistance. Step-by-Step Solution: Write the constant-pressure filtration equation: dV/dt = (ΔP * A) / (μ * (R_c + R_m)).Identify inverse dependencies: μ and (R_c + R_m) in the denominator reduce flow rate as they rise.Select the single factor asked: viscosity of filtrate (μ) is an explicit inverse factor. Verification / Alternative check: Experimentally, heating viscous slurries (thereby lowering μ) increases filtration rate, confirming the inverse relationship with μ. Why Other Options Are Wrong: Filtering area & pressure difference: both are in the numerator; rate increases with these, not decreases. Combined cake and medium resistance: also an inverse factor, but the question asks for one factor; among the given choices allowing exactly one correct, viscosity is selected to maintain unique correctness. Both (a) and (b): incorrect because (a) contains variables that increase rate, not decrease it. Common Pitfalls: Confusing effects of viscosity vs. density; overlooking cake compressibility which makes R_c grow with ΔP; assuming temperature changes only affect solubility and not μ. Final Answer: Viscosity of the filtrate

Question 10

In thin-walled pressure vessels (mechanical design), the “hoop stress” refers specifically to which type of stress acting around the shell of a cylindrical tank?

Accepted Answer

Introduction / Context: In mechanical and process equipment design, thin cylindrical shells (such as storage tanks, boilers, and heat-exchanger shells) develop distinct stress components when subjected to internal pressure. Two principal membrane stresses are important for safe design: the hoop (circumferential) stress and the longitudinal (axial) stress. Correctly identifying the hoop stress helps engineers size the wall thickness and select materials to prevent failure. Given Data / Assumptions: Thin-walled cylinder assumption (wall thickness much smaller than diameter). Uniform internal pressure acting on the inner surface. Elastic behavior; neglecting local discontinuities and nozzle effects for the concept. Concept / Approach: Hoop stress acts tangentially around the circumference of the cylinder as the shell “tries to split open” along a longitudinal line. Under thin-wall theory, hoop stress is larger than longitudinal stress by a factor of two for a closed-end cylinder at the same pressure and radius, hence it is often the governing stress state for thickness calculation. Step-by-Step Solution: Recognize that internal pressure creates tensile stresses within the shell.Hoop (circumferential) stress acts around the cylinder’s circumference; longitudinal stress acts along its length.Radial stress through the wall is small compared with membrane stresses under thin-wall assumptions.Therefore, “hoop stress” specifically means circumferential tensile stress. Verification / Alternative check: From thin-wall formulas: hoop stress σ_h = p * r / t; longitudinal stress σ_l = p * r / (2 * t). The larger value and direction confirm its circumferential tensile nature. Why Other Options Are Wrong: Radial: small through-thickness stress; not the hoop stress. Compressive: internal pressure creates tension in the wall, not compression. Longitudinal: a real component, but different from hoop stress. Common Pitfalls: Confusing hoop with longitudinal stress; applying thick-wall formulas when the thin-wall criterion is not satisfied; ignoring joint efficiency and corrosion allowance in real designs. Final Answer: circumferential tensile

Question 11

Distillation hydraulics: which factors primarily determine vapor entrainment from one tray to the next in a column?

Accepted Answer

Introduction / Context: Entrainment in tray columns occurs when vapor carries liquid droplets upward to the tray above. Excessive entrainment reduces efficiency, causes contamination between sections, and increases pressure drop. Designers must control operating conditions and geometry that influence entrainment. Given Data / Assumptions: A tray (sieve/valve/cap) distillation column in steady operation. Standard hydrocarbon or similar system without unusual foaming tendency. Focus on mechanical/operating variables affecting entrainment. Concept / Approach: Three parameters dominate entrainment. Larger plate spacing gives more disengagement height, reducing droplet carryover. Greater liquid depth (froth height) tends to increase liquid holdup and the chance for droplet formation and carryover. Higher vapor velocity increases shear at the gas–liquid interface and droplet acceleration, amplifying entrainment. Hence all listed factors are relevant together. Step-by-Step Solution: Consider plate spacing: increasing spacing promotes droplet disengagement and reduces carryover.Consider liquid depth: deeper froth increases droplet formation and residence, favoring entrainment.Consider vapor velocity: higher velocity imparts more momentum to droplets, carrying them upwards.Conclusion: all three significantly determine entrainment. Verification / Alternative check: Empirical entrainment correlations and vendor guidelines relate entrainment to F-factor (velocity–density measure), froth height, and tray spacing, confirming multi-factor control. Why Other Options Are Wrong: Any single-factor answer is incomplete; entrainment is multivariate. “None of these” contradicts well-established tray hydraulics. Common Pitfalls: Operating too close to flooding; ignoring foaming tendency; using insufficient spacing that prevents disengagement. Final Answer: All (a), (b) and (c).

Question 12

On tray columns, a “calming section” before the downcomer is provided primarily to achieve which objective?

Accepted Answer

Introduction / Context: Tray hydraulics aim to balance good mass transfer with stable liquid handling. A “calming section” (also called a quiet zone) is a region near the outlet weir where froth subsides, allowing vapor disengagement from the liquid prior to entry into the downcomer. This improves downcomer capacity and reduces choking and bypassing. Given Data / Assumptions: Conventional tray with outlet weir and a downcomer. Significant froth on the active tray area upstream of the weir. Normal distillation service without special foaming inhibitors. Concept / Approach: In the active area, vapor bubbles through liquid creating froth. If this froth enters the downcomer, the entrained vapor occupies volume, reduces liquid residence time, and can cause downcomer backup or flooding. The calming section allows bubbles to disengage, converting froth to clearer liquid before overflow over the weir and entry into the downcomer. Step-by-Step Solution: Identify the hydraulic bottleneck: downcomers must pass mostly liquid, not vapor–liquid froth.Provide a calm area (reduced bubbling) near the outlet.Disengage bubbles so liquid enters the downcomer with minimal entrained vapor.Result: improved capacity and stable operation. Verification / Alternative check: Tray design handbooks specify quiet-zone length as a fraction of tray chord; poor quiet-zone design correlates with downcomer choke and premature flooding. Why Other Options Are Wrong: Reducing discharge fluctuation is not the primary function. Better vapor–liquid contact occurs in the active area, not in a calming zone. Cooling is unrelated; temperatures are set by column hydraulics/thermodynamics. Common Pitfalls: Too short a calming section; insufficient outlet weir length; allowing froth to spill directly into the downcomer. Final Answer: Permit release of entrained vapor from the liquid before it enters the downcomer

Question 13

Shell-and-tube exchangers: what is the primary purpose of straight tie rods installed through the baffle stack?

Accepted Answer

Introduction / Context: In shell-and-tube heat exchangers, a series of transverse baffles guides shell-side flow across the tube bundle to enhance heat transfer and support the tubes. Straight tie rods run the length of the baffle stack, threading and clamping the baffles together in their designed sequence and spacing. Given Data / Assumptions: Conventional TEMA-style exchanger with drilled baffles and tie rods. Tubes are fixed into tubesheets via rolling and/or welding (a separate function). Normal thermal expansion is accommodated by expansion joints or floating-head designs. Concept / Approach: Tie rods do not fix tubes to tubesheets or absorb shell expansion. Instead, they maintain the mechanical integrity of the baffle stack so that the intended flow pattern (crossflow, window flow) and tube support spacing are preserved during assembly, operation, and handling of the bundle. Step-by-Step Solution: Recognize separate roles: tubesheets grip tubes; shell/nozzles handle pressure; baffles shape shell-side flow and support tubes.Tie rods pass through aligned holes in baffles and are nutted to clamp them into a rigid stack.This prevents relative movement and preserves designed spacing, ensuring performance and mechanical support. Verification / Alternative check: Standard exchanger drawings show multiple tie rods spaced circumferentially to balance loads; spacers or sleeves may be used to set exact gaps between baffles. Why Other Options Are Wrong: Fixing tubes in position is the tubesheet’s job. Thermal expansion is handled by design features like floating heads or expansion joints. Changing fluid properties is unrelated to tie rods. Common Pitfalls: Insufficient tie-rod tension or number leading to baffle flutter; misalignment causing tube wear. Final Answer: Hold the baffles in position and maintain spacing

Question 14

Actual operation of a bubble-cap distillation column: which variables are higher at the bottom than at the top of the tower?

Accepted Answer

Introduction / Context: Distillation columns operate with thermal and hydraulic gradients from bottom (reboiler) to top (condenser). Understanding which variables increase or decrease along the height helps diagnose performance, set controls, and interpret composition profiles. Given Data / Assumptions: Standard fractionation tower with a reboiler at the bottom and a condenser at the top. Countercurrent vapor–liquid contact on trays or packing. No unusual feeds that invert normal gradients. Concept / Approach: Because of static head and pressure drop through internals, the bottom operates at higher pressure than the top. The reboiler adds heat, so temperatures are higher at the bottom and decline toward the top where heat is removed in the condenser. While vapor molecular weight can vary with composition, it is not universally higher at the bottom for every system. Similarly, actual molar vapor flow can vary by section and heat balance and is not guaranteed to be greater at the bottom than at the top in all operations. Step-by-Step Solution: Recognize pressure gradient: bottom pressure > top due to hydrostatic head and frictional losses.Recognize temperature gradient: reboiler at bottom raises temperature; condenser at top lowers temperature.Eliminate variables that are not universally higher at the bottom (molar vapor flow, vapor molecular weight). Verification / Alternative check: Process data trends and tower profiles consistently show bottom temperature/pressure maxima for typical hydrocarbon separations. Why Other Options Are Wrong: Molal vapor flow and vapor molecular weight depend on compositions and energy balances; they are not always higher at the bottom. “All of the above” is therefore not generally true. Common Pitfalls: Assuming constant molar overflow without checking energy input/removal; generalizing composition trends to every system. Final Answer: Pressure and temperature

Question 15

Heads for process vessels: the usual apex (included) angle selected for conical bottom heads is most commonly which of the following?

Accepted Answer

Introduction / Context: Conical heads are widely used at the bottoms of reactors, crystallizers, and storage vessels to aid drainage and solids removal. The “apex angle” (included cone angle) affects headroom, holdup, and the ability to avoid solids buildup. Industry practice gravitates to certain standard angles for fabrication convenience and process performance. Given Data / Assumptions: Typical chemical-process vessels handling liquids or slurries. Trade-off between steep cones (better drain) and shallow cones (less height). Common plate fabrication and forming constraints apply. Concept / Approach: An apex angle near 60° is common because it offers good drainage while keeping vessel height manageable. Steeper cones (smaller angles) may be used for heavy slurries or self-draining requirements, but 60° remains a widely adopted “default” in many industries and standards unless special needs dictate otherwise. Step-by-Step Reasoning: Balance drainage needs vs. vessel height and fabrication complexity.Select a standard angle that suppliers can readily fabricate and that meets most process requirements.Identify 60° as the commonly used apex angle for conical bottoms. Verification / Alternative check: Vendor catalogs and mechanical design guides often list 60° cones as standard offerings, with other angles available on request. Why Other Options Are Wrong: 30° or 45° may be used for special cases but are not the most common default. 75° and 90° become too shallow, increasing holdup and risking poor drainage. Common Pitfalls: Ignoring solids-handling: even at 60°, internals and outlets must avoid dead zones; neglecting headroom and nozzle clearances when selecting the cone angle. Final Answer: 60°

Question 16

Gas absorption design: the “absorption factor” is defined using slopes as A = (slope of operating line) / (slope of equilibrium line). Which ratio expresses this?

Accepted Answer

Introduction / Context: In gas absorption, the absorption factor simplifies stage calculations and helps screen solvent-to-gas ratios. Using a linear equilibrium relation y* = m x and an operating line y = y1 + (L/G)(x − x1), the absorption factor A relates mass-transfer driving forces to operating conditions. Given Data / Assumptions: S1 = slope of equilibrium line = m. S2 = slope of operating line = L/G (on appropriate coordinates). Linear equilibrium and dilute systems assumptions apply for the definition. Concept / Approach: By definition, A = (L/G) / m = S2 / S1. Values of A > 1 generally indicate favorable absorption (sufficient solvent flow), whereas A close to or below 1 indicates more trays or higher solvent rates are needed for the same removal. Step-by-Step Solution: Write equilibrium slope as m = S1.Write operating slope as L/G = S2.Compute A = S2/S1. Verification / Alternative check: Classic stagewise design methods (Kremser equations) use A directly; plugging in S2/S1 matches the textbook definition. Why Other Options Are Wrong: S1/S2 or products/inverses do not match the definition. Sums of slopes are not used for A. Common Pitfalls: Using inconsistent coordinates or units so that S2 is not L/G; applying A outside the linear-dilute regime. Final Answer: S2/S1

Question 17

Piping terminology: the “nominal size” (nominal bore, NPS/NB) of a pipe primarily indicates which diameter for design and specification purposes?

Accepted Answer

Introduction / Context: Engineers commonly specify piping by its nominal size (NPS/NB) and schedule. While the exact inner diameter varies with schedule (wall thickness), the nominal size historically tracks the inside diameter for small-to-midsize pipes, serving as the primary flow-carrying indicator, whereas the outside diameter is standardized by NPS series. Given Data / Assumptions: Standard steel pipe per common specifications (e.g., ASME B36.10M/B36.19M). Focus on what the “nominal size” conceptually indicates. Schedules (wall thicknesses) modify the precise ID. Concept / Approach: For most sizes, the NPS is a name that historically approximated the inside diameter. Although OD is fixed for each NPS, the nominal designation guides designers about the flow capacity, which relates to ID. Hence, when asked which diameter the nominal size indicates, the answer is the inner diameter (not exact, but the indicated one). Step-by-Step Solution: Recognize that NPS fixes OD while schedule fixes wall thickness.Resulting ID = OD − 2 * thickness; it varies with schedule but relates to the “nominal bore.”Therefore, nominal size indicates the inner diameter used for flow considerations. Verification / Alternative check: Pipe charts show constant OD for a given NPS and changing ID with schedule; the term “NB” literally means nominal bore (inside diameter). Why Other Options Are Wrong: Outer diameter is standardized but not what “nominal size” indicates conceptually. “Approximate” without identifying which diameter is ambiguous. “None” is incorrect; the convention exists. Common Pitfalls: Assuming nominal size equals exact ID for all schedules; confusing tubing (often sized by OD) with pipe (by NPS). Final Answer: inner

Question 18

Minor losses via fittings: using the equivalent-length method (Le/D), typical values for a 45° elbow and a 180° close return bend are approximately which pair?

Accepted Answer

Introduction / Context: Pressure drop in pipelines arises from straight-run friction and additional “minor” losses due to fittings, valves, and bends. A common estimation tool is the equivalent-length method, which expresses a fitting’s loss as an equivalent length of straight pipe, Le, that would cause the same frictional loss as the fitting. Engineers often memorize or look up representative Le/D values to make quick calculations during preliminary design. Given Data / Assumptions: Single-phase, incompressible flow in a standard industrial piping system. Typical commercial elbows and close return bends (not long-radius specialty items). Desire for order-of-magnitude design values rather than exact catalog numbers. Concept / Approach: Minor-loss coefficients (K) correlate to Le/D through Le/D = K / f, where f is the Darcy friction factor. Reference tables often provide average Le/D directly for common fittings based on typical Reynolds number ranges and surface roughness. Among choices given, a 45° elbow near Le/D ≈ 40–50 and a 180° close return bend near Le/D ≈ 70–80 are representative quick-estimate values for many water/utility services. Step-by-Step Solution: Identify fitting type: 45° elbow and 180° close return bend.Recall representative Le/D values from standard tables/charts.Match to the closest option pair: about 45 and about 75. Verification / Alternative check: Loss manuals (e.g., Crane-style compilations) show that return bends incur substantially larger losses than single elbows, consistent with the chosen pair. Exact values vary by radius and Reynolds number, but the pair (45, 75) reflects typical practice values. Why Other Options Are Wrong: Very small values (5 and 10) underestimate losses for most standard fittings. Very large values (180–500) grossly overstate equivalent lengths for common sizes. Common Pitfalls: Using Le/D blindly without considering f; mixing K and Le/D data; ignoring fitting radius and entrance effects that can change losses. Final Answer: 45 and 75

Question 19

Rotary dryers: the solids retention (residence) time is governed by which set of design and operating variables?

Accepted Answer

Introduction / Context: Rotary dryers are widely used in minerals, fertilizers, and chemical industries. The residence time of solids inside the rotating drum controls moisture removal and product quality. Correctly identifying the factors that influence residence time is essential for capacity sizing and product consistency. Given Data / Assumptions: Cylindrical rotary dryer operating at steady state. Solids advance by a combination of cascading, showering from flights, and axial transport due to slope and rotation. No unusual internals beyond conventional flights. Concept / Approach: Residence time increases as rotational speed decreases (less forward motion per unit time) and as slope decreases (flatter drums hold solids longer). Longer drums naturally give longer paths. Flight design (number, angle, pattern) dictates how solids are lifted and dropped, which affects axial velocity and holdup. Therefore, rpm, slope & length, and flight arrangement together determine retention time. Step-by-Step Solution: Identify transport drivers: drum rotation (rpm) and inclination (slope) set axial movement.Recognize geometric path length: longer drums → longer residence time.Account for internals: flight design modifies holdup and advance rate.Conclusion: all listed variables govern residence time. Verification / Alternative check: Semi-empirical residence-time correlations include terms for rotational speed, drum slope, length, fill, and flighting factors, confirming multi-parameter dependence. Why Other Options Are Wrong: Any single-variable answer is incomplete. “None” contradicts practice and design correlations. Common Pitfalls: Neglecting particle size distribution and stickiness (which alter holdup); assuming scale-up without re-optimizing flights and rpm. Final Answer: all (a), (b) and (c)

Question 20

For extremely hazardous material storage, how can hazards due to small relief-valve seat leakage be mitigated most effectively?

Accepted Answer

Introduction / Context: Relief valves can pass trace amounts of process fluid through the seat even when “closed.” For extremely hazardous, toxic, or pyrophoric services, even a tiny leakage to the discharge header or atmosphere creates an unacceptable risk. A standard safeguards question in process safety is how to mitigate this normal seat leakage while retaining full overpressure protection. Given Data / Assumptions: Service contains extremely hazardous material (toxic/flammable/corrosive). Conventional spring-loaded relief valve provided for overpressure protection. Goal is to avoid routine fugitive emissions through the valve seat under normal operation. Concept / Approach: The proven practice is to install a rupture diaphragm (rupture disk) upstream of the relief valve in a “tell-tale” configuration. The solid disk provides a bubble-tight barrier during normal operation, eliminating seat leakage to the relief header. When overpressure occurs, the disk bursts at a calibrated pressure, allowing the relief valve to function normally. A small tell-tale connection between disk and valve ensures any unexpected disk failure is detected. Step-by-Step Solution: Identify the hazard: continuous micro-leakage past relief valve seats.Choose a mitigation that is tight in normal service: a rupture diaphragm upstream of the relief valve.Confirm the diaphragm does not compromise protection: it has a set burst pressure and full flow area sized with the valve.Add monitoring: a tell-tale line to detect disk integrity loss. Verification / Alternative check: This arrangement is widely used in chlorine, phosgene, HF, toxic solvent, and lethal-service applications to combine leak-tight isolation with code-acceptable overpressure relief performance. Why Other Options Are Wrong: Perimeter dikes: control liquid spills around tanks; they do not stop valve seat leakage.Surge chamber: mitigates hydraulic transients, not fugitive emissions through valve seats.None of these: incorrect because rupture diaphragms are a recognized safeguard. Common Pitfalls: Omitting tell-tale connections, mis-sizing burst pressure relative to set pressure, or forgetting that a downstream rupture disk can cause “chattering” unless properly vented. Final Answer: Rupture diaphragm installed in tandem with the relief valve

Process Equipment and Plant Design Questions