Question 1

In riveted joint design for mechanical fabrication, identify the joint pattern in which rivets in successive rows are placed directly opposite one another.

Accepted Answer

Introduction / Context: Riveted joints are classic permanent fastenings used in boilers, bridges, tanks, and pressure vessels. Two common pitch arrangements for multiple rows are chain and zig-zag (staggered). Recognizing these layouts helps in stress analysis, load distribution, and leak tightness considerations. Given Data / Assumptions: Multiple rows of rivets connect overlapping plates. Row pitch and transverse pitch are set per design codes. We compare geometric patterns only. Concept / Approach: In chain riveting, rivets in adjacent rows lie on the same transverse line, i.e., directly opposite each other. In zig-zag riveting, rows are staggered, so rivets in one row lie midway between rivets in adjacent rows. Diamond patterns are specialty layouts, not typical for straight lap joints. Step-by-Step Solution: Visualize two parallel rows: if rivets align vertically → chain riveting.If they alternate (staggered) → zig-zag riveting.Diamond pattern forms a rhombus cluster, not a straight multirow lap joint pattern. Verification / Alternative check: Design handbooks illustrate chain riveting with coincident rivet centers in adjacent rows along the same transverse pitch line. Why Other Options Are Wrong: Zig-zag: explicitly staggered, not opposite. Diamond and hybrid patterns: specialized arrangements, not the standard “opposite” definition. Crossed: not a standard term for row layout in lap joints. Common Pitfalls: Confusing “pitch” terminology (longitudinal vs transverse) and misreading simple diagrams. Final Answer: Chain riveting

Question 2

Height Equivalent to a Theoretical Plate (HETP):
Which operating and hardware variables does the experimentally measured HETP depend upon in gas–liquid operations (distillation, absorption/stripping, humidification/dehumidification)?

Accepted Answer

Introduction / Context: HETP translates packed-column performance into an equivalent number of ideal stages. Designers use HETP to size column height once the number of theoretical plates is determined from equilibrium calculations (McCabe–Thiele or rigorous VLE mass transfer models). Given Data / Assumptions: Packed column handling two phases (gas and liquid). Measured HETP reflects hydrodynamics and mass transfer under specific test conditions. We consider practical dependencies observed in industry. Concept / Approach: HETP is not a universal constant. It depends on packing geometry (random saddles, rings, structured packing), packing size (surface area and void fraction), flow rates (affecting film thickness, wetting, and flooding proximity), and mixture properties/compositions (affecting diffusivities, interfacial tension, and equilibrium slopes). Step-by-Step Solution: Packing type/size sets a baseline mass transfer area a and pressure drop per meter.Flow rates determine hydrodynamic regime (loading/flooding) and interfacial renewal → changes k_G, k_L, and overall K-values.Compositions alter equilibrium slopes (m-values) and driving forces → effective height per stage changes. Verification / Alternative check: Vendor charts provide HETP ranges for the same packing at different liquid/gas loads and compositions, confirming multi-factor dependence. Why Other Options Are Wrong: Only one factor (a, b, or c) is incomplete; practice shows all three matter. “Constant HETP”: unrealistic outside a narrow operating window. Common Pitfalls: Using catalog HETP without correcting for system properties; ignoring scale-up effects and maldistribution. Final Answer: All of the above (flow rates, packing type/size, and concentrations)

Question 3

Mechanics concepts — identify the wrong statement:
Consider brittle versus ductile strength, thick cylinder hoop stress distribution, and column failure modes. Which statement below is incorrect?

Accepted Answer

Introduction / Context: Basic mechanics compares material behavior under tension and compression, evaluates stress distributions in pressure components, and contrasts failure by crushing versus elastic instability (buckling). Spotting incorrect generalizations prevents design errors. Given Data / Assumptions: Brittle materials: low tensile ductility, strong in compression. Ductile materials: exhibit yielding and plastic flow before failure. Thick cylinders: non-uniform hoop stress highest at the bore (inner radius). Long columns: Euler buckling often governs far below crushing strength. Concept / Approach: Brittle materials (e.g., cast iron, ceramics) typically have compressive strength > tensile strength, making statement (a) correct. Thick cylinder hoop stress is indeed maximum at the inside surface due to radial gradients, so (c) is correct. Buckling load is lower than crushing load for slender columns, so (d) is correct. Ductile metals usually have compressive strength comparable to or higher than tensile yield; the claim that their compressive strength is less is generally false, hence (b) is the wrong statement. Option (e) is also an incorrect generalization; however, only one answer should be selected, so we consider (e) a distractor that is not present in most standard sets; the truly tested contrast targets (b). Step-by-Step Reasoning: Check brittle vs tensile/compressive strengths → (a) aligns with data.Thick cylinder theory (Lame’s equations) → hoop stress peaks at inner radius → (c) correct.Long columns: P_cr (Euler) ≪ crushing → (d) correct.Ductile metals: compressive ≥ tensile yield → statement (b) is wrong. Verification / Alternative check: Materials handbooks show mild steel compressive yield similar to tensile yield; ceramics show large compressive/tensile disparity. Why Other Options Are Wrong: (a), (c), (d) agree with standard mechanics. (e) exaggerates ductile behavior; yet the intended single incorrect statement in classical sets is (b), which clearly contradicts data. Common Pitfalls: Confusing ductile yielding with brittle fracture criteria; ignoring geometry on column stability. Final Answer: The compressive strength of a ductile material is less than its tensile strength.

Question 4

Industrial mixing — paddle agitators:
Select the typical speed range (revolutions per minute) for industrial paddle agitators used for low-to-medium viscosity fluids.

Accepted Answer

Introduction / Context: Paddle agitators are radial-flow, low-shear impellers suited to blending, solid suspension (with limitations), and heat transfer in tanks where gentle circulation is preferred. Their operating speeds are much lower than those of high-shear impellers like turbines. Given Data / Assumptions: Standard tank sizes in typical chemical plants. Newtonian or mildly non-Newtonian fluids of low-to-medium viscosity. Electric motor with gearbox or VFD speed control. Concept / Approach: Power draw and flow regime depend on tip speed and Reynolds number. Paddle impellers trade shear for broad circulation, so they typically operate in tens of rpm, not hundreds or thousands. Step-by-Step Reasoning: Estimate tip speed = π * D * N; for D ≈ 0.3–1.5 m and N ≈ 20–100 rpm, tip speeds remain modest (order of 0.3–8 m/s).Compare with turbine impellers, which frequently run at several hundred rpm for the same tank size.Thus a practical paddle speed window is 20–100 rpm for common services. Verification / Alternative check: Vendor datasheets and mixing handbooks list paddle ranges typically starting near 20 rpm and topping near 100–150 rpm depending on duty. Why Other Options Are Wrong: 1–5 rpm or 5–10 rpm: too low for effective bulk circulation in most sizes. 500–750 rpm and 1000–2000 rpm: characteristic of smaller high-shear impellers (e.g., Rushton turbines), not paddles in production tanks. Common Pitfalls: Assuming “faster is better”; excessive rpm increases vortexing and power without proportional mixing benefits for paddles. Final Answer: 20 to 100 rpm

Question 5

Control valves — application limits:
Needle valves are precise throttling devices. In which service are they generally not used?

Accepted Answer

Introduction / Context: Control valves regulate flow, pressure, or level. Needle valves feature a slender, tapered plug and fine-pitch stem threads, delivering precise metering of small flow rates. Their geometry dictates where they excel and where they do not. Given Data / Assumptions: Needle valves provide small flow coefficients (Cv) and excellent resolution. They are typically constructed in small sizes (fractional to about 1–2 inches nominal). System may require high turndown and leak-tight shutoff at low flows. Concept / Approach: The practicality of a needle design diminishes as pipe size increases because the long, tapered stem would need to accommodate very large flow passages, becoming mechanically unwieldy and causing excessive pressure drop or poor controllability. For large lines, globe, ball, butterfly, or segmental ball valves are preferred depending on service. Step-by-Step Reasoning: Match device to duty: small Cv and precise resolution → needle valves in small lines.Large diameter lines require higher Cv and robust internals → other valve types.Therefore, needle valves are generally not used for very large diameter pipes. Verification / Alternative check: Standards and catalogs list needle valves primarily up to small sizes; large sizes are rare and impractical. Why Other Options Are Wrong: High-pressure precise throttling, accurate low-flow control, small-bore lines, and sampling: typical needle valve applications. Common Pitfalls: Confusing needle with globe valves; assuming the same trim scale applies to all line sizes. Final Answer: Very large diameter pipes

Question 6

Vessel supports — choose the correct application:
Saddle supports are primarily used to support which class of process vessels?

Accepted Answer

Introduction / Context: Mechanical support design must accommodate vessel geometry, weight distribution, thermal expansion, and external loads. Saddle supports are a standard solution for horizontal cylindrical vessels such as storage tanks, heat-recovery drums, and separators. Given Data / Assumptions: Vessel is a right circular cylinder lying horizontally. Two saddles typically spaced symmetrically support the shell. Loads include self-weight, contents, wind/seismic reactions, and thermal growth. Concept / Approach: Saddles cradle the curved shell, distributing bearing pressure and minimizing local stress concentrations. One saddle is often fixed; the other allows sliding to accommodate axial thermal expansion. Vertical vessels instead use skirts or legs; spheres use columns or skirts with different load paths. Step-by-Step Reasoning: Identify geometry: horizontal cylinder → shell curvature suits saddle contact.Support spacing determined by bending moment minimization and nozzle loads.Thermal expansion considered via sliding saddle or Teflon pads. Verification / Alternative check: Industry standards (e.g., Pressure Vessel Handbook) illustrate saddle supports on horizontal drums; vertical columns use skirts with anchor bolts. Why Other Options Are Wrong: Tall vertical/thick vertical: use skirts or legs. Spherical: use column legs (multi-supports), not saddles. Square silos: flat-bottom or leg supports. Common Pitfalls: Placing saddles too close to heads causing high midspan bending; ignoring nozzle-induced loads in support spacing. Final Answer: Horizontal cylindrical vessels

Question 7

Distillation column sizing parameter:
Which factor is primarily used to set (determine) the diameter of a distillation column during design?

Accepted Answer

Introduction / Context: Column design separates plate-to-plate (or height) requirements from hydraulic capacity. Once the number of theoretical stages is set by equilibrium, the diameter is chosen to prevent flooding and ensure adequate disengagement at the allowable vapor velocity. Given Data / Assumptions: Specified vapor and liquid traffic at design conditions. Tray or packing type known to estimate capacity factors. Acceptable approach to flooding set by safety margins (e.g., 70–85%). Concept / Approach: Superficial vapor velocity determines entrainment, weeping, and downcomer backup. Correlations (Souders–Brown for packings and trays, or vendor capacity factors) translate allowable velocity into required cross-sectional area; diameter follows from A = V̇ / v_s. Step-by-Step Solution: Compute vapor volumetric flow at operating conditions.Select allowable velocity from flooding correlations for the chosen internals.Calculate active area = flow / velocity → convert to diameter accounting for downcomers and tray layouts. Verification / Alternative check: Hydraulic rating software and design manuals produce the same diameter when fed with vapor rate and chosen percent of flooding. Why Other Options Are Wrong: Theoretical plates affect height, not diameter. Static submergence and weir length tune tray hydraulics but are not the primary diameter driver. Reboiler duty influences vapor rate, but diameter is ultimately set by allowable velocity, not duty alone. Common Pitfalls: Ignoring vapor surges and turndown; failing to subtract downcomer area from active area during sizing. Final Answer: Allowable vapour (vapor) velocity through the active area

Question 8

Tray internals — bubble cap sizing:
Select the most common standard bubble-cap size combination used in industrial trays (cap diameter with riser diameter).

Accepted Answer

Introduction / Context: Bubble-cap trays are legacy yet still-encountered distillation/absorption internals. Size standardization simplifies fabrication and performance prediction. Typical cap and riser diameters are chosen to balance pressure drop, capacity, and froth contact. Given Data / Assumptions: Industrial-scale column trays with moderate vapor/liquid loads. Use of standardized caps and risers from historic catalogs. Focus on “most common” rather than niche or miniature lab sizes. Concept / Approach: A 6″ bubble cap with a 4″ riser is a widely referenced standard combination for production trays, offering adequate area and manageable pressure drop. Smaller sizes like 1″ with 0.5″ riser are laboratory or very light-duty; mismatched options (e.g., riser larger than cap) are impractical. Step-by-Step Reasoning: Select a size that suits typical tray spacing and active area.Ensure cap diameter > riser diameter to provide annular slots and vapor distribution.6″/4″ pairing satisfies these design heuristics for many services. Verification / Alternative check: Classic tray design references list common caps in the 4–8″ range with risers about 2–4″, with 6″/4″ frequently cited as standard. Why Other Options Are Wrong: 1″/0.5″: too small for most industrial duties. 8″/1″: disproportionate; would restrict vapor severely. 4″ cap with 8″ riser: geometrically nonsensical. 3″/2″: used in small duties but not “most common.” Common Pitfalls: Assuming cap trays are universally optimal; modern designs often prefer sieve or valve trays or structured packing for efficiency and cost. Final Answer: 6″ cap with 4″ riser

Question 9

Cyclone separators — pressure drop effect:
For a given particle size distribution, how does increasing the pressure drop across a cyclone affect its dust collection efficiency?

Accepted Answer

Introduction / Context: Cyclone separators remove particulates by imparting tangential velocity, generating centrifugal forces that drive particles to the wall for collection. Hydraulic resistance (pressure drop) reflects the intensity of swirl and gas acceleration, both of which influence separation performance. Given Data / Assumptions: Particle size distribution fixed; gas properties and cyclone geometry constant. Pressure drop increase is achieved by higher inlet velocity or design tuning. Operation away from extreme fouling or severe re-entrainment. Concept / Approach: Collection efficiency correlates with the particle cut size d50, which decreases as tangential velocity and residence time increase. Higher inlet velocity raises centrifugal acceleration a_c ≈ v_θ^2 / r, improving the likelihood that particles overcome turbulent diffusion and are collected, at the cost of higher pressure drop. Step-by-Step Reasoning: Raise inlet velocity → higher swirl intensity.Higher swirl → stronger centrifugal force → lower effective cut size.Lower cut size → higher overall collection efficiency for a fixed PSD. Verification / Alternative check: Empirical correlations (e.g., Stairmand, Lapple) show efficiency rising with velocity (and thus ΔP), barring excessive erosion or re-entrainment at very high loads. Why Other Options Are Wrong: Decrease/Unaffected: contradict observed dependence on swirl intensity. Unpredictable based only on dust chemistry: geometry and hydrodynamics dominate. Zero due to re-entrainment: re-entrainment can occur at extremes, but not the general trend. Common Pitfalls: Ignoring power costs and erosion at higher ΔP; not accounting for parallel cyclones to limit velocity while meeting efficiency. Final Answer: Increase

Question 10

In plate-type heat exchangers used in chemical process industries, what is the typical thickness range (in millimetres) for the single-piece pressed heat-transfer plates that have grooves and corrugations for turbulence and strength?

Accepted Answer

Introduction / Context: Plate-type heat exchangers are widely used for liquid–liquid and liquid–two-phase services because their corrugated plates create high turbulence, large heat-transfer coefficients, and compact footprints. An important specification is the thickness of the heat-transfer plates, which must balance mechanical strength, corrosion allowance, and thermal performance. Given Data / Assumptions: The plates are single-piece pressings with grooves and corrugations. Material is typically stainless steel, titanium, or other corrosion-resistant alloys. Application is general process duty (not extreme pressure/erosion cases). Concept / Approach: Thinner plates reduce thermal resistance and improve overall heat-transfer coefficient U, but too-thin plates may deform under pressure or corrode quickly. Industry practice selects a moderate thickness that supports gasket compression and resists fatigue from flow-induced vibrations. Step-by-Step Solution: Identify common plate thicknesses used across vendors for standard duties.Compare with ranges proposed in the options.Select the range that reflects mainstream specifications for corrugated plates. Verification / Alternative check: Typical vendor datasheets list plate thicknesses around 0.4, 0.5, 0.6, and 0.7 mm for stainless steels, with heavier plates used only for special duties. This aligns with a 0.3–0.8 mm band for most services. Why Other Options Are Wrong: 1.25 to 3.125 mm: Excessively thick for standard plate exchangers; would degrade heat transfer and add cost. 3.5 to 7.0 mm and 8 to 12 mm: Typical of pressure-retaining shells or tube sheets, not thin transfer plates. 0.05 to 0.1 mm: Too thin to maintain integrity and gasket sealing under operating pressures. Common Pitfalls: Confusing plate thickness with frame/cover plate thickness; overlooking that higher corrosion allowance is usually handled by material selection rather than drastic thickness increases. Final Answer: 0.3 to 0.8 mm

Question 11

Cooling-water fouling factors: For cooling-water services in heat exchanger design, the fouling factor typically lies in the range 0.001 to 0.003 in which set of units?

Accepted Answer

Introduction / Context: The fouling factor accounts for additional thermal resistance caused by deposits, scaling, and biofouling on heat-transfer surfaces. Appropriate selection of fouling factors is critical to ensure realistic exchanger sizing and reliable operation in cooling-water duties. Given Data / Assumptions: Cooling water of typical industrial quality. Fouling factor range specified: 0.001 to 0.003 (English units). We are identifying the correct dimensional form corresponding to that numerical range. Concept / Approach: Fouling resistance R_f adds to the overall thermal resistance and has the same units as 1/U (the inverse of overall heat-transfer coefficient). In English units, U is BTU/(hr·ft²·°F), hence R_f has units of (hr·ft²·°F)/BTU, which is equivalently written as (BTU/hr·ft²·°F)^-1. Step-by-Step Solution: Identify U units in English: BTU/(hr·ft²·°F).Therefore, R_f units = 1/U = (hr·ft²·°F)/BTU.The mathematically equivalent notation is (BTU/hr·ft²·°F)^-1, matching the given numerical range. Verification / Alternative check: Design manuals commonly cite cooling-water fouling factors around 0.001–0.002 (hr·ft²·°F)/BTU. Writing these as the reciprocal of U’s units is standard shorthand, which corresponds to option (a). Why Other Options Are Wrong: (b) and (c) are SI-based inverses; the stated numerical range is not directly transferable without conversion. (d) has incorrect dimensional length in the denominator (m instead of m²). (e) shows the correct dimension but not the exact notation offered in the options; the question’s intended match is the reciprocal-unit form in (a). Common Pitfalls: Mixing SI and English units or forgetting that fouling resistance is an added inverse-U term leading to incorrect sizing margins. Final Answer: (BTU/hr·ft²·°F)^-1

Question 12

In continuous distillation design, the optimum reflux ratio is selected primarily on the basis of which consideration?

Accepted Answer

Introduction / Context: Choosing the reflux ratio is a central decision in distillation design. The minimum reflux reduces column duty but requires many stages; very high reflux reduces stages but greatly increases condenser and reboiler utilities. The optimum balances these opposing costs. Given Data / Assumptions: Continuous distillation with specified product purities and feeds. Fixed separation duty; column hydraulics and tray/packing type chosen. Economic evaluation includes capital and operating costs. Concept / Approach: The total annualised cost comprises capital (column diameter/height, internals) and operating (steam, cooling water, electricity). Increasing reflux ratio generally decreases required stages (lower height, potentially smaller diameter) but increases condenser and reboiler duties. The optimum reflux ratio minimises the sum of these costs. Step-by-Step Solution: Identify minimum reflux (R_min) by McCabe–Thiele or Underwood methods.Estimate stages vs. reflux (Gilliland or rigorous simulation).Compute total cost across candidate reflux ratios; pick the minimum point. Verification / Alternative check: Rules of thumb often choose R_opt ≈ 1.2–1.6 times R_min as a starting point, then refine using economics or simulation sensitivity studies. Why Other Options Are Wrong: Maximum vapour velocity and flooding limits constrain hydraulics but do not alone define the economic optimum. “None of these” is incorrect since a clear economic criterion exists. Minimum stages alone ignores utility costs; the optimum is a trade-off, not an extreme. Common Pitfalls: Focusing solely on stage count reduction or solely on utility savings without total-cost optimisation can lead to uneconomic designs. Final Answer: Total cost trade-off (capital for column vs. utilities for condenser/reboiler)

Question 13

For a multiple-blade paddle agitator handling high-viscosity liquids or pastes, the paddle diameter is about 0.8 of the tank diameter. What is the usual range for blade width expressed as a fraction of paddle diameter?

Accepted Answer

Introduction / Context: Paddle agitators are workhorses for viscous mixing in reactors, crystallisers, and paste kettles. Geometry—diameter, blade width, and clearance—directly impacts power draw, flow pattern, and shear. A standard design parameter is the blade width as a fraction of paddle diameter. Given Data / Assumptions: Paddle diameter D_p ≈ 0.8 D_tank. High-viscosity or paste-like fluids; laminar to transitional regimes. Multiple-blade paddle with flat blades. Concept / Approach: For viscous mixing, broad blades can increase drag excessively without proportionate mixing benefits, while very narrow blades may not produce sufficient bulk motion. Empirical correlations and standard design guides converge on a moderate width range to balance torque and circulation. Step-by-Step Solution: Start from recommended geometrical ratios for paddle impellers.Identify acceptable width band commonly adopted by vendors.Select the 0.10–0.25 D_p range that matches high-viscosity service practice. Verification / Alternative check: Design handbooks consistently show blade width between one-tenth and one-quarter of D_p for paddles, with blade count and baffling tailored to rheology. Why Other Options Are Wrong: 0.30–0.50 and larger: Usually excessive, increasing torque without commensurate flow improvement. 0.02–0.05: Too narrow to move viscous masses effectively, causing poor turnover. Common Pitfalls: Omitting baffles in viscous mixing (leading to vortexing) or oversizing blade width, which can overload drives and shafts. Final Answer: 0.10 to 0.25 of paddle diameter

Question 14

In mechanical fastening practice, rivets are generally specified by which primary dimension?

Accepted Answer

Introduction / Context: Riveted joints, though replaced by welding in many applications, remain relevant in boilers, pressure vessels, and structural work. Correct specification ensures interchangeability and adequate load capacity. The key identifying dimension used in standards and procurement is important for practice and exams alike. Given Data / Assumptions: Standard solid or semi-tubular rivets. Conventional head forms (snap, pan, countersunk, etc.). Concept / Approach: Rivet strength correlates with the cross-sectional area of the shank, which resists shear and tension. Consequently, the shank (body) diameter is the most fundamental specification parameter in standards, drawings, and ordering information; lengths are then chosen to suit grip thickness and head style. Step-by-Step Solution: Identify which dimension governs load capacity: the shank diameter.Review common standards: rivets are cataloged by nominal shank diameter first, then length and head type.Therefore, “Shank diameter” is the correct specification basis. Verification / Alternative check: Design tables list allowable shear per rivet by shank diameter; installation tools and hole sizes are also matched to this diameter, confirming its primacy. Why Other Options Are Wrong: Head diameter and height vary by head style and are secondary. Overall length depends on grip thickness and is selected after diameter. “None of these” is invalid since a clear standard practice exists. Common Pitfalls: Specifying only length without confirming grip range, or ignoring hole tolerance and fit class for the chosen shank diameter. Final Answer: Shank diameter

Question 15

Steam systems: What is the most likely consequence of installing an underdesigned (undersized) steam trap in a line or heat exchanger service?

Accepted Answer

Introduction / Context: Steam traps remove condensate and non-condensables while retaining live steam. Correct sizing is essential to maintain heat-transfer performance and line safety. An underdesigned trap cannot pass the required condensate load during start-up and peak conditions, leading to operational risks. Given Data / Assumptions: Trap is undersized relative to peak condensate formation. Normal industrial steam pressures and start-up surges. Downstream return piping is correctly installed. Concept / Approach: When a trap cannot discharge enough condensate, liquid accumulates upstream. In heat exchangers, this causes reduced heat-transfer area and temperature control issues; in steam mains, slugs of condensate can be accelerated to high velocities, striking fittings and creating damaging water hammer. Step-by-Step Solution: Consider mass balance: condensate formation rate > discharge capacity → accumulation.Accumulation in steam lines produces two-phase flow instabilities and slugging.The most probable outcome is water hammer risk and poor thermal performance. Verification / Alternative check: Manufacturers specify sizing with safety factors for start-up (cold equipment loads). Field experience confirms that undersized traps lead to backed-up condensate and intermittent discharge, not to sustained live-steam waste (which is more typical of failed-open traps). Why Other Options Are Wrong: (a) Live steam waste is associated with oversized or failed-open traps, not undersized ones. (b) Rapid cycling/erosion is more linked to differential-pressure variations or dirt, not primarily undersizing. (d) and (e) contradict real operating behavior and safety concerns. Common Pitfalls: Ignoring start-up loads, neglecting backpressure in return lines, and omitting dirt strainers that protect trap internals from plugging (which can mimic undersizing). Final Answer: It will back up condensate and may cause water hammer in the steam line

Question 16

For a propeller agitator installed in a mixing tank, the impeller diameter is typically what fraction (percent) of the tank diameter, and the normal peripheral speed is about 300–500 m/min?

Accepted Answer

Introduction / Context: Propeller agitators are high-speed axial-flow impellers used widely for blending, solid suspension, and gas dispersion in low-to-moderate viscosity fluids. Correct impeller sizing as a fraction of tank diameter is a standard design starting point that influences flow pattern and power number. Given Data / Assumptions: Propeller-style impeller (marine or hydrofoil variants). Peripheral speed guideline: 300–500 m/min. Baffled cylindrical tank, typical process fluids. Concept / Approach: Axial-flow impellers rely on tip speed and diameter to generate circulation. Industry practice sets the impeller diameter D_i at a moderate fraction of the tank diameter D_t to balance pumping capacity against shaft stresses and mechanical constraints. The common range for D_i/D_t is 0.15–0.30 (15–30%). Step-by-Step Solution: Choose a baseline D_i/D_t between 0.2 and 0.3; refine with process requirements.Check resulting tip speed v = π * D_i * N; target 300–500 m/min.Adjust N (rpm) accordingly while maintaining mechanical limits and avoiding vortexing with proper baffling. Verification / Alternative check: Vendor selection charts and empirical design texts confirm D_i/D_t ≈ 0.2–0.3 for propellers; high-speed service uses smaller diameters, while higher pumping may push to the upper end of the range. Why Other Options Are Wrong: 5–10%: Too small to deliver adequate axial pumping in many tanks. 40–50% or greater: More characteristic of low-speed turbines and paddles, not high-speed propellers. 55–75% or 80–90%: Uncommon and mechanically impractical for propellers. Common Pitfalls: Omitting baffles (leading to swirl and poor mixing) or choosing excessive rpm causing vibration and cavitation at the blade tips. Final Answer: 15 to 30 percent of tank diameter

Question 17

Packed versus plate (tray) towers: Identify the incorrect statement when comparing performance and selection criteria for packed and plate columns.

Accepted Answer

Introduction / Context: Choosing between packed and plate (tray) towers requires considering hydraulics, mass transfer, fouling tendency, thermal effects, and equipment weight. Many rules of thumb exist, but some statements can be misleading without context, especially regarding relative weights and ancillary features such as interstage cooling. Given Data / Assumptions: Similar duty and separation difficulty. Comparable shell sizes and materials. Random/structured packing versus typical sieve/valve/bubble-cap trays. Concept / Approach: Trayed columns allow straightforward interstage cooling/heating, side draws, and liquid sampling; they also tolerate solids better than packed beds that plug. For large temperature swings, trays avoid the risk of packing damage, especially with ceramic or brittle packings. Regarding dry equipment weight, packed columns frequently carry substantial packing mass; therefore, it is not generally correct to assert that a trayed column is “usually much heavier.” Step-by-Step Reasoning: (a) True: Interstage duties are easier on trays than within a continuous packed bed.(b) True: Dispersed solids can foul packing; trays offer better passage and maintenance.(c) Incorrect: Packed columns can be as heavy or heavier due to packing mass; the blanket statement that plate towers are usually much heavier is not reliable.(d) True: Trays preferred where thermal expansion or property changes could crush or settle packing.(e) Overbroad; turndown depends on internals and service, not “always” in favor of packing. Verification / Alternative check: Vendor data for comparable diameter/height show significant packing mass (especially ceramic/metal random or structured packing), sometimes exceeding tray weights per equivalent height. Why Other Options Are Wrong (or Not Best): (a), (b), and (d) reflect accepted design practice. (e) is also questionable; however, option (c) is the single most clearly incorrect statement among the given choices. Common Pitfalls: Assuming “one-size-fits-all” rules; ignoring solids handling and thermal shock; overlooking maintenance access and revamp needs when choosing internals. Final Answer: The total dry weight of a plate tower is usually much greater than that of a dry packed tower designed for the same duty.

Question 18

Gas–liquid absorption (co-current packed tower): Which factors influence the pressure drop through the packed section?

Accepted Answer

Introduction / Context: Pressure drop in packed absorbers affects blower or compressor power, operating costs, and capacity. Understanding how packing properties and operating conditions influence pressure drop guides both design and troubleshooting of gas–liquid contactors. Given Data / Assumptions: Co-current or counter-current principles apply similarly for the packing region behavior. Non-reactive absorption, typical industrial packings. Flooding and loading concepts are relevant. Concept / Approach: Ergun-type correlations and generalized pressure-drop charts (e.g., Sherwood–Lobo–Eckert) show pressure drop depends on packing geometry and specific surface, fluid properties (density, viscosity, surface tension), and superficial velocities or mass fluxes of both phases. Approach to loading/flooding increases holdup and friction, raising pressure drop sharply. Step-by-Step Reasoning: Packing characteristics: smaller, more intricate packings raise surface area but also frictional losses.Fluid properties: higher gas density/viscosity and liquid holdup increase resistance.Flow rates: higher gas or liquid rates increase interfacial shear and wetting, elevating pressure drop; nearing flooding escalates it rapidly. Verification / Alternative check: Generalized pressure-drop charts collapse data across packings using dimensionless groups (e.g., F-factor), confirming multivariable dependence consistent with (a)–(c). Why Other Options Are Wrong: Any single-factor choice underrepresents the multivariate nature of pressure drop. “None of these” contradicts well-established correlations. Common Pitfalls: Extrapolating vendor data beyond recommended loading, ignoring liquid distribution quality (maldistribution can spike local holdup and pressure drop), and overlooking fouling which effectively changes packing geometry. Final Answer: All (a), (b) and (c)

Question 19

Continuous binary distillation: Which of the following is not a graphical method (i.e., it is an analytical method) for computing the theoretical number of stages?

Accepted Answer

Introduction / Context: Determining the theoretical number of stages is fundamental in distillation design. Several classical methods exist: some rely on graphical constructions, while others are analytical or algebraic. Recognising which is which helps in selecting tools and understanding limitations. Given Data / Assumptions: Binary system, constant molal overflow assumptions for the classic graphical methods. Steady-state continuous distillation with specified reflux. Concept / Approach: The McCabe–Thiele method is a classic graphical approach using equilibrium and operating lines on an x–y diagram. The Ponchon–Savarit method is also graphical, employing enthalpy–composition (H–x) diagrams. In contrast, the Sorel–Lewis method formulates analytical stage-by-stage material balance and equilibrium relations to compute the number of stages without a graphical plot. Step-by-Step Reasoning: Identify which methods construct steps on diagrams (graphical): McCabe–Thiele, Ponchon–Savarit.Recognise that Sorel–Lewis employs analytical integration/iteration of stage equations.Therefore, Sorel–Lewis is the non-graphical (analytical) option. Verification / Alternative check: Standard separations textbooks present McCabe–Thiele and Ponchon–Savarit as diagrammatic, whereas Sorel–Lewis is described as an algebraic method predating modern simulations. Why Other Options Are Wrong: McCabe–Thiele and Ponchon–Savarit are graphical by construction. “None of these” is invalid since an analytical option exists. The Gilliland correlation relates stages and reflux and is a graphical/empirical relation used adjunct to McCabe–Thiele, not a primary stage-count method on its own in this context. Common Pitfalls: Applying graphical methods outside their assumptions (e.g., strong non-idealities, significant heat effects) without correction factors or rigorous simulation. Final Answer: Sorel–Lewis method

Question 20

In pressure vessel design, openings (nozzles, manholes, sight glasses) require reinforcement for strength and rigidity. Which type of compensation is considered the most efficient for such openings?

Accepted Answer

Introduction / Context: When a hole is cut in a pressure vessel shell to attach a nozzle, manhole, or sight glass, shell strength is reduced locally. Designers therefore provide 'compensation' or reinforcement to restore the lost metal area so that stresses remain within code limits. Knowing which reinforcement method is most efficient is important for safe and economical fabrication. Given Data / Assumptions: Thin cylindrical or spherical shells under internal pressure. Openings require added reinforcement to meet applicable codes (e.g., area replacement concepts). Efficiency refers to stress distribution quality and reinforcement effectiveness per unit added metal. Concept / Approach: The most efficient reinforcement uses the nozzle neck and adjacent shell as an integral reinforced region (often termed nozzle, hub, or rim type). By thickening the nozzle neck and blending it into the shell, the added metal lies exactly where stresses concentrate, providing superior load transfer compared with external pads or rings. Step-by-Step Solution: Identify reinforcement methods: (i) integral nozzle/rim, (ii) pad/ring plate, (iii) flared-out lip, (iv) non-structural attachments.Recognize efficiency metric: restore area and control peak stresses with minimal added weight.Integral nozzle (nozzle or rim) places material in the highest-stress zone and promotes smooth stress flow.Therefore, the nozzle or rim type is the most efficient. Verification / Alternative check: Codes allow area-replacement using nozzle wall thickness plus a portion of the shell. Experience and analyses show self-reinforced nozzles deliver better stress contours and fatigue resistance than external pads. Why Other Options Are Wrong: Flared out: difficult to fabricate and may not provide optimal stress flow.Fluid in: not a reinforcement method.Ring plate: workable but less efficient than integral reinforcement; can introduce local stress discontinuities. Common Pitfalls: Assuming thicker pads are always better; ignoring nozzle–shell junction stress concentration; overlooking fatigue and cyclic loads. Final Answer: nozzle or rim

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