Q: Cylindrical storage tanks: roof column (internal support) requirements are primarily driven by span. For which tank size category is roof column support typically required?

Introduction / Context: Fixed-roof storage tanks (e.g., cone roof) must support roof dead load, live load (snow, maintenance), and wind uplift. Whether internal columns are needed depends largely on roof span and framing efficiency. Given Data / Assumptions: Conventional atmospheric cylindrical steel tanks. Standard roof types (cone or dome) with typical structural framing. Design per common industrial standards for snow/wind loads. Concept / Approach: As tank diameter increases, roof span and bending moments in roof framing increase rapidly. Beyond a certain diameter, practical roof plate thickness and rafter sizes become excessive without intermediate support. Central columns (or multiple columns) reduce span and member sizes, providing an economical and safe solution for large-diameter tanks. Step-by-Step Solution: Relate roof load effects to span (diameter); larger diameter → larger bending moments.Recognize that small tanks can use self-supporting roofs, but large ones need internal columns.Choose “large diameter tanks.” Verification / Alternative check: Fabricator guidelines specify self-supporting cone roofs up to limited diameters; above these, column-supported roofs are standard. Why Other Options Are Wrong: Small diameter: Span is short; self-supporting roofs are common.Small diameter tall tanks: Height does not govern roof span capacity.All tanks: Overly broad; many small tanks do not require columns. Common Pitfalls: Ignoring corrosion allowance on columns in corrosive service; overlooking interference with mixers or internal floating roofs. Final Answer: large diameter tanks.

Q: For a large high-pressure pipeline, which stress consideration chiefly determines the minimum wall thickness during design?

Introduction / Context: Pressure piping is sized primarily to resist circumferential (hoop) stress from internal pressure. Correctly identifying the governing stress ensures that required wall thicknesses meet code and safety margins for burst and leak integrity under operating and test conditions. Given Data / Assumptions: Long straight run of large-diameter pipe at high internal pressure. Design per standard pressure piping codes with joint efficiency and corrosion allowance considered separately. No unusual external loads beyond typical supports. Concept / Approach: For thin-walled cylinders, internal pressure produces hoop stress σh = p * D / (2 * t) and longitudinal stress σL = p * D / (4 * t). Since σh is twice σL, hoop stress generally governs minimum wall thickness. Codes incorporate allowable stress, weld efficiency, and allowances, but the primary driver remains hoop stress. Step-by-Step Solution: Write hoop stress relation: σh = p * D / (2 * t).Rearrange for thickness: t = p * D / (2 * σ_allow * E) with code factors.Confirm longitudinal stress is lower, thus non-controlling for straight runs. Verification / Alternative check: Code formulas (e.g., Barlow’s equation basis) for pressure design thickness emphasize hoop stress; longitudinal loads are addressed by closures or special cases. Why Other Options Are Wrong: (a) End loads affect local regions and closures, not typical run thickness. (b) Bends and dynamics require reinforcement/support checks, not baseline run thickness. (d) Thermal stresses are important for flexibility but do not set pressure minimum thickness. (e) Torsion is not normally governing for straight pressure runs. Common Pitfalls: Ignoring joint efficiency, corrosion/erosion allowances, or test pressure multipliers; misapplying thick-wall formulas when t/D is small. Final Answer: Circumferential (hoop) wall tension due to internal pressure

Q: Shell-side pressure drop comparison: in a shell-and-tube exchanger, which baffle type typically produces the highest shell-side pressure drop for a given duty?

Introduction / Context: Baffles control shell-side crossflow, heat-transfer coefficient, and tube support. The choice of baffle affects pressure drop, fouling tendency, and vibration. Knowing which baffle produces the highest pressure drop helps balance thermal and hydraulic design targets. Given Data / Assumptions: Comparable shell size and tube bundle; same heat duty and flow rate. Single-phase shell-side flow. Typical cut and spacing practices for each baffle type. Concept / Approach: Segmental baffles force fluid to repeatedly cross the tube bundle at right angles, creating strong crossflow and high turbulence. This enhances heat transfer but also produces higher pressure drop relative to designs that permit more longitudinal flow (e.g., disk-and-ring, orifice, or helical baffles). Step-by-Step Solution: Compare flow patterns: segmental → strong crossflow; disk-and-ring → alternating annular passages; orifice → partial crossflow; helical → continuous spiral, lower pressure drop.For the same duty, segmental baffles yield the highest shell-side ΔP in most standard configurations.Therefore, the baffle type with maximum ΔP is single-segmental. Verification / Alternative check: Thermal rating correlations show segmental baffles achieve high shell-side h at the cost of ΔP, while helical and disk-and-ring reduce ΔP for similar duty. Why Other Options Are Wrong: (a), (c), and (e) provide lower ΔP for equivalent conditions. (d) is incorrect because baffle type strongly influences hydraulics. Common Pitfalls: Ignoring vibration support requirements when reducing ΔP; using identical spacing/cuts across types without re-rating. Final Answer: Single-segmental baffles

Question 1

Turbulent flow in a smooth new pipe (engineering correlations): which expression gives the Fanning friction factor f as a function of Reynolds number NRe in the range ~4×10^3 to 1×10^5?

Accepted Answer

Introduction / Context: Pressure drop predictions in pipelines require a reliable friction factor. For smooth, new pipes with fully developed turbulent flow, empirical correlations provide quick estimates before detailed roughness-based charts (e.g., Moody) are consulted. Given Data / Assumptions: Smooth, new pipe with negligible roughness. Fanning friction factor f is used (note: Darcy–Weisbach factor is 4f). Flow is fully turbulent with Reynolds number roughly between 4×10^3 and 1×10^5. Concept / Approach: The Blasius-type correlation for smooth pipes in terms of the Fanning factor is f = 0.079 * NRe^-0.25. A common source of confusion is the Darcy factor, which would be f_D = 0.316 * NRe^-0.25. Distinguishing which definition is used is crucial to avoid a factor-of-four error. Step-by-Step Solution: Identify the factor requested: Fanning friction factor f.Recall the Blasius correlation for smooth pipes: f = 0.079 * NRe^-0.25.Select the option matching this formula. Verification / Alternative check: Cross-check against Moody chart: for NRe = 10^5 in a smooth tube, Fanning f ≈ 0.003–0.004, consistent with 0.079 * 10^-1.25 ≈ 0.0044. Why Other Options Are Wrong: 0.316 * NRe^-0.25: This is the Darcy factor, not the Fanning factor.0.22 * NRe^0.5: Dimensionally and physically incorrect; friction factor decreases with increasing Re.64 / NRe: Laminar-flow Fanning correlation (f = 16/NRe); not valid for turbulent flow. Common Pitfalls: Mixing Fanning and Darcy conventions; applying smooth-pipe correlations to rough pipes without correction. Final Answer: f = 0.079 * NRe^-0.25

Question 2

Thin cylindrical vessels under internal pressure: if two vessels have the same wall thickness but different diameters, which one can withstand the higher internal pressure before reaching the same hoop stress limit?

Accepted Answer

Introduction / Context: For thin-walled cylinders, the dominant stress from internal pressure is the circumferential (hoop) stress. Understanding how geometry influences allowable pressure is fundamental in preliminary sizing and material selection. Given Data / Assumptions: Same material and same wall thickness t for both vessels. Thin-wall assumption applies (t ≪ d). Internal pressure only; no significant external loads. Concept / Approach: The hoop stress for a thin cylinder is σ_h = p d / (2 t). For a given allowable stress and fixed t, the allowable pressure scales inversely with diameter: p_allow ∝ 1/d. Thus, reducing diameter increases the pressure that can be sustained before reaching the same stress limit. Step-by-Step Solution: Write σ_h = p d / (2 t).For fixed σ_allow and t, solve p = 2 t σ_allow / d.Smaller d → larger p, hence the smaller diameter vessel withstands higher pressure. Verification / Alternative check: Doubling diameter halves allowable pressure at unchanged thickness and allowable stress; this simple proportionality check confirms the conclusion. Why Other Options Are Wrong: Larger dia vessel / larger dia long vessel: Both have higher hoop stress at the same pressure; thus lower allowable pressure for the same thickness.“Same strength irrespective of diameter”: Incorrect; the hoop-stress formula shows explicit dependence on d. Common Pitfalls: Confusing longitudinal with hoop stress; applying thick-wall formulas to thin shells. Final Answer: Smaller dia vessel.

Question 3

Packed or plate column performance metric: in commercial operations, the practical representative values of HETP (height equivalent to a theoretical plate) commonly fall within which approximate range in metres?

Accepted Answer

Introduction / Context: HETP (height equivalent to a theoretical plate) is a convenient way to relate mass transfer efficiency to tower height for both packings and trays (by analogy). Knowing typical ranges helps in quick screening and sanity checks before detailed vendor rating. Given Data / Assumptions: Industrial columns operating away from extremes (no very low liquid rates or very viscous systems). Reasonably designed distributors for packed towers; standard tray hydraulics. Normal surface tensions and moderate relative volatilities. Concept / Approach: For many systems, practical HETP values lie in the sub-metre range. Good random packing or modern trays often deliver HETP roughly 0.4–0.9 m, depending on loading, physical properties, and fouling tendencies. Substantially lower values typically require high-performance structured packings under ideal conditions, while higher values indicate poor contacting, maldistribution, or off-design operation. Step-by-Step Solution: Relate separation duty (number of theoretical stages) to tower height via HETP.Apply typical commercial experience: H ≈ N * HETP with HETP ≈ 0.4–0.9 m.Choose the range that reflects mainstream practice. Verification / Alternative check: Vendor datasheets for common random packings (e.g., 1–2 inch sizes) often report HETP in this neighborhood for hydrocarbon service with good distribution. Why Other Options Are Wrong: 0.1–0.2: Too optimistic for general services; requires exceptional conditions/packings.0.2–0.5: Lower end may occur, but the full practical span is better captured by 0.4–0.9.1.2–1.5: Typically indicates underperforming contact or very difficult systems. Common Pitfalls: Using a single HETP for all loads; ignoring distributor quality which dominates packed-tower efficiency. Final Answer: 0.4–0.9

Question 4

Tube-side convective coefficient in a shell-and-tube exchanger: beyond which approximate Reynolds number does the influence of L/D (tube length-to-diameter ratio) on the inside film coefficient essentially vanish for turbulent flow?

Accepted Answer

Introduction / Context: In internal convection, entry-length effects can make the heat transfer coefficient depend on tube length. Once fully developed turbulent flow is established, the sensitivity to L/D largely disappears, and standard correlations in terms of Reynolds and Prandtl numbers suffice. Given Data / Assumptions: Single-phase flow inside circular tubes. Turbulent regime with conventional fluids (Pr ≈ 0.7–10). Engineering interest in when L/D ceases to matter appreciably. Concept / Approach: Hydrodynamic and thermal entry lengths are short in turbulent flow compared with laminar flow, and they scale weakly with Reynolds number. Practical design practice treats L/D influence as negligible beyond a sufficiently high Reynolds number where the bulk of the tube length is fully developed. Step-by-Step Solution: Recognize that for Re well into turbulence, Nu correlations (e.g., Dittus–Boelter) ignore L/D.Adopt a conservative threshold Re ≈ 10,000 beyond which entrance effects are minimal for typical L/D in exchangers.Hence, choose 10,000 as the point where L/D influence effectively vanishes. Verification / Alternative check: Comparisons of Sieder–Tate and Dittus–Boelter correlations show modest differences for Re > 10^4, supporting negligible entry-length impact on hi over normal exchanger L/D values. Why Other Options Are Wrong: 1000 / 3000 / 5000: May still exhibit measurable developing-flow effects, particularly for shorter tubes or higher Prandtl fluids. Common Pitfalls: Confusing hydrodynamic entrance effects with thermal ones; extending this rule to laminar/transitional regimes where L/D is important. Final Answer: 10000

Question 5

Vessel supports: for which type of equipment is a skirt support the most appropriate and commonly used solution from structural and thermal viewpoints?

Accepted Answer

Introduction / Context: Process vessels require supports that safely transmit loads (weight, wind, seismic, thermal) to foundations. Support selection depends on geometry, size, and operating conditions. Skirt supports are a standard choice in many plants. Given Data / Assumptions: Cylindrical pressure or storage vessels. Outdoor installation subject to wind and thermal expansion. Need for access and nozzle clearance near the bottom head. Concept / Approach: A skirt support is a cylindrical shell welded to the vessel bottom head, transferring loads axially to a base ring and anchor bolts. It provides excellent resistance to overturning moments from wind/seismic on tall vertical equipment while keeping the shell free of local leg loads. It also accommodates thermal expansion via a defined hot-to-cold interface and allows insulation clearance. Step-by-Step Solution: Identify vessel category needing overturning resistance: tall vertical columns, reactors, and towers.Select support that gives strong moment capacity and clean load path: skirt support.Conclude that “tall vertical” vessels are the best match. Verification / Alternative check: Design standards and vendor catalogues pair skirts with columns/towers, saddles with horizontal vessels, and legs/lugs for small vertical drums. Why Other Options Are Wrong: Small/large horizontal: Better served by saddles.Thick walled: Wall thickness alone does not dictate the support type; geometry and moment loads do. Common Pitfalls: Locating heavy nozzles on skirts without considering differential expansion; underestimating anchor bolt design for overturning. Final Answer: tall vertical

Question 6

Agitated tanks and baffles: under which condition is it acceptable to eliminate baffles because swirling is naturally suppressed by fluid properties?

Accepted Answer

Introduction / Context: Baffles prevent vortex formation and tangential swirling in mechanically agitated tanks. However, the need for baffles depends on fluid rheology and operating conditions. Very viscous liquids exhibit such high damping that swirling is minimal even without baffles. Given Data / Assumptions: Newtonian liquids unless otherwise noted. Standard radial or axial-flow impellers. Goal is to identify the regime where baffles can be omitted without compromising mixing objectives. Concept / Approach: At high viscosity, Reynolds number is very low; flow is laminar and dominated by viscous forces. Tangential circulation is weak and a stable free-surface vortex does not form easily. Designers commonly eliminate baffles above a high-viscosity threshold to reduce fabrication complexity and cleaning issues. Step-by-Step Solution: Relate need for baffles to Reynolds number and vortex tendency.Note that for μ ≳ 600 poise, viscous damping is so strong that baffles are unnecessary in most cases.Select the high-viscosity option. Verification / Alternative check: Mixing handbooks list rules of thumb: install baffles for low–moderate viscosities; omit for very high viscosities where laminar impellers (helical ribbon, anchor) are used. Why Other Options Are Wrong: Low viscosity: Needs baffles to prevent vortexing.Large diameter tanks: Size alone does not eliminate swirling; baffles are still beneficial.None of these: Incorrect because high viscosity is a valid case. Common Pitfalls: Ignoring non-Newtonian behavior; assuming high viscosity always guarantees mixing quality (power and impeller selection still matter). Final Answer: high viscosity liquids (> 600 poise).

Question 7

Log-mean temperature difference (LMTD) versus other means: for heat exchangers with two inlet temperatures, how does LMTD compare to the arithmetic and geometric means across typical flow arrangements?

Accepted Answer

Introduction / Context: The logarithmic mean temperature difference (LMTD) is the exact temperature driving force for true countercurrent or cocurrent exchangers with constant specific heats and no phase change. Understanding its relation to arithmetic and geometric means offers quick consistency checks during design. Given Data / Assumptions: Two temperature differences at the ends: ΔT1 and ΔT2, both positive. No internal heat sources/sinks; constant properties. Standard cocurrent or countercurrent arrangements. Concept / Approach: For positive ΔT1 and ΔT2, the logarithmic mean LM(ΔT1, ΔT2) lies between the geometric mean GM and the arithmetic mean AM. Inequality: AM ≥ LM ≥ GM. This stems from the properties of means and the convexity of the logarithm function used in the LMTD definition. Step-by-Step Solution: Define LMTD = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2).Recall the inequality among means: AM ≥ LM ≥ GM for positive unequal values.Conclude LMTD is less than AM but greater than GM. Verification / Alternative check: Test with ΔT1 = 40, ΔT2 = 20: AM = 30; GM ≈ 28.28; LMTD ≈ 28.85 → indeed GM < LMTD < AM. Why Other Options Are Wrong: “Always more than AM”: violates basic inequality of means.“May be either more or less”: incorrect—ordering is fixed for positive ΔTs. Common Pitfalls: Using end temperatures instead of end temperature differences; applying LMTD correction factors (F_T) without verifying flow configuration. Final Answer: is always less than arithmetic mean value, but more than geometric mean value.

Question 8

Cylindrical storage tanks: roof column (internal support) requirements are primarily driven by span. For which tank size category is roof column support typically required?

Accepted Answer

Introduction / Context: Fixed-roof storage tanks (e.g., cone roof) must support roof dead load, live load (snow, maintenance), and wind uplift. Whether internal columns are needed depends largely on roof span and framing efficiency. Given Data / Assumptions: Conventional atmospheric cylindrical steel tanks. Standard roof types (cone or dome) with typical structural framing. Design per common industrial standards for snow/wind loads. Concept / Approach: As tank diameter increases, roof span and bending moments in roof framing increase rapidly. Beyond a certain diameter, practical roof plate thickness and rafter sizes become excessive without intermediate support. Central columns (or multiple columns) reduce span and member sizes, providing an economical and safe solution for large-diameter tanks. Step-by-Step Solution: Relate roof load effects to span (diameter); larger diameter → larger bending moments.Recognize that small tanks can use self-supporting roofs, but large ones need internal columns.Choose “large diameter tanks.” Verification / Alternative check: Fabricator guidelines specify self-supporting cone roofs up to limited diameters; above these, column-supported roofs are standard. Why Other Options Are Wrong: Small diameter: Span is short; self-supporting roofs are common.Small diameter tall tanks: Height does not govern roof span capacity.All tanks: Overly broad; many small tanks do not require columns. Common Pitfalls: Ignoring corrosion allowance on columns in corrosive service; overlooking interference with mixers or internal floating roofs. Final Answer: large diameter tanks.

Question 9

In tray hydraulics for distillation, what operating condition most commonly causes back-trapping (reverse liquid flow under the downcomer skirt or across the tray)? Provide the primary cause without assuming mechanical damage.

Accepted Answer

Introduction / Context: Back-trapping on distillation trays is an undesirable hydraulic condition in which liquid flows backward under a downcomer skirt or across the deck, upsetting mass transfer and tray efficiency. Understanding the root causes—especially process operating variables such as vapor rate and liquid gradient—is essential for troubleshooting columns and preventing capacity loss or flooding. Given Data / Assumptions: Conventional crossflow tray (sieve, valve, or bubble-cap) with a downcomer and outlet weir. Column is mechanically intact; no collapsed internals. Back-trapping refers to reverse liquid flow driven by excessive head differences. Concept / Approach: Liquid flows by gravity across the tray from inlet to outlet, passing over a weir into the downcomer. A large liquid head difference (high gradient) between adjacent regions creates a driving force that can push liquid under skirts or through clearances in the wrong direction, especially when local vapor distribution is uneven. The main controllable contributor is excessive liquid gradient caused by high froth heights, maldistribution, or too much residence time on the deck. Step-by-Step Solution: Recognize that liquid gradient = difference in froth/liquid head from one side of the tray to the other.Back-trapping occurs when this head exceeds sealing capacity at skirts/clearances, pushing liquid backward.Conditions that increase gradient include high weir loads, poor distribution, or incorrect bubbling area leading to localized high froth depth.Therefore the primary cause is excessive liquid gradient over the tray. Verification / Alternative check: Field observations show that leveling the tray, adjusting vapor/liquid rates, or reducing weir load (thus head) eliminates back-trapping without changing reflux ratio alone—supporting the head-driven mechanism. Why Other Options Are Wrong: (a) Low vapor velocity tends to cause weeping rather than back-trapping. (b) High vapor velocity increases entrainment and jet flooding, not primarily reverse liquid flow. (d) Low reflux ratio reduces liquid load and gradient, often helping, not causing back-trapping. (e) A very small weir height can affect sealing, but the dominant driver for back-trapping is head gradient across the tray. Common Pitfalls: Confusing back-trapping with weeping; blaming vapor rate alone without measuring liquid head; overlooking tray leveling and downcomer seal design. Final Answer: Excessive liquid gradient (large liquid head difference) over the tray

Question 10

Sieve plate vs. bubble-cap plate: which statement about weir design and downcomer residence time is incorrect for practical distillation column design?

Accepted Answer

Introduction / Context: Tray weir design—height and length—affects liquid head, residence time, and froth behavior. While sieve and bubble-cap trays share many hydraulic principles, certain design choices differ because cap trays rely on positive vapor sealing through slots and often operate with higher liquid depths for stable performance. Given Data / Assumptions: Industrial columns operating near atmospheric to moderate pressures. Comparable tray spacings and capacities. Standard design practices for weir height: sieve plates typically lower than bubble-cap plates. Concept / Approach: Bubble-cap trays employ risers and caps that force vapor through submerged slots. To maintain a good liquid seal and reduce vapor backflow through clearances, cap trays frequently use a higher weir height than sieve trays. Weir length and downcomer sizing target similar residence times for liquid disengagement, so broad similarity can be expected there, but equal weir height across types is not a safe general rule. Step-by-Step Solution: Compare weir height norms: bubble-cap often 50–150 mm; sieve commonly lower.Assess downcomer and residence: both tray types require adequate seal and disengagement, leading to similar residence criteria.Weir length is a geometric parameter set by column diameter and hydraulics and can be similar between types.Thus, the claim of “same weir height” for both is incorrect. Verification / Alternative check: Pilot plant data and vendor guidelines confirm that higher weir heights are common on bubble-cap plates to promote sealing across a wider turndown and to stabilize froth depth. Why Other Options Are Wrong: (a) Reasonable—residence time aims are similar. (b) Plausible—length is often governed by column geometry. (d) True—bubble-cap weirs are typically higher. (e) True—both height and length are selected to meet sealing and disengagement requirements. Common Pitfalls: Assuming a single “best” weir height independent of tray type; ignoring tray turndown requirements; confusing length with height. Final Answer: Weir height on a bubble-cap plate is the same as that on a sieve plate

Question 11

For a large high-pressure pipeline, which stress consideration chiefly determines the minimum wall thickness during design?

Accepted Answer

Introduction / Context: Pressure piping is sized primarily to resist circumferential (hoop) stress from internal pressure. Correctly identifying the governing stress ensures that required wall thicknesses meet code and safety margins for burst and leak integrity under operating and test conditions. Given Data / Assumptions: Long straight run of large-diameter pipe at high internal pressure. Design per standard pressure piping codes with joint efficiency and corrosion allowance considered separately. No unusual external loads beyond typical supports. Concept / Approach: For thin-walled cylinders, internal pressure produces hoop stress σh = p * D / (2 * t) and longitudinal stress σL = p * D / (4 * t). Since σh is twice σL, hoop stress generally governs minimum wall thickness. Codes incorporate allowable stress, weld efficiency, and allowances, but the primary driver remains hoop stress. Step-by-Step Solution: Write hoop stress relation: σh = p * D / (2 * t).Rearrange for thickness: t = p * D / (2 * σ_allow * E) with code factors.Confirm longitudinal stress is lower, thus non-controlling for straight runs. Verification / Alternative check: Code formulas (e.g., Barlow’s equation basis) for pressure design thickness emphasize hoop stress; longitudinal loads are addressed by closures or special cases. Why Other Options Are Wrong: (a) End loads affect local regions and closures, not typical run thickness. (b) Bends and dynamics require reinforcement/support checks, not baseline run thickness. (d) Thermal stresses are important for flexibility but do not set pressure minimum thickness. (e) Torsion is not normally governing for straight pressure runs. Common Pitfalls: Ignoring joint efficiency, corrosion/erosion allowances, or test pressure multipliers; misapplying thick-wall formulas when t/D is small. Final Answer: Circumferential (hoop) wall tension due to internal pressure

Question 12

Shell-side pressure drop comparison: in a shell-and-tube exchanger, which baffle type typically produces the highest shell-side pressure drop for a given duty?

Accepted Answer

Introduction / Context: Baffles control shell-side crossflow, heat-transfer coefficient, and tube support. The choice of baffle affects pressure drop, fouling tendency, and vibration. Knowing which baffle produces the highest pressure drop helps balance thermal and hydraulic design targets. Given Data / Assumptions: Comparable shell size and tube bundle; same heat duty and flow rate. Single-phase shell-side flow. Typical cut and spacing practices for each baffle type. Concept / Approach: Segmental baffles force fluid to repeatedly cross the tube bundle at right angles, creating strong crossflow and high turbulence. This enhances heat transfer but also produces higher pressure drop relative to designs that permit more longitudinal flow (e.g., disk-and-ring, orifice, or helical baffles). Step-by-Step Solution: Compare flow patterns: segmental → strong crossflow; disk-and-ring → alternating annular passages; orifice → partial crossflow; helical → continuous spiral, lower pressure drop.For the same duty, segmental baffles yield the highest shell-side ΔP in most standard configurations.Therefore, the baffle type with maximum ΔP is single-segmental. Verification / Alternative check: Thermal rating correlations show segmental baffles achieve high shell-side h at the cost of ΔP, while helical and disk-and-ring reduce ΔP for similar duty. Why Other Options Are Wrong: (a), (c), and (e) provide lower ΔP for equivalent conditions. (d) is incorrect because baffle type strongly influences hydraulics. Common Pitfalls: Ignoring vibration support requirements when reducing ΔP; using identical spacing/cuts across types without re-rating. Final Answer: Single-segmental baffles

Question 13

For incompressible flow in a circular pipe at fixed capacity (constant volumetric flow rate), how does required head (frictional head loss) vary with pipe diameter D, assuming similar roughness and length?

Accepted Answer

Introduction / Context: Sizing process lines requires understanding how frictional head loss depends on diameter at a set flow rate. This relation drives energy consumption and pumping cost and explains why larger diameters can dramatically reduce head and power for the same capacity. Given Data / Assumptions: Single-phase, incompressible liquid; steady flow. Circular pipe of length L and diameter D; similar roughness. Constant volumetric flow rate Q. Concept / Approach: Use the Darcy–Weisbach equation: h_f = f * (L/D) * (V^2 / (2g)). At fixed Q, velocity V = Q / A and A ∝ D^2, so V ∝ 1/D^2 and V^2 ∝ 1/D^4. Substituting gives h_f ∝ (L/D) * (1/D^4) = L * 1/D^5 (neglecting the weak dependence of f on Reynolds number for the main trend). Thus, at constant capacity, frictional head varies approximately as 1/D^5—an extremely strong sensitivity. Step-by-Step Solution: Start: h_f = f * (L/D) * (V^2 / (2g)).With Q fixed, V = 4Q / (π D^2) → V^2 ∝ 1/D^4.Therefore h_f ∝ (1/D) * (1/D^4) = 1/D^5 (dominant dependence). Verification / Alternative check: Engineering nomographs and pump system curves show steep head reduction with increased diameter at constant Q, consistent with ≈ D^−5 scaling in turbulent regimes when friction factor changes modestly. Why Other Options Are Wrong: (a) and (b) underestimate the dependence; (d) inverts the trend; (e) contradicts fundamental hydraulics. Common Pitfalls: Forgetting that friction factor f can change with Re; ignoring minor losses (they follow similar velocity-squared trends); applying the result to compressible gas without correction. Final Answer: Proportional to 1/D^5

Question 14

Pressure vessel shell design: if weld joint efficiency is 1.0 for longitudinal seams (parallel to the axis) and 0.8 for circumferential (girth) seams, which efficiency should be used in the shell thickness formula for an internally pressurised cylin…

Accepted Answer

Introduction / Context: For internally pressurised cylindrical shells, the governing stress for required thickness is usually circumferential (hoop) stress. The associated limiting joint is the longitudinal seam because it is aligned parallel to the axis and is stressed by hoop tension. Codes therefore require the longitudinal seam joint efficiency in the thickness formula. Given Data / Assumptions: Thin-wall cylinder under internal pressure. Joint efficiencies: longitudinal seam = 1.0; circumferential (girth) seam = 0.8. Standard code formula for shell thickness includes joint efficiency E. Concept / Approach: Hoop stress σh = p * D / (2 * t) acts to separate the shell along a longitudinal plane; thus the longitudinal seam carries hoop stress and dictates the shell’s pressure integrity. The joint efficiency E used in the formula must correspond to the seam stressed by hoop tension—i.e., the longitudinal seam efficiency. If longitudinal E is larger than the girth seam’s E, shell thickness is set by E = 1.0, while girth joints are checked separately for axial stress and quality. Step-by-Step Solution: Identify the governing stress: hoop stress.Map governing stress to seam orientation: hoop tension → longitudinal seam.Use E = E_longitudinal = 1.0 in the thickness formula; verify girth seam for axial stress and joint quality. Verification / Alternative check: Code commentary and textbooks align the weld efficiency in shell equations with the seam parallel to the axis because it restrains hoop separation. Why Other Options Are Wrong: (a) Uses the girth seam’s E, not governing for hoop. (b) and (d) mix efficiencies without basis. (e) ignores code requirements and reality of weld quality. Common Pitfalls: Confusing which seam is stressed by which principal stress; forgetting separate checks for heads and girth seams; neglecting corrosion allowance. Final Answer: 1.0 (longitudinal seam efficiency)

Question 15

Relative plate thicknesses in vertical storage tanks: how do the bottom and roof plate thicknesses typically compare with the cylindrical shell thickness?

Accepted Answer

Introduction / Context: Atmospheric and low-pressure vertical storage tanks are designed so that the cylindrical shell sustains hydrostatic pressure and wind/seismic loads, while the bottom and roof primarily provide containment and closure. Recognizing the typical thickness hierarchy helps in preliminary design and cost estimation. Given Data / Assumptions: Vertical, cylindrical storage vessels for liquids at near-ambient conditions. Bottom plates resting on a foundation or annular ring; roof plates forming a fixed roof (e.g., cone or dome). No special vacuum or pressure design beyond normal venting. Concept / Approach: The shell experiences the highest membrane stresses from hydrostatic head and environmental loads, so it generally requires greater thickness. The roof carries comparatively small loads (self-weight, occasional snow/wind), and the bottom is supported by the foundation. Therefore, roof and bottom plates are typically thinner, while shell courses often get thicker toward the base where liquid head is greatest. Step-by-Step Solution: Identify major load paths: shell → hydrostatic and lateral loads.Bottom → supported; thickness driven by corrosion and local support details.Roof → light loads; thickness driven by stiffness and corrosion allowance.Conclusion: bottom and roof plates are usually thinner than shell courses. Verification / Alternative check: Common standards (e.g., API 650 practice) show graduated shell thickness with typically lighter roof/bottom plates subject to minimum practical and corrosion allowances. Why Other Options Are Wrong: (a) and (e) contradict common practice; (c) ignores graduated shell thickness; (d) overstates variability—while materials and temperature matter, the usual pattern remains thinner roof/bottom. Common Pitfalls: Over-thickening the roof and bottom without corrosion rationale; ignoring bottom annular plate requirements near shell for settlement and corrosion. Final Answer: Both are usually thinner than the shell

Question 16

Comparing operating pressures: how does the typical bubble-cap diameter used in high-pressure distillation columns compare to that used in similar vacuum columns?

Accepted Answer

Introduction / Context: Bubble-cap size affects slot area, vapor distribution, mechanical robustness, and hydraulic performance. Operating pressure changes vapor density and volumetric rates, which in turn influence appropriate cap dimensions for stable tray operation without excessive pressure drop or maldistribution. Given Data / Assumptions: Comparing otherwise similar services and column diameters. High-pressure service has higher vapor density and lower volumetric flow for the same mass rate. Mechanical constraints require adequate thickness and rigidity of caps. Concept / Approach: At higher pressure, for the same mass flow, vapor volumetric flow is smaller, so less slot area is needed to maintain target vapor velocities. Designers therefore can use smaller bubble caps (or fewer/lower slot area) to achieve the desired vapor distribution and froth. Conversely, under vacuum, high volumetric flows require larger cap diameters and more open area to avoid excessive jet velocities and pressure drop. Step-by-Step Solution: Relate vapor volumetric rate to pressure: higher pressure → higher density → lower volume flow.Target slot velocity and pressure drop guide required open area.Thus, caps in high-pressure service can be smaller to provide the correct hydraulic performance. Verification / Alternative check: Vendor tray sizing charts show cap diameter/open area trending downward with increased operating pressure for the same capacity objective. Why Other Options Are Wrong: (b) Opposite to volume-flow logic; (c) ignores pressure effects; (d) and (e) over-simplify—weir height and metallurgy matter but do not solely determine cap size. Common Pitfalls: Forgetting that density changes with pressure alter vapor velocities; using vacuum-service cap sizes at pressure leads to over-capacity, maldistribution, or high ΔP. Final Answer: Smaller in high-pressure columns

Question 17

Packed towers using Pall rings: redistributors are typically installed every 6 m or 5–10 times the column diameter (whichever is less). What is the recommended maximum packing size relative to column diameter?

Accepted Answer

Introduction / Context: Random packing size selection balances pressure drop, capacity, and mass-transfer efficiency. Oversized packing relative to the column diameter causes wall effects and poor liquid distribution, while undersized packing increases pressure drop and risk of flooding. Given Data / Assumptions: Pall ring random packing in gas–liquid service. Reasonable distributor quality; redistributors installed per guidance (6 m or 5–10 D). Standard industrial turndown and fouling considerations. Concept / Approach: To maintain an adequate number of pieces across the cross-section and avoid channeling, the maximum packing size is limited to a small fraction of the column diameter. A widely applied rule is to keep packing size below roughly one-tenth to one-fifteenth of the column diameter, ensuring many packing elements span the cross-section for good distribution and efficiency. Step-by-Step Solution: Relate packing size to column diameter to minimize wall/channeling effects.Select maximum size ≈ D/10 to D/15 to ensure sufficient count across the area.Use redistributors to correct inevitable maldistribution over height. Verification / Alternative check: Packed tower design charts and vendor catalogs recommend limiting element size to about 0.07–0.10 D for most services, aligning with the 1/10–1/15 guideline. Why Other Options Are Wrong: (b) Too large—risk of severe maldistribution; (c) may be overly small for economy; (d) unrealistic; (e) false—diameter matters for packing size selection. Common Pitfalls: Ignoring distributor quality; assuming vacuum service allows arbitrarily large packing; neglecting fouling tendencies when selecting size. Final Answer: About 1/10 to 1/15 of the column diameter

Question 18

Cooling water selection in heat exchangers: which single property of liquid water most strongly explains why it is the most widely used industrial coolant?

Accepted Answer

Introduction / Context: Choosing an efficient, readily available coolant is central to heat exchanger design in chemical and process industries. Water is almost universally preferred where freezing, scaling, or corrosion risks can be managed. This question asks which single thermophysical property most strongly explains that preference and ties directly to basic heat transfer principles and energy balances used by engineers during cooling-water system design. Given Data / Assumptions: Aqueous cooling water at near-ambient conditions is compared with other potential coolants. Standard metallic heat-exchanger surfaces and typical industrial temperature ranges are assumed. We focus on the dominant property governing heat-storage capacity per unit mass. Concept / Approach: For sensible cooling or heating, the thermal energy change is Q = m * Cp * ΔT, where Cp is the specific heat at constant pressure. A higher Cp means a given mass flow rate can carry more heat per degree of temperature change. Among common, safe, inexpensive liquids, liquid water has an unusually high Cp, enabling smaller flow rates or smaller heat-transfer areas for the same duty, often outweighing other considerations when water quality is acceptable. Step-by-Step Solution: Recognize that coolant selection for sensible heat removal is governed primarily by Q = m * Cp * ΔT.Compare typical Cp values: water's Cp is high relative to most oils and many other liquids.Conclude that high specific heat is the decisive property explaining its widespread use. Verification / Alternative check: In practical exchanger sizing, a higher Cp reduces required mass flow for a fixed duty and temperature rise, lowering pumping power and pipe sizes. Where corrosion or fouling is controlled (materials selection, treatment), water typically provides the best overall economics. Why Other Options Are Wrong: Low corrosiveness: Untreated water can be corrosive; corrosion control is managed via materials and chemistry rather than being inherently “low.” Low dirt factor: Fouling risk with water exists; treatment and filtration mitigate it. Low viscosity: Water's viscosity is helpful for pumping, but Cp dominates heat-carrying capacity. Common Pitfalls: Confusing ease of pumping or availability with the fundamental thermophysical driver of heat capacity; overlooking water quality management requirements (scaling, microbiological control). Final Answer: High specific heat

Question 19

Tray column performance: which of the following statements about plate (tray) efficiency and spacing is incorrect?

Accepted Answer

Introduction / Context: Tray (plate) efficiency summarizes how closely real mass transfer approaches equilibrium in distillation/absorption columns. It depends on hydrodynamics: vapor and liquid contact time, dispersion, entrainment, weeping, and geometry (weirs, hole size, spacing). This item asks you to identify if any of the listed heuristics are incorrect, reflecting standard design and operating behavior of trayed columns. Given Data / Assumptions: Sieve/valve/bubble-cap trays with conventional downcomers. Non-foaming or mildly foaming systems within normal operating ranges. “Efficiency” refers to overall or Murphree-like tendencies, not a single universal constant. Concept / Approach: Tray efficiency tends to rise with vapor rate up to an optimum before entrainment/flooding degrade performance. Adequate liquid depth over active area improves vapor dispersion and contact, especially when initial depth is shallow. Plate spacing must avoid excessive vapor velocities that cause carryover and poor contacting; too tight spacing often reduces disengagement and hurts efficiency. Step-by-Step Solution: Evaluate (a): Rising vapor rate generally increases mass-transfer driving/contact until loading/entrainment limits.Evaluate (b): More submergence above orifices/slots promotes dispersion and suppresses weeping; the benefit is notable when initial depth is low (< ~1 inch).Evaluate (c): Small spacing can force high vapor velocities and poor disengagement, hurting efficiency.Therefore no statement is wrong; select “None of these.” Verification / Alternative check: Design heuristics from tray vendors/handbooks show efficiency improvements with moderate vapor rates and proper liquid head. Typical plate spacing choices (e.g., 18–24 inches) ensure adequate disengagement and efficiency. Why Other Options Are Wrong (as “wrong” choices): (a) is consistent with practice up to the entrainment limit. (b) reflects common experience: shallow heads underperform; increasing to a reasonable head often improves contacting. (c) is a known hydrodynamic limitation of overly tight spacing. Common Pitfalls: Assuming efficiency rises indefinitely with vapor rate (it does not), or that deeper liquid is always better (excessive head increases pressure drop and may cause other limits). Final Answer: None of these.

Question 20

Long-tube vertical (LTV) evaporator design checks: which statement is incorrect for typical LTV geometry and operation?

Accepted Answer

Introduction / Context: Long-tube vertical evaporators are workhorses for concentrating relatively clean liquids at moderate temperature differences. Understanding their geometry and normal operating levels is essential for sizing, pressure-drop estimation, and boiling behavior (nucleate vs. film). This question tests recognition of standard LTV features and typical ranges found in practice and handbooks. Given Data / Assumptions: Conventional LTV with a steam-heated shell and liquor boiling inside vertical tubes. Standard industrial scales matching common design references. Moderate fouling and non-extreme viscosities. Concept / Approach: LTVs generally use relatively small-diameter tubes (centimeters) and lengths of a few meters to encourage vigorous two-phase flow and high heat-transfer coefficients. Steam on the shell and liquor inside tubes is the canonical arrangement. Maintaining liquor level around one-third to one-half of tube height ensures proper boiling zone development while preventing dryout at the tube top and avoiding excessive static head. Step-by-Step Solution: Check (a): Typical tube sizes 3–6 cm by 3–6 m are consistent with standard LTV practice.Check (b): Steam-to-shell and liquor-in-tubes is the common configuration.Check (c): Liquid level maintained at roughly 1/3–1/2 tube height is a widely cited operating guideline.Thus none of the statements are wrong; select “None of these.” Verification / Alternative check: Textbook schematics and vendor literature show similar dimensions and level recommendations to foster stable boiling and good heat transfer with manageable pressure drop. Why Other Options Are Wrong (as “wrong” choices): Options (a), (b), and (c) are each correct statements for typical LTV designs. Common Pitfalls: Confusing LTV with short-tube or falling-film evaporators; reversing the placement of steam/liquor; misinterpreting the level guidance as an exact value rather than a practical range. Final Answer: None of these.

Process Equipment and Plant Design Questions