Question 1

Column tray hydraulics: The main purpose of providing stepping on fractionation/absorption trays is to ________.

Accepted Answer

Introduction:Tray design must accommodate specified vapor and liquid loads without flooding or weeping. “Stepping” (multi-pass or stepped trays) is one of several layout strategies used when large liquid rates must traverse each stage while maintaining adequate contacting area and controllable liquid gradients. Given Data / Assumptions: Conventional cross-flow trays (sieve/valve/bubble-cap types). High liquid throughput relative to column diameter. Objective: maintain efficiency without excessive froth height or weir loading. Concept / Approach:When liquid rate is high, a single pass across the tray can yield too short a path, excessive velocity, and maldistribution. Stepped or multi-pass arrangements split the liquid into parallel paths, lowering path length and local velocities, improving froth uniformity, and keeping the tray within hydraulic limits. This is distinct from adjusting weir heights or downcomer areas alone. Step-by-Step Solution:Identify the limitation: high L requires larger active area and manageable velocities.Apply stepping/multi-pass trays to divide the flow and reduce hydraulic gradient.Result: improved capacity and operation at large liquid flows. Verification / Alternative check:Tray vendor catalogs show multi-pass trays specified specifically for high-L services to maintain efficiency and capacity. Why Other Options Are Wrong: Residence time/pressure drop: may change as a consequence but are not the primary purpose. “Improve flow condition” is vague; the specific driver is large liquid load. Lowering weir height is a separate hydraulic adjustment. Common Pitfalls:Attempting to handle very high liquid loads by only increasing downcomer area; tray active area must also be managed with layout changes. Final Answer:facilitate handling of large liquid flow rate

Question 2

Packed tower hydraulics (preloading region): How does pressure drop Δp vary with superficial gas mass velocity G?

Accepted Answer

Introduction:Understanding how pressure drop scales with gas throughput in packed towers is crucial for capacity checks and energy estimates. In the preloading (non-flooding) regime with good liquid distribution, the pressure drop follows predictable correlations derived from momentum balance and empirical fits (e.g., generalized pressure drop correlations). Given Data / Assumptions: Packed absorption/stripping tower operating below loading/flooding. Clean service; negligible fouling. Liquid rate held constant while gas rate varies. Concept / Approach:Inertial losses dominate in the preloading region, giving a quadratic dependence of pressure drop on gas mass velocity: Δp ∝ G^2. This mirrors frictional losses in many turbulent flows where dynamic pressure scales with velocity squared. As flooding is approached, the relationship becomes steeper due to interaction with liquid holdup and maldistribution. Step-by-Step Solution:Use generalized packed-bed correlation forms where friction factor and Re terms lead to Δp ∝ G^2 when other variables are fixed.Confirm that operation is below loading so liquid holdup changes are modest.Conclude that Δp varies approximately with the square of G. Verification / Alternative check:Packed-bed Ergun-type relations and vendor charts show nearly quadratic pressure-drop scaling in this region. Why Other Options Are Wrong: Linear or square-root dependence understates the inertial contribution. Independence from G is physically incorrect. Inverse dependence contradicts frictional flow behavior. Common Pitfalls:Extrapolating the quadratic law into the loading/flooding regime without accounting for increased holdup and entrainment. Final Answer:Δp = G^2

Question 3

Impeller scaling at constant power input (turbulent regime): If impeller diameter Di is increased by 20%, by what factor must the speed N be decreased to keep power constant?

Accepted Answer

Introduction:In fully turbulent mixing with constant power number (Np), the impeller power draw scales as P ∝ ρ * N^3 * Di^5. Designers frequently adjust diameter and speed to meet power constraints or to retrofit vessels. This problem asks how to adjust speed when diameter increases by 20% while keeping P constant. Given Data / Assumptions: Fully turbulent regime; Np is constant. Fluid density ρ constant; no aeration effects. Initial power P held constant after diameter change. Concept / Approach:With P ∝ N^3 * Di^5, holding P constant implies N^3 * Di^5 = constant. If Di,new = 1.2 * Di,old, then N_new^3 * (1.2^5) * Di,old^5 = N_old^3 * Di,old^5. Canceling common terms gives N_new = N_old / (1.2)^(5/3). Thus, speed must be decreased by a factor (1.2)^(5/3). Step-by-Step Solution:Start with P ∝ N^3 * Di^5.Set P_new = P_old ⇒ N_new^3 * Di_new^5 = N_old^3 * Di_old^5.Substitute Di_new = 1.2 * Di_old.Solve: N_new = N_old / (1.2)^(5/3). Verification / Alternative check:Dimensional consistency and known scale-up rules (constant tip speed or constant power per volume) align with this result; here it is constant power with constant Np. Why Other Options Are Wrong: (1.2)^(2/3) or (3/5) mismatch the required exponent 5/3 from P-scaling. (1.2)^(3/2) or (1.2)^(1/2) are unrelated to the N^3 * Di^5 relationship. Common Pitfalls:Using constant tip-speed (N * Di) instead of constant power scaling; they lead to different exponents and design outcomes. Final Answer:(1.2)^(5/3)

Question 4

Fouling factor in heat exchanger design: On which parameters does the fouling factor chiefly depend?

Accepted Answer

Introduction:Fouling adds thermal resistance, raises pressure drop, and shortens run length in heat exchangers. The “fouling factor” is a design allowance based on expected deposit formation. Recognizing what drives fouling helps select velocities, materials, and cleaning schedules. Given Data / Assumptions: Conventional shell-and-tube or plate exchangers in process service. Fouling types include particulate deposition, chemical scaling, biofouling, and corrosion products. Concept / Approach:Fouling severity depends on the fluid’s chemical tendencies (e.g., scaling propensity), the amount and character of suspended matter, and hydrodynamics. Higher velocities can reduce settling and promote shear removal of deposits, while low velocities encourage deposition. Chemistry (pH, hardness, polymerization tendency) and solids load are equally important. Step-by-Step Solution:Assess fluid chemistry (a): dictates scaling/coking/biofouling mechanisms.Assess velocity (b): shear stress at the wall controls deposition vs. resuspension.Assess solids (c): more or stickier particulates increase fouling risk.Conclusion: fouling factor depends on all three. Verification / Alternative check:Industry fouling guidelines (e.g., TEMA/HEI) provide different allowances for different fluids and velocities, confirming the multi-factor dependence. Why Other Options Are Wrong: Limiting to any one parameter misses the coupled nature of fouling. Wall material affects adhesion/corrosion but does not solely determine fouling resistance; fluid-side factors dominate the allowance. Common Pitfalls:Selecting a single “standard” fouling factor without considering service-specific chemistry and velocity can lead to under- or over-design. Final Answer:all (a), (b) and (c).

Question 5

Steam-side film coefficient (rule of thumb): For preliminary design under ordinary conditions, a reasonable steam-side heat transfer coefficient is about ________ kcal/hr·m²·°C.

Accepted Answer

Introduction:When sizing condensers or reboilers quickly, engineers often use a steam-side film coefficient based on condensation of saturated steam on clean surfaces with good drainage. This provides an order-of-magnitude estimate for overall heat-transfer coefficients before detailed calculations and vendor data are available. Given Data / Assumptions: Condensing steam on the shell or tube side under ordinary conditions. Clean surfaces; reasonably good condensate drainage; non-condensables minimal. Coefficient expressed in kcal/hr·m²·°C (engineering units as stated). Concept / Approach:Film condensation coefficients for saturated steam on metallic surfaces typically fall in the several thousand to more than ten thousand kcal/hr·m²·°C range depending on orientation, surface condition, and condensate behavior. A common rule-of-thumb value used for preliminary design is approximately 7000–8000 kcal/hr·m²·°C, with 7500 being a representative number. Step-by-Step Solution:Select an estimate consistent with ordinary, clean conditions.Use the mid-range rule-of-thumb ≈ 7500 kcal/hr·m²·°C.Adopt 7500 as the design placeholder pending detailed checks. Verification / Alternative check:Textbook examples and vendor literature show similar magnitudes for film condensation, with adjustments for orientation, non-condensables, and flooding. Why Other Options Are Wrong: 1250 or 2500: Too low for clean condensing steam films; might reflect gas-side coefficients. 15000: Possible in special cases but high for ordinary conditions. 500: Far too low. Common Pitfalls:Ignoring the significant impact of non-condensables, condensate flooding, and surface condition, which can lower the effective coefficient substantially. Final Answer:7500

Question 6

Tray selection in distillation design: Which tray flow arrangement is generally recommended for a distillation column with a small diameter (up to about 4 ft ≈ 1.2 m)?

Accepted Answer

Introduction / Context:Choosing the correct tray arrangement is fundamental in distillation column design. Small-diameter columns have different hydraulics from large towers. This question tests knowledge of when to use cross-flow, radial-flow, split-flow, or cascade arrangements for stable operation, adequate capacity, and reasonable pressure drop. Given Data / Assumptions: Column diameter up to about 4 ft (≈ 1.2 m). Conventional tray column operating at typical refinery/petrochemical conditions. Objective is good contacting efficiency with practical weir and downcomer layout. Concept / Approach:Cross-flow trays send liquid across the tray from an inlet downcomer to an outlet downcomer while vapor rises through perforations or valves. For small diameters (up to ~4 ft), cross-flow trays are practical because downcomer and active areas can be proportioned without excessive maldistribution. Radial-flow and split-flow arrangements are primarily used in larger columns to shorten liquid path length and maintain uniform froth behavior across very wide trays. Cascade trays are specialized contacting devices, not the standard choice for small towers. Step-by-Step Solution:Identify the diameter regime: small (≤ 4 ft).Evaluate feasible arrangements: cross-flow is standard and well-proven for small diameters.Radial or split flow becomes advantageous as diameter increases to maintain tray efficiency.Hence, the recommended arrangement is cross flow. Verification / Alternative check:Design practice and tray vendor guidelines routinely specify single-pass cross-flow trays for small columns due to simple layout and reliable hydraulics. Why Other Options Are Wrong:Radial flow: typically adopted for large diameters to reduce path length. Split flow: also a large-diameter solution to balance flows. Cascade: niche application; not the default for small towers. Common Pitfalls: Assuming multi-pass or split-flow always improves performance; in small shells, complexity can hurt hydraulics. Ignoring downcomer area requirements; too many passes can crowd small trays. Final Answer:Cross flow

Question 7

Mechanical design of exchangers: For a carbon steel shell in a shell-and-tube heat exchanger, the minimum shell thickness (including corrosion allowance) depends on shell diameter and typically falls in which range (in mm)?

Accepted Answer

Introduction / Context:Shell thickness in heat exchangers must satisfy code rules for pressure, temperature, corrosion allowance, and fabrication. Designers consult standards to choose a minimum wall thickness that balances safety and economy. This question checks practical knowledge of the typical range for carbon steel shells. Given Data / Assumptions: Material: carbon steel. Thickness includes corrosion allowance. Thickness depends on shell diameter within common industrial sizes. Concept / Approach:Minimum thickness increases with shell diameter and design conditions. For many moderate-pressure, moderate-diameter shells, practical minimums for carbon steel (inclusive of corrosion allowance) commonly fall in a single-digit to low double-digit millimeter range. Values significantly below ~5 mm are rarely acceptable for shells under pressure; very high minimums (≥ 12 mm) are associated with large diameters or higher pressures. Step-by-Step Solution:Recognize that extremely thin shells (3–5 mm) are uncommon for pressure shells.Typical practice indicates a range around 5–11 mm for many standard sizes and pressures.Therefore, select 5–11 mm as the representative range. Verification / Alternative check:Engineering handbooks and vendor data for common shell sizes align with minimum nominal thickness values in the single-digit millimeter range plus corrosion allowance, yielding totals around 5–11 mm for many services. Why Other Options Are Wrong:3–5 mm: generally insufficient for pressure shells. 12–18 mm: too high as a typical minimum; applies to larger or higher-pressure designs. 8–15 mm overlaps but exceeds common lower bounds; 5–11 mm better reflects the full typical span. Common Pitfalls: Ignoring corrosion allowance or mill tolerance when quoting “minimums.” Assuming one minimum fits all; code calculations govern the exact value. Final Answer:5–11 mm

Question 8

Vessels, fouling, and trays: Identify the WRONG statement among the following equipment-related assertions.

Accepted Answer

Introduction / Context:Process equipment design involves standardized components and well-understood hydraulics. This question mixes vessel closures, fouling tendencies of waters, and tray internals to test conceptual understanding and ability to spot an incorrect claim. Given Data / Assumptions: Pressure vessels above atmospheric pressure require suitable heads. River water vs. sea water fouling tendency comparison. Bubble-cap tray construction: riser (chimney), cap, slots, downcomer, weir. Concept / Approach:Formed heads (e.g., hemispherical, ellipsoidal, torispherical) are standard for pressurized cylindrical vessels. Sea water generally has higher fouling/scaling propensity than river water due to salts and biological content, so river water’s fouling factor being lower is reasonable. On bubble-cap trays, risers carry vapour from the tray deck to beneath the cap; liquid flows across the tray and into downcomers. Therefore, saying risers facilitate both liquid and vapour flow is incorrect. Step-by-Step Solution:Check (a): True — formed heads are standard for pressure vessels.Check (b): True — sea water tends to foul more than river water.Check (c): False — risers conduct vapour only; liquid does not flow through risers.Hence, the WRONG statement is (c). Verification / Alternative check:Tray internals diagrams show vapour rising through risers under caps while liquid flows over the active area and weirs to downcomers. Why Other Options Are Wrong (i.e., not the incorrect statements):(a) and (b) are consistent with standard practice. (d) claims both (b) and (c) are wrong, which conflicts with (b) being correct. Common Pitfalls: Confusing risers with downcomers; only downcomers carry liquid between trays. Assuming all waters foul similarly; salinity and biology matter. Final Answer:Risers on bubble-cap trays in distillation columns facilitate the flow of both liquid and vapour.

Question 9

Shell-and-tube hydraulics: In a multipass shell-and-tube heat exchanger, the shell-side cross-flow area does NOT depend on which of the following?

Accepted Answer

Introduction / Context:Shell-side pressure drop and heat transfer in a shell-and-tube exchanger are strongly tied to the cross-flow area between baffles. Accurately estimating this area is central to predicting velocities, pressure drop, and vibration risks. This question probes which geometric factors influence that area. Given Data / Assumptions: Multipass shell-and-tube configuration with segmental baffles. Conventional tube patterns and clearances. We focus on qualitative dependencies. Concept / Approach:Shell-side cross-flow area depends on the baffle window geometry and the flow lanes across the tube bundle. Baffle spacing sets the flow path length and the number of cross-flow sections. Clearances (shell-to-bundle, baffle cut, tube-to-baffle holes) influence leakages and effective area. Tube pitch determines how densely tubes are packed, changing the free area available for cross flow. Therefore, the area is influenced by all listed parameters. Step-by-Step Solution:Recognize key contributors: baffle window geometry and inter-tube spacing.Baffle spacing affects cross-flow section geometry and number.Clearances alter leakage and effective flow lanes.Tube pitch changes porosity of the tube bundle, thus free area.Conclusion: it depends on all the listed factors. Verification / Alternative check:Rating methods (e.g., Bell–Delaware) explicitly include correction factors for baffle spacing, leakages/clearances, and bundle porosity set by pitch. Why Other Options Are Wrong:Claiming independence from baffle spacing, clearances, or pitch contradicts established shell-side hydraulics. Common Pitfalls: Ignoring leakage streams; they can dominate shell-side performance. Assuming pitch affects only heat transfer surface; it also changes free flow area. Final Answer:None of these (it depends on all listed parameters)

Question 10

Two CSTRs in series: For reactions of order greater than one, which size arrangement maximizes performance at a given overall conversion, and which reactor should be placed first?

Accepted Answer

Introduction / Context:This design question in chemical reaction engineering asks how to size and order two continuous stirred-tank reactors (CSTRs) in series when the intrinsic reaction order n > 1. The goal is to achieve a specified overall conversion with minimum volume (or, equivalently, to maximize performance at fixed total volume). Given Data / Assumptions: Two mixed flow reactors (CSTRs) in series. Overall conversion target is fixed. Single, irreversible reaction with apparent order n > 1. Isothermal operation and identical feed composition to the train. Concept / Approach:For n > 1, the instantaneous rate r = k * C^n is highly sensitive to concentration. Higher concentrations at the reactor inlet provide disproportionately higher rates. Placing the larger volume first exposes more fluid to high-concentration conditions for longer residence time, harvesting the strongly concentration-dependent rate advantage and reducing the total volume needed for the target conversion. Step-by-Step Solution: Recognize r(C) increases superlinearly with C for n > 1.A larger first reactor keeps bulk concentration higher longer, giving more conversion per unit volume.The second, smaller reactor then polishes the conversion where concentration is already lower and rates are slower. Verification / Alternative check:Graphical design with 1/(-r_A) versus X shows the CSTR area rectangles. For n > 1, the first rectangle area (at lower X, higher C) benefits more from larger volume, minimizing the sum of areas (i.e., total volume). Why Other Options Are Wrong: Equal-sized reactors: Not optimal for n > 1; it wastes high-concentration potential. Smaller first: Misses the rate benefit at high C, increasing total volume. None of these: The recommended arrangement is the larger reactor first. Common Pitfalls:Confusing CSTR behavior with PFR. While a PFR naturally exploits high concentration at the inlet, CSTRs require deliberate volume placement to mimic that advantage. Final Answer:The larger reactor should be placed first.

Question 11

Valve headloss comparison: For fully open valves, how does the loss coefficient compare for a gate valve versus a globe valve, and what is a typical magnitude?

Accepted Answer

Introduction / Context:Designers often use valve loss coefficients (K) or equivalent lengths (L_e/D) to estimate pressure drops in piping networks. This question benchmarks the relative headloss for fully open gate and globe valves, which is crucial in pump sizing and energy audits. Given Data / Assumptions: Valves are fully open, clean, and in turbulent service. Gate valves present a nearly straight-through path; globe valves force the flow to turn, causing larger losses. Losses expressed as K (dimensionless) or as equivalent length L_e/D are standard approximations. Concept / Approach:Fully open gate valves typically have very low K values—only a small fraction of those for globe valves. Globe valves, with tortuous flow paths, exhibit significantly higher losses. A commonly used order-of-magnitude for a fully open gate valve is a single-digit L_e/D, whereas globe valves can be orders of magnitude larger, reflecting much higher K values. Step-by-Step Solution: Identify geometry: gate ≈ streamlined; globe ≈ sharp turns.Relate geometry to K: gate K ≪ globe K under identical conditions.Use typical data: K_gate small; L_e/D of a fully open gate is commonly of order ~7 (single digits). Verification / Alternative check:Standard headloss tables show fully open gate valves with small K and L_e/D values (single digits), and globe valves with much larger values, validating the order-of-magnitude statements. Why Other Options Are Wrong: (a) is opposite of reality; gate valves are not more lossy than globe valves when fully open. (b) captures the relative magnitude (much less). (c) gives a representative single-digit figure often cited for a fully open gate valve’s equivalent length. Common Pitfalls:Confusing throttling (partially open) behavior with fully open behavior; globe valves are intended for throttling and remain lossy even fully open, while gate valves are intended primarily for on/off service. Final Answer:Both (b) and (c).

Question 12

Ponchon–Savarit vs. McCabe–Thiele: What extra advantages does the enthalpy–composition method provide for binary distillation design?

Accepted Answer

Introduction / Context:Two classic graphical techniques for binary distillation are McCabe–Thiele (x–y diagram) and Ponchon–Savarit (enthalpy–composition diagram). Understanding their differences is essential for accurate stage and duty estimates, especially when heats of mixing and sensible-heat effects are significant. Given Data / Assumptions: Binary distillation under steady operation. Enthalpy changes may not be negligible. Ideal or non-ideal behavior may be present. Concept / Approach:McCabe–Thiele uses an x–y equilibrium diagram and assumes constant molar overflow (CMO), which implies horizontal operating lines and often neglects enthalpy variations. Ponchon–Savarit uses an h–x (or H–x) chart with tie lines, capturing both composition and enthalpy simultaneously. This enables direct reading of stage-to-stage energy balances and utility duties. Step-by-Step Solution: Map feed, q-line, and operating conditions onto an enthalpy–composition diagram.Step off stages using equilibrium tie lines and overall/partial energy balances.Read condenser and reboiler duties directly from the enthalpy differences on the diagram. Verification / Alternative check:When heats of mixing are appreciable or when CMO fails, Ponchon–Savarit typically predicts a different number of stages and more accurate heat loads than McCabe–Thiele, consistent with rigorous simulations. Why Other Options Are Wrong: Each statement (a), (b) and (c) is correct; therefore “All (a), (b) and (c)” is the best choice. Common Pitfalls:Applying McCabe–Thiele blindly under strong non-idealities or large heat effects; ignoring energy balances can lead to significant duty errors. Final Answer:All (a), (b) and (c).

Question 13

Elliptical (2:1) dished heads on pressure vessels: select the correct combined statements about strength and recommended use.

Accepted Answer

Introduction / Context:Head geometry affects pressure containment, fabrication ease, and cost. The 2:1 elliptical (ellipsoidal) head is a widely used compromise between the strongest hemisphere and the more economical torispherical head. This item reviews practical design-level comparisons recognized in vessel practice. Given Data / Assumptions: Comparisons are qualitative/typical for identical shell thickness and diameter. Materials, joint efficiencies, and code details are assumed comparable. Concept / Approach:Hemispherical heads have the best stress distribution and highest pressure rating for a given thickness and diameter. Elliptical 2:1 heads are slightly weaker but still strong and compact, frequently specified for moderate-to-high pressures. They can be considered similar in strength to a matching seamless cylindrical shell section under analogous code formulae, acknowledging practical approximations. Step-by-Step Solution: Recognize geometry ranking: hemisphere > 2:1 elliptical > torispherical.Note common practice: 2:1 elliptical heads are standard above moderate pressures.Relative strength comparisons support the listed statements as practical rules of thumb. Verification / Alternative check:Code design equations (e.g., thin-shell formulas) and vendor charts show required thickness relationships that align with the indicated qualitative comparisons. Why Other Options Are Wrong: Each separate statement is broadly accepted in vessel practice; the combined option reflects conventional guidance. Common Pitfalls:Over-interpreting approximate ratios as exact; always use governing pressure vessel codes and material allowables for final design thickness. Final Answer:All (a), (b) and (c).

Question 14

Head geometry terminology: In a formed head, the crown radius and knuckle radius refer respectively to which sections?

Accepted Answer

Introduction / Context:Pressure vessel heads combine multiple geometric regions: a central dish, a toroidal knuckle, and sometimes a straight flange. Accurate terminology is vital for fabrication drawings and code calculations. Given Data / Assumptions: A formed head consists of a central dished portion and a surrounding toroidal knuckle transitioning to the shell or flange. Standard head types include elliptical, torispherical, and hemispherical. Concept / Approach:The crown radius R_c describes the radius of curvature of the central dished region. The knuckle radius r_k is the toroidal corner radius that blends the dish into the shell/straight flange. This language is consistent across head drawings and specifications. Step-by-Step Solution: Identify the dish: center portion → crown radius.Identify the corner torus: blending region → knuckle radius.Match to options → (a) correctly pairs the terms and regions. Verification / Alternative check:Vendor catalogs and code sketches (e.g., torispherical heads) label R for crown and r for knuckle consistently. Why Other Options Are Wrong: Options (b), (c), and (d) misassign the radii to the wrong regions or to the straight flange, which does not define a curvature radius in the same sense. Common Pitfalls:Confusing the knuckle with a small fillet; the knuckle is a toroidal segment characterized by its own radius. Final Answer:Central dished section and corner torus section.

Question 15

When is an LMTD correction factor required in heat exchanger design?

Accepted Answer

Introduction / Context:The Log-Mean Temperature Difference (LMTD) method is a cornerstone of exchanger sizing. For complex flow arrangements, a correction factor F modifies the ideal LMTD to account for departure from pure countercurrent or cocurrent flow. Given Data / Assumptions: Design at steady state with no phase change (for simplicity). Shell-and-tube exchangers often use multiple shell or tube passes. Concept / Approach:Pure counterflow or pure parallel-flow exchangers have known temperature profiles and require no correction (F = 1). Multipass or crossflow arrangements distort the temperature driving-force distribution; hence, a correction factor F (0 < F ≤ 1) must be applied with the LMTD to estimate true performance. Step-by-Step Solution: Identify flow pattern: multipass shell-and-tube → nonideal temperature profile.Use LMTD with correction: ΔT_lm,true = F * ΔT_lm,ideal.Obtain F from standard charts using P and R ratios (temperature effectiveness parameters). Verification / Alternative check:Compare with the ε–NTU method; both should yield consistent duties when properties and areas are aligned. Why Other Options Are Wrong: Double-pipe in pure counterflow has F ≈ 1; no correction needed. Fouling affects U, not the LMTD correction directly. A simple counterflow also has F = 1 by definition. Common Pitfalls:Forgetting to check F ≥ 0.75–0.8 (typical design guidance) to avoid thermally inefficient arrangements. Final Answer:Multipass shell-and-tube heat exchanger.

Question 16

Continuous distillation at fixed throughput: As the external reflux ratio is increased, which operating cost component decreases?

Accepted Answer

Introduction / Context:For a binary distillation column producing fixed top and bottom specifications at constant throughput, changing the reflux ratio trades capital against operating costs. Understanding these trade-offs is essential in economic optimization. Given Data / Assumptions: Top and bottom purities and feed rate are fixed. Reflux ratio is varied from minimum upward. Column design scales with required stages and internal flows. Concept / Approach:Increasing reflux ratio from minimum reduces the number of theoretical stages (steeper operating line) and thus can initially reduce tower height and tray count, lowering fixed charges. However, higher reflux increases internal liquid and vapour traffic, raising both condenser and reboiler duties and therefore increasing utility costs. Step-by-Step Solution: At low reflux (near minimum): many stages required → higher capital.Increase reflux: fewer stages → initial capital reduction.But L and V inside the column rise with reflux → higher steam and cooling-water costs. Verification / Alternative check:McCabe–Thiele constructions illustrate the reduction in stages as R increases; energy balances show rising condenser and reboiler loads with larger reflux flows. Why Other Options Are Wrong: Cooling-water (b) and steam (d) costs increase, not decrease, with higher reflux. Internal vapour and liquid loads (c) increase, not decrease. Common Pitfalls:Assuming there is monotonic capital reduction; beyond a point, column diameter may increase due to hydraulic limits, partially offsetting earlier capital savings. Final Answer:Fixed charges initially (due to fewer theoretical stages required).

Question 17

Rectifying section operating line: When does its slope become unity in a binary distillation column?

Accepted Answer

Introduction / Context:The operating line in the rectifying section relates vapour and liquid compositions via the external reflux. Its slope is a direct function of the reflux ratio and is a key feature of McCabe–Thiele construction. Given Data / Assumptions: Binary distillation, constant molar overflow approximation. Rectifying operating line: y = (R/(R+1)) x + x_D/(R+1). Concept / Approach:The slope of the rectifying operating line equals R/(R+1). As R → ∞ (total reflux), slope → 1 and the intercept tends to 0, collapsing the operating line onto the 45° diagonal. This condition yields the minimum number of theoretical stages (but infinite utilities). Step-by-Step Solution: Slope m = R/(R+1).If R = 0 → m = 0 (horizontal line).If R → ∞ → m → 1 (unity slope). Verification / Alternative check:Graphing m versus R confirms the asymptote at 1 as R grows large, consistent with textbook derivations. Why Other Options Are Wrong: R = 0 gives slope 0, not 1. R = 1 gives slope 1/2. Minimum reflux gives a line tangent to the equilibrium curve, not slope 1. Common Pitfalls:Confusing minimum reflux (minimum stages infinite) with total reflux (minimum stages finite); they are opposite extremes. Final Answer:At total (infinite) reflux.

Question 18

Supports for vertical process vessels: Which of the following is NOT used for vertical vessels?

Accepted Answer

Introduction / Context:Support selection depends on vessel orientation, size, and thermal expansion needs. Correct supports are critical for mechanical integrity and nozzle alignment. Given Data / Assumptions: Vessels are cylindrical. Vertical vessels are mounted upright on foundations or structures. Concept / Approach:Vertical vessels are commonly supported by skirts (for tall/heavy towers), columns or legs (for smaller vessels), or brackets (for wall/structure mounting). Saddles, by contrast, cradle a horizontal cylinder and are inappropriate for vertical orientation. Step-by-Step Solution: Identify typical vertical supports: skirts, legs/columns, brackets.Recognize saddles: designed for horizontal vessels with two cradles supporting shell curvature.Therefore, saddles are not used for vertical vessels. Verification / Alternative check:Mechanical design handbooks depict standard support details; vertical vessels rarely, if ever, use saddles. Why Other Options Are Wrong: Brackets, skirts, and columns are well-established supports for vertical vessels. Common Pitfalls:Assuming one support fits all orientations; each has distinct load paths and thermal considerations (e.g., skirts accommodate nozzle loads and differential expansion). Final Answer:Saddles.

Question 19

Shell-and-tube exchanger layout: What is the usual minimum recommended baffle spacing relative to shell diameter D?

Accepted Answer

Introduction / Context:Baffles in shell-and-tube heat exchangers promote crossflow and increase heat transfer coefficients, but spacing that is too small can cause high pressure drop and vibration problems, while spacing that is too large reduces heat transfer effectiveness. Given Data / Assumptions: Single-segmental baffles in a conventional shell-and-tube exchanger. Design rules of thumb guide preliminary layouts. Concept / Approach:A common guideline is to keep baffle spacing in the range of about 0.2 D to 1.0 D, with a typical minimum of approximately 0.2 D (and often not less than a practical lower bound, e.g., around 50 mm to 2 inches). This ensures sufficient flow redirection while avoiding excessive pressure drop and blockage. Step-by-Step Solution: Select baffle spacing ≥ 0.2 D as a minimum.Adjust spacing to balance heat transfer coefficient and shell-side pressure drop.Check vibration and fouling tendencies during detailed design. Verification / Alternative check:Thermal design software and correlations (e.g., Bell–Delaware method) confirm that very tight spacing produces high pressure drop with diminishing returns on heat transfer area effectiveness. Why Other Options Are Wrong: 0.5 D, 0.66 D, 0.80 D may be acceptable spacings in some designs but are not the typical minimum recommendation. Common Pitfalls:Ignoring vibration risks or cleaning access; excessively close baffles complicate maintenance and can exacerbate fouling issues. Final Answer:0.2 D

Question 20

In plate-and-frame filter presses used for solid–liquid separation, how does the thickness of the frame compare with the thickness of the plates? Provide the best practical comparison based on their functions (cake space versus drainage/support).

Accepted Answer

Introduction / Context:Plate-and-frame filter presses are widely used in chemical, pharmaceutical, and mineral processes for batch solid–liquid separation. Understanding the geometry of the “plate” and the “frame” clarifies why their thicknesses differ and how that affects cake formation, filtrate flow, and mechanical strength. Given Data / Assumptions: The plate provides drainage paths (grooves or cloth support) and mechanical rigidity. The frame primarily provides the void space in which the filter cake forms. The press operates at a pressure that compacts the cake inside the frame volume. Concept / Approach:The frame must be thick enough to accommodate the desired cake thickness at the selected cycle time and pressure drop. Plates, in contrast, are designed to be strong and sufficiently stiff while minimizing hydraulic resistance; their functional need is not to provide cake volume but to support cloths and convey filtrate through channels. Step-by-Step Solution: Relate function to geometry: cake volume is provided by the frame, hence frame thickness > plate thickness.Consider capacity: thicker frame → larger cake volume per cycle → fewer changeovers for the same throughput.Check hydraulics: plate grooves/ports direct filtrate; increasing plate thickness does not add cake capacity. Verification / Alternative check:Equipment catalogs show frames specified by “cake thickness” (e.g., 25 mm, 32 mm), while plate thickness is primarily a mechanical design parameter, commonly lower than frame thickness for the same press size. Why Other Options Are Wrong: Less/same thickness: would restrict cake capacity or confuse plate and frame functions. Either less than or equal to: ignores the standard design intent to house cake in the frame. Varies randomly: design follows process requirements, not randomness. Common Pitfalls:Assuming thicker plates increase capacity; confusing recessed-plate (chamber) presses with true plate-and-frame designs. Final Answer:More than the plate thickness

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