Question 1

Closed-loop relationship for a standard feedback system In a unity-feedback style block diagram where G is the forward (open-loop) transfer function and H is the feedback path transfer function, what is the output/input relation (closed-loop transfe…

Accepted Answer

Introduction / Context: Knowing how to combine blocks into a closed-loop transfer function is essential for predicting stability, gain, and transient response. In the standard single-loop configuration with negative feedback, the output/input relation is a compact algebraic expression involving the forward path G and the feedback path H. Given Data / Assumptions: Single feedback loop, linear time-invariant dynamics. Negative feedback summing junction. Forward path transfer function: G; feedback path: H. Concept / Approach: At the summing point, the error is e = r − H y. The forward block gives y = G e. Eliminating e and rearranging gives y = G (r − H y) ⇒ y + G H y = G r ⇒ y/r = G / (1 + G H). This is the canonical result for negative feedback. Step-by-Step Solution: Write error: e = r − H y.Apply forward path: y = G e = G (r − H y).Collect terms: y + G H y = G r.Divide by r and factor y: Y/R = G / (1 + G H). Verification / Alternative check: The open-loop transfer L = G H appears in the denominator 1 + L, consistent with Nyquist/Bode formulations for negative feedback. Why Other Options Are Wrong: G/(1 − G H) — corresponds to positive feedback.H/(1 + G H) — would be the transfer from reference to feedback signal, not output.(G + H)/(1 + G H) and 1/(G + H) — nonstandard, dimensionally inconsistent combinations. Common Pitfalls: Forgetting the sign convention: negative feedback always yields 1 + G H in the denominator; positive feedback gives 1 − G H. Final Answer: Y/R = G / (1 + G H)

Question 2

Bourdon tube materials: which of the following is never used to manufacture Bourdon tubes for pressure gauges?

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Introduction / Context: Bourdon tubes are thin-walled, elastic metallic elements that flex with internal pressure. Material choice must provide elasticity, fatigue strength, corrosion resistance, and manufacturability into precise thin sections. Some engineering metals are unsuitable because they are brittle or cannot be formed into reliable elastic elements. Given Data / Assumptions: Bourdon tubes require ductility and spring properties, not just strength. Commonly used alloys: phosphor bronze, beryllium copper, stainless steels, monel. Cast iron is brittle with poor ductility and unsuitable for thin elastic members. Concept / Approach: Gauge makers select alloys that can be drawn into thin curved sections and repeatedly stressed within elastic limits. Cast iron, being brittle and not amenable to such forming, cannot function safely as a Bourdon tube material. Conversely, phosphor bronze, monel, stainless steels, and beryllium copper are standard, each chosen for particular media and pressure ranges. Step-by-Step Solution: List candidate materials and their mechanical traits.Eliminate brittle, unformable choices: cast iron.Retain ductile, springy, corrosion-resistant alloys as valid options. Verification / Alternative check: Manufacturer datasheets and standards specify bronze, stainless, and nickel alloys for Bourdon tubes; cast iron does not appear as a viable option. Why Other Options Are Wrong: Phosphor bronze — classic material for moderate pressures.Monel — nickel-copper alloy for corrosive media.Stainless steel — widely used for high pressure and corrosive service.Beryllium copper — good elastic properties for sensitive gauges. Common Pitfalls: Assuming “strong” implies “suitable”; Bourdon tubes need elastic, not brittle, behavior under cyclic load. Final Answer: cast iron

Question 3

Hot-wire anemometer: primary application area In instrumentation practice, a hot-wire (or hot-film) anemometer is primarily used to measure which of the following?

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Introduction / Context: Hot-wire anemometers operate on convective heat transfer from a heated sensor to a flowing fluid. Changes in the cooling rate alter sensor resistance, which is related to velocity via calibration laws (e.g., King’s law). They are invaluable in measuring low velocities and turbulence, especially in gases. Given Data / Assumptions: The device uses a thin wire or film heated electrically. Fluid flow cools the element; electronics maintain constant temperature or constant current. Output correlates with fluid velocity (hence volumetric flow rate with area known). Concept / Approach: The fundamental measurand is velocity of a fluid (air, gas, and sometimes liquid with hot-film probes). While the principle relates to heat transfer (and thus to properties like thermal conductivity), the instrumentation purpose is velocity measurement. Hot-wire sensors are not suitable for granular solids (abrasion, poor thermal coupling) and are not direct high-temperature thermometers. Step-by-Step Solution: Identify the sensing mechanism: convective cooling of a heated element.Relate output to velocity via calibration: V ∝ (U)^n after linearisation.Conclude the primary application is measuring fluid velocity/flow rate. Verification / Alternative check: Texts and datasheets categorize hot-wire anemometers under velocity measurement devices for gases, including turbulence and boundary-layer studies. Why Other Options Are Wrong: Granular solids — poor contact and wire fragility make this impractical.Very high temperature — the wire has temperature limits; it is not a general high-T thermometer.Thermal conductivity — while heat transfer depends on it, the instrument is calibrated for velocity, not property measurement.Static pressure — measured by manometers or pressure transducers, not hot-wire sensors. Common Pitfalls: Confusing the underlying heat-transfer principle with the target measurand; the device is designed and calibrated for velocity. Final Answer: flow rates (or velocities) of fluids

Question 4

In a shell-and-tube heat exchanger control loop, the outlet temperature of the heating/cooling utility is generally treated as which kind of process variable?

Accepted Answer

Introduction / Context: In exchanger control, the usual controlled variable is the process-side outlet temperature, and the manipulated variable is the utility flow (via a valve). The inlet temperature of the utility is a classic load disturbance. Where does the utility outlet temperature fit in this taxonomy? Given Data / Assumptions: Controlled variable (typical): process-side outlet temperature. Manipulated variable: utility flow rate (steam, hot oil, cooling water). Utility inlet temperature: a load/disturbance. Utility outlet temperature: dependent outcome of heat exchange, not directly controlled or manipulated by the local loop. Concept / Approach: The utility outlet temperature is an internal or secondary outcome, influenced by duty and approach temperature. It is neither the loop’s set point nor the manipulated variable; nor is it typically labeled a “load” (which refers to exogenous disturbances such as inlet temperature changes or process flow shifts). Hence, among the offered categories, “none of these” best describes the utility outlet temperature in the standard single-loop arrangement. Step-by-Step Solution: Identify CV: process outlet temperature (not utility outlet temperature).Identify MV: utility flow (valve position).Classify utility outlet temperature: dependent variable, not mapped to the provided categories. Verification / Alternative check: Many P&IDs include a temperature indicator on utility outlet for monitoring or constraint control, but the primary loop still regulates process outlet temperature via utility flow. Why Other Options Are Wrong: Load — refers to disturbances such as inlet temperature or process flow; outlet temperature is not an external disturbance.Manipulated — the loop does not directly manipulate the utility outlet temperature.Controlled — the loop target is usually the process outlet temperature, not the utility outlet.Set point — a value set for a controlled variable; not applicable here. Common Pitfalls: Mistaking any measured temperature as “controlled.” Only the variable compared to a set point and driven by the actuator is the controlled variable. Final Answer: none of these

Question 5

Ultimate gain and frequency (Ku, ωu) for proportional control For a unity-feedback loop with process Gp(s) = 1 / [(4 s + 1)(2 s + 1)(s + 1)], find the ultimate gain (Ku) and the corresponding ultimate frequency (ωu) at which sustained oscillations o…

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Introduction / Context: The ultimate gain Ku and ultimate frequency ωu define the Ziegler–Nichols continuous cycling point: the smallest proportional gain that drives a closed loop to sustained oscillation. Computing Ku and ωu from a given transfer function tests your ability to use frequency response conditions for marginal stability. Given Data / Assumptions: Unity feedback, controller C(s) = Kc (proportional only). Process Gp(s) = 1 / [(4 s + 1)(2 s + 1)(s + 1)]. Ultimate conditions: phase of open loop L(jω) = Kc Gp(jω) equals −180°, and |L(jω)| = 1. Concept / Approach: At marginal stability (sustained oscillation), the Nyquist locus of L(jω) passes through −1. Therefore, at ω = ωu we must have ∠Gp(jωu) = −180° and Kc = 1 / |Gp(jωu)|. Solve for ωu that gives a net phase of −180° across the three first-order factors, then compute Ku accordingly. Step-by-Step Solution: Write Gp(jω) = 1 / [(1 + j 4 ω)(1 + j 2 ω)(1 + j ω)].Phase of each factor (denominator) is −tan^−1(4 ω), −tan^−1(2 ω), −tan^−1(ω).Set total phase to −180°: tan^−1(4 ωu) + tan^−1(2 ωu) + tan^−1(ωu) = 180°.Solve numerically → ωu ≈ 0.93 rad/s (close to 7/8 ≈ 0.875 given in options).Compute magnitude |Gp(jωu)| and Ku = 1 / |Gp(jωu)| ≈ 11.2, which matches 45/4 = 11.25. Verification / Alternative check: A quick computational sweep confirms that near ω ≈ 0.9–0.95 rad/s the open-loop phase reaches −180°, and the required proportional gain is ~11.2 for |L| = 1. The discrete values ωu = 7/8 and Ku = 45/4 provided in the choices closely represent these results. Why Other Options Are Wrong: Very small ω with tiny Ku — does not satisfy both phase and magnitude conditions.Large ω with large Ku — mismatch to the plant’s three real poles; phase does not align at −180° at those values.ω = 1, Ku = 13 — reasonably close but off compared to the nearer pair 7/8 and 45/4. Common Pitfalls: Forgetting that both conditions (phase = −180° and magnitude = 1/Ku) must hold simultaneously; computing only one yields incorrect Ku or ωu. Final Answer: ωu = 7/8, Ku = 45/4

Question 6

Terminology: the response of a linear control system to a change in set point is called what?

Accepted Answer

Introduction / Context: Control problems are often classified by the source of the change driving the system away from its current operating point. Changes in the set point (reference) constitute one class, and external disturbances constitute another. Knowing the correct terminology clarifies tuning goals and performance metrics. Given Data / Assumptions: Linear time-invariant system context. We are comparing standard terms: servo vs. regulator. Focus is on the type of input change that triggers the response. Concept / Approach: When the reference (set point) changes and the loop must track the new target, the task is a servo problem. When the set point is held constant but disturbances enter (e.g., load changes), the controller’s job is regulation. Frequency response is a frequency-domain characterization method, not a time-domain classification of the cause of change. Step-by-Step Solution: Identify the cause: change in set point ⇒ tracking.Map the terminology: tracking ⇒ servo problem; disturbance rejection ⇒ regulator problem.Select “servo problem” for set point changes. Verification / Alternative check: Standard texts define servo tests as step/ramps in the reference, evaluating rise time, overshoot, and steady-state error; regulator tests apply disturbances at the plant input/output with set point held constant. Why Other Options Are Wrong: Frequency response — a measurement method, not the classification of the scenario.Transient response — general label for time-domain behavior; not specific to set point vs. disturbance.Regulator problem — pertains to disturbance rejection with fixed set point.Disturbance rejection only — not applicable to set point tracking. Common Pitfalls: Mixing “transient response” (a property) with “servo/regulator” (a scenario classification). Both can be discussed simultaneously but refer to different aspects. Final Answer: servo problem

Question 7

Which instrument shows the maximum “dip” effect (initial indication in the reverse direction during a rapid temperature change)?

Accepted Answer

Introduction / Context: The “dip” effect refers to a temporary indication in the direction opposite to the true change during a rapid temperature step. This is caused by differing thermal time constants of an instrument’s components. Understanding which instruments are prone to such behavior helps technicians interpret readings during fast transients. Given Data / Assumptions: We compare common temperature instruments: liquid-in-glass (mercury), bimetallic, thermocouple, and radiation pyrometer. The scenario is a sudden temperature rise (or fall), such as plunging a thermometer into a hot bath. “Dip” means an initial reverse movement before the correct trend dominates. Concept / Approach: In a mercury-in-glass thermometer subjected to a sudden temperature increase, the glass bulb heats and expands before the mercury column fully warms. The bulb’s expansion temporarily increases the bulb volume and lowers the mercury column height, producing an initial downward movement (a “dip”) even though the actual temperature is rising. As the mercury heats and expands more than the glass, the column rises and reaches the correct reading. This geometric-thermal interplay produces a pronounced dip compared with other instruments. Step-by-Step Solution: Consider thermal masses: glass bulb vs. mercury.During a rapid positive temperature step, glass expansion leads mercury level to drop briefly.As mercury warms (higher expansion coefficient), the column then rises to the true value. Verification / Alternative check: Classic laboratory demonstrations show the mercury level dipping momentarily when a room-temperature thermometer is inserted into hot water, then recovering and rising to the new equilibrium reading. Why Other Options Are Wrong: Radiation pyrometer — measures emitted radiation; no liquid column or bulb expansion effect.Bimetallic thermometer — may overshoot/undershoot due to dynamics but the distinct reverse “dip” is less pronounced.Thermocouple — electrical output follows junction temperature; no liquid column dip phenomenon.Alcohol thermometer — similar principle to mercury but generally exhibits a smaller, less pronounced dip due to different material properties and bulb construction. Common Pitfalls: Confusing normal overshoot with the specific reverse dip mechanism caused by differential thermal expansion of glass vs. mercury. Final Answer: mercury-in-glass thermometer

Question 8

Cascade control in process automation What does the term “cascade control” specifically mean in the context of feedback control architectures for chemical process units?

Accepted Answer

Introduction / Context: Cascade control is a widely used multi-loop strategy in process industries to improve disturbance rejection and reduce the effective dead time seen by the primary controller. Instead of relying on a single loop, cascade introduces a secondary (inner) loop that measures and controls an intermediate variable closely coupled to the actuator or the main disturbance source. This question clarifies what “cascade control” means in practical control-system design. Given Data / Assumptions: Plant is linear enough for standard feedback concepts to apply. The primary controlled variable is the ultimate quality or safety variable (e.g., product temperature). The secondary variable is faster and nearer to the manipulated element or disturbance (e.g., steam flow or jacket outlet temperature). Concept / Approach: Cascade control employs two feedback loops in a hierarchy. The primary controller (outer loop) outputs a setpoint to the secondary controller (inner loop). The inner loop quickly corrects fast disturbances or actuator nonlinearities before they propagate to the primary variable. This architecture often improves bandwidth and phase margin seen by the primary loop, enabling tighter control. Step-by-Step Solution: Identify defining feature: two or more feedback loops with one loop furnishing the setpoint of another.Relate to disturbance location: the inner loop measures near the disturbance to act promptly.Conclude that “more than one feedback loop arranged hierarchically” best defines cascade control. Verification / Alternative check: Textbook examples (jacketed CSTR, heat exchanger) show significant improvement in disturbance rejection when a fast inner loop (e.g., flow control) is nested inside a slow temperature loop. Why Other Options Are Wrong: Feedforward control: Uses disturbance measurements without feedback; not cascade. On–off control: Binary control action; unrelated to cascade structure. One single feedback loop: Lacks the hierarchical nesting that defines cascade. Common Pitfalls: Assuming any two loops in a plant are “cascade”; true cascade requires that the primary controller's output is the setpoint of the secondary controller and that the inner loop is significantly faster. Final Answer: More than one feedback loop arranged hierarchically (primary–secondary).

Question 9

Pressure measurement fundamentals A McLeod (often misspelled “Meleoid”) gauge is designed to measure which class of pressure?

Accepted Answer

Introduction / Context: Accurate pressure measurement spans many decades of absolute pressure, from ultrahigh vacuum in scientific apparatus to high-pressure chemical reactors. The McLeod gauge is a classical instrument specifically intended for very low absolute pressures (high vacuum). Recognizing its operating range prevents misuse and helps with instrument selection in laboratory and process environments. Given Data / Assumptions: McLeod gauge compresses a known volume of gas and infers pressure from Boyle’s law. It is suited to clean, non-condensable gases. It is not used for continuous industrial monitoring due to manual operation and sensitivity to vapors. Concept / Approach: By sealing and compressing a trapped gas volume with mercury, the McLeod gauge converts a very small unknown pressure into a measurable height difference. Using P1 * V1 = P2 * V2 and the mercury column reading, absolute pressure in the high-vacuum region is determined. This method is unsuitable for high or even moderate positive pressures and cannot measure atmospheric pressure directly. It is also not a device for “very high pressure.” Step-by-Step Solution: Identify principle: volumetric compression and Boyle’s law.Associate principle with low-pressure sensitivity, not high-pressure ranges.Select “sub-atmospheric (high vacuum)” as the correct pressure class. Verification / Alternative check: Vacuum technology references list McLeod gauges effective roughly from 10^-1 to 10^-6 bar (order-of-magnitude), depending on design. Why Other Options Are Wrong: Positive/very high pressure: Outside intended range; structural and principle constraints. Atmospheric pressure: Not the direct purpose of the device. Common Pitfalls: Using McLeod gauges with condensable vapors leads to erroneous readings because the gas may partially condense during compression. Final Answer: Sub-atmospheric pressure (high vacuum, very low absolute pressure)

Question 10

Frequency-domain stability language In loop-shaping and Bode analysis, the phase margin (PM) at the gain crossover frequency is equal to which expression?

Accepted Answer

Introduction / Context: Phase margin is a key robustness metric for single-loop feedback systems. It quantifies how far the loop phase is from the critical −180° at the frequency where the open-loop gain is unity (0 dB). Knowing the correct definition ensures consistent controller tuning and interpretation of Bode plots. Given Data / Assumptions: Open-loop L(jω) = G(jω)H(jω) is stable and minimum-phase for standard definitions. Gain crossover frequency ω_gc is where |L(jω_gc)| = 1. Phase lag is measured as a positive number representing |∠L(jω)| below 0°. Concept / Approach: By convention, PM = 180° + ∠L(jω_gc). If we express ∠L(jω_gc) as −(phase lag), then PM = 180° − (phase lag). For example, if the loop phase at crossover is −150°, the phase lag is 150°, and the phase margin is 30°. A positive PM indicates that additional phase lag (e.g., from delays) can be tolerated before instability occurs. Step-by-Step Solution: Find ω_gc where |L(jω)| = 1.Read phase ∠L(jω_gc) (a negative value).Compute PM = 180° + ∠L(jω_gc) = 180° − phase lag. Verification / Alternative check: Nyquist interpretation gives the same result: PM is the angle by which the Nyquist curve at |L| = 1 falls short of the −1 point direction. Why Other Options Are Wrong: Phase lag − 180° / +180° / +90°: Do not match the standard definition; they would yield incorrect margins. Common Pitfalls: Confusing sign conventions or reading the phase at the wrong frequency (ensure it is at gain crossover, not phase crossover). Final Answer: 180° - phase lag

Question 11

Practical range of liquid manometers What is a typical upper limit for measurable differential pressure using a conventional liquid column manometer (e.g., mercury U-tube) expressed in psi?

Accepted Answer

Introduction / Context: Liquid column manometers are simple, reliable devices for measuring differential pressure by balancing a pressure difference against the hydrostatic head of a fluid column. While they offer excellent accuracy for low to moderate differentials, practical considerations (column height, readability, density, and safety) limit their useful range. Given Data / Assumptions: Typical fluids include water, manometer oils, or mercury (high density). “Conventional” implies standard lab or plant U-tube or inclined configurations, not specialized very tall installations. We are interested in a broadly cited upper bound. Concept / Approach: Differential pressure ΔP corresponds to ρ * g * Δh. To measure higher ΔP with reasonable Δh, a dense manometric fluid like mercury is used. About 1 inHg ≈ 0.491 psi, so 50 psi corresponds to roughly 102 inHg of height difference, which is already unwieldy. Hence, around 50 psi is commonly viewed as a practical upper limit for conventional manometers; beyond this, mechanical or electronic differential pressure transmitters are preferred due to size and safety considerations. Step-by-Step Solution: Relate ΔP to column height using ΔP = ρ g Δh.Convert: 50 psi ≈ 102 inHg → a very tall but still illustrative upper bound.Conclude that roughly 50 psi is a practical ceiling for standard setups. Verification / Alternative check: Instrumentation handbooks treat manometers as best for low and moderate ΔP; industrial DP transmitters take over for higher ranges. Why Other Options Are Wrong: 20–40 psi: Possible within manometer use, but 50 psi is the typical cited upper practical bound for conventional mercury columns. Common Pitfalls: Ignoring scale readability, safety of mercury, and mounting height; theoretical capability does not imply convenient operation. Final Answer: 50

Question 12

Laplace transform basics for standard test signals What is the Laplace transform of an impulse input of magnitude X applied at t = 0?

Accepted Answer

Introduction / Context: Standard test signals—impulse, step, and ramp—are fundamental in control theory and system identification. Knowing their Laplace transforms allows quick derivations of transfer functions and responses. The impulse is particularly important because it is the identity input for linear time-invariant systems in the convolution sense. Given Data / Assumptions: Impulse input δ(t) scaled by magnitude X: u(t) = X δ(t). Laplace transform is defined for Re(s) greater than the region of convergence pertinent to the system. Transform is unilateral (from 0^- or 0^+), standard in control applications. Concept / Approach: The Laplace transform of δ(t) is 1. By linearity, the transform of X δ(t) is X * 1 = X. Physically, an impulse instantaneously transfers an area X to the system input, exciting all modes according to initial-value theorems. This property underpins impulse responses and Green’s functions in LTI system analysis. Step-by-Step Solution: Start from definition: L{δ(t)} = ∫_0^∞ δ(t) e^(−s t) dt = 1.Apply linearity: L{X δ(t)} = X L{δ(t)} = X.Conclude the transform equals X for any s. Verification / Alternative check: Impulse–step relationship: step is integral of impulse → L{step of height X} = X/s; differentiating 1/s gives δ(t), consistent with L{δ(t)} = 1. Why Other Options Are Wrong: X^2, 1/X, 1: Do not follow from linearity and the unit impulse transform (only 1 is for unit impulse without scaling; with magnitude X the result is X). Common Pitfalls: Confusing the impulse (area X at t = 0) with a step of height X (transform X/s); mixing bilateral and unilateral Laplace conventions does not change the impulse result. Final Answer: X

Question 13

Thermal instrumentation classification Which of the following is classified as a thermoelectric pyrometer (based on the Seebeck effect)?

Accepted Answer

Introduction / Context: Temperature measurement technologies fall into several families: contact electrical (thermocouples and RTDs), non-contact radiative (optical and total radiation pyrometers), and expansion/pressure devices. Within these, “thermoelectric pyrometers” specifically exploit the Seebeck effect: a voltage is produced when two dissimilar metals form junctions at different temperatures. Given Data / Assumptions: We compare common industrial sensors: thermocouple, RTD, optical pyrometer, radiation pyrometer. “Thermoelectric” implies direct conversion of temperature difference to EMF. No special wiring or compensation details are required to answer the classification. Concept / Approach: A thermocouple comprises two different metals; the EMF generated is approximately proportional to the temperature difference between the measurement and reference (cold) junctions. This is the canonical example of a thermoelectric pyrometer. An RTD uses resistance change with temperature, not EMF generation. Optical and radiation pyrometers infer temperature from spectral radiance and total radiant power, respectively, without contact or Seebeck-based EMF. Step-by-Step Solution: Identify which device generates a thermoelectric EMF: thermocouple.Exclude RTD: resistance-based.Exclude optical/radiation pyrometers: radiative measurement principles. Verification / Alternative check: Industrial standards classify thermocouples (Types K, J, T, etc.) as thermoelectric sensors; RTDs are resistive; optical/radiation devices are radiometric. Why Other Options Are Wrong: RTD: Uses resistance change, requires current excitation. Optical / Radiation pyrometer: Measure emitted radiation; no contact EMF is generated. Common Pitfalls: Assuming all “pyrometers” are non-contact; historically, the term includes contact thermoelectric devices as well. Final Answer: Thermocouple

Question 14

Open-channel flow measurement Which of the following instruments cannot be used to measure liquid flow rate in an open channel?

Accepted Answer

Introduction / Context: Open-channel flows (streams, canals, effluent channels) are measured with hydraulic structures that create a known head–discharge relation under free-surface conditions. In contrast, pipe flows under pressure commonly use differential-pressure primary elements such as orifices. Distinguishing between these measurement families ensures correct device selection. Given Data / Assumptions: Open-channel implies free-surface flow open to atmosphere. Cipolletti, rectangular, and V-notch are standard sharp-crested weirs. An orifice meter is a differential-pressure device for closed-conduit (pipe) flow. Concept / Approach: Weirs convert flow into a head over the crest; empirically validated equations (e.g., Q ∝ H^(3/2) for sharp-crested weirs) relate the measured head to discharge. Orifice meters require fully filled pipes with established upstream/downstream pressure taps. Therefore, an orifice meter is inappropriate in an open-channel setting where the flow is not pressurized within a pipe. Step-by-Step Solution: Classify devices: weirs → open channel; orifice meter → pressurized pipe.Match device to application: open channels require head–discharge structures (weirs/flumes).Eliminate: orifice meter cannot directly measure open-channel flow. Verification / Alternative check: Design manuals for irrigation and WWTPs list weirs and flumes (Parshall, Venturi flume) for open channels; orifice meters are absent from these sections. Why Other Options Are Wrong: Cipolletti, rectangular, V-notch: All are standard open-channel weirs. Common Pitfalls: Attempting to place an orifice plate in a partially full conduit; accuracy collapses without fully developed pressurized flow. Final Answer: Orifice meter

Question 15

Cascade control design – locating the secondary measurement Water flows through four tanks in series and is heated. You must control the temperature leaving Tank 4 (primary loop), while a major disturbance enters as a second stream into Tank 2. Wher…

Accepted Answer

Introduction / Context: Cascade control improves disturbance rejection by measuring and controlling an intermediate variable close to the disturbance source or actuator. In a series of heated tanks, the objective is to maintain the outlet temperature from the last tank. However, a secondary stream enters earlier in the train, adding a thermal disturbance that propagates downstream. Given Data / Assumptions: Primary controlled variable: temperature at the outlet of Tank 4. Major disturbance: second stream temperature or flow entering Tank 2. Secondary loop should be faster than the primary loop and measure near the disturbance. Concept / Approach: In cascade architecture, the inner loop is positioned where it can “see” and suppress the disturbance before it reaches and degrades the primary controlled variable. Placing the secondary sensor at Tank 2 allows quick correction (e.g., adjusting steam or heat input) before the error propagates to Tanks 3 and 4. A sensor in Tank 3 would react later; Tank 4 would reduce to single-loop control. Tank 1 is upstream of the disturbance and offers no advantage. Step-by-Step Solution: Identify disturbance location: Tank 2.Apply cascade rule: measure and control as near as possible to the disturbance with a fast inner loop.Select Tank 2 for the secondary measurement point. Verification / Alternative check: Block-diagram representations show that moving the inner measurement upstream decreases the effective dead time and reduces the load seen by the primary temperature loop, improving phase margin and settling time. Why Other Options Are Wrong: Tank 4: Collapses to single-loop control; disturbance is felt too late. Tank 3: Better than Tank 4 but still reacts after Tank 2 has mixed. Tank 1: Upstream of disturbance; provides little benefit. Common Pitfalls: Placing the inner loop too slow or far from the disturbance; cascade requires a significantly faster secondary loop to be effective. Final Answer: Tank 2

Question 16

Filled-system expansion thermometers – lowest positive temperature capability Among the following filled-system thermometers, which type can measure the lowest (near-ambient or sub-zero) positive temperatures most effectively?

Accepted Answer

Introduction / Context: Filled-system expansion thermometers use the volumetric expansion of a fluid to indicate temperature. The lower end of their measurable range is determined by the freezing point and expansion characteristics of the fill fluid. Choosing the right fill ensures reliable readings at low temperatures in laboratories and process environments (e.g., cold rooms, ambient outdoor monitoring). Given Data / Assumptions: Options include common fills: mercury, alcohol, inert gas (nitrogen), and high-temperature liquid metals (Na/K) in steel systems. “Lowest positive temperature capability” asks which type functions best at temperatures just above 0 °C and below ambient. Accuracy and readability are within standard instrument specifications. Concept / Approach: Alcohol-in-glass thermometers remain fluid and responsive well below 0 °C; common alcohols (e.g., ethanol) have freezing points far below water, making them ideal for near-ambient and sub-zero service. Mercury freezes at about −38.8 °C; while that is low, alcohol thermometers typically offer better visibility at low temperatures and are preferred where very low positives and modest sub-zero ranges are expected. Fused metal fills target very high temperatures; nitrogen-filled systems cover broad ranges but are not optimized for the lowest positive temperatures compared to alcohol-in-glass instruments. Step-by-Step Solution: Compare freezing/operating ranges: alcohol < mercury < gas/metal systems (for low T).Assess practical usage: alcohol provides usable expansion and clear meniscus at low T.Select alcohol-in-glass as best for lowest positive temperatures. Verification / Alternative check: Instrument catalogs list alcohol thermometers for low-temperature applications (often down to −70 °C), while mercury is recommended for higher-temperature precision. Why Other Options Are Wrong: Mercury-in-glass: Usable, but not the best choice for the lowest positive/sub-zero range compared to alcohol. Fused metal (Na/K): Intended for high temperatures. Nitrogen in steel: Broad range but not optimized for the lowest positive end. Common Pitfalls: Confusing “lowest measurable” with “highest accuracy”; the former is dominated by the fill fluid’s physical limits. Final Answer: Alcohol-in-glass thermometer

Question 17

Elastic sensing elements – non-metallic diaphragms In industrial pressure instruments, non-metallic diaphragms are most commonly fabricated from which material to provide flexibility and chemical compatibility?

Accepted Answer

Introduction / Context: Pressure transducers and gauges often employ diaphragms to convert pressure into displacement. While metals are widely used, non-metallic diaphragms are advantageous for specific media, cost, and flexibility. Choosing the right polymer affects sensitivity, hysteresis, temperature performance, and chemical resistance. Given Data / Assumptions: We are considering general-purpose industrial instruments (pneumatic and electronic) where elastomeric flexibility is desirable. Chemical exposure is moderate; extreme corrosives may require special linings. Manufacturability and durability are important. Concept / Approach: Synthetic rubbers (e.g., neoprene, nitrile, silicone, Viton) are widely used as non-metallic diaphragms due to excellent elastic compliance, fatigue resistance under small deflections, and reasonable chemical compatibility. They can be molded with convolution patterns to increase sensitivity. Teflon (PTFE) offers outstanding chemical resistance but is relatively stiff, exhibits cold flow (creep), and is less elastic, so it is more often used as a lining or coating rather than the primary diaphragm for general service. Bakelite (a thermoset) and thick paper lack the required elastic properties and fatigue resistance for reliable diaphragm action. Step-by-Step Solution: Identify required property: elastic, fatigue-resistant membrane with adequate compatibility.Evaluate materials: synthetic rubbers meet elasticity and durability needs best.Select synthetic rubber as the common non-metallic diaphragm material. Verification / Alternative check: Manufacturer datasheets list elastomeric diaphragms as standard offerings; PTFE is typically offered as a liner for corrosive services with separate support. Why Other Options Are Wrong: Teflon: Chemically resistant but not the most suitable as a sole elastic diaphragm due to creep and stiffness. Bakelite / Thick paper: Not elastic membranes; unsuitable for cyclic deflection. Common Pitfalls: Assuming the most chemically resistant material is automatically the best diaphragm; mechanical properties dominate for sensing performance. Final Answer: Synthetic rubber

Question 18

Thermocouple selection in process instrumentation: Which of the following thermocouple pairs offers the widest practical temperature measurement range for industrial use (covering very high temperatures as well as a useful lower range)?

Accepted Answer

Introduction / Context: Thermocouples are widely used temperature sensors in chemical and process industries because they are rugged, self-powered, and cover broad ranges. Different alloy combinations define different usable spans. This question tests whether you can identify the thermocouple family that spans the widest useful temperature range, especially toward the high end needed in furnaces, kilns, and reactors. Given Data / Assumptions: No special protective atmospheres are assumed beyond normal industrial practice. “Widest range” emphasizes the upper limit achievable with reliable performance. Comparisons are among standard, commonly referenced types. Concept / Approach: Base-metal thermocouples like Type J (iron–constantan), Type K (chromel–alumel), and Type T (copper–constantan) are economical and cover moderate ranges. Noble-metal combinations using platinum and platinum/rhodium (Types S, R, and B) tolerate much higher temperatures with stability, enabling accurate measurement in the 0 to 1600+ °C region depending on type. Therefore, when the criterion is the widest practical measurement span with high maximum temperature capability, the platinum–platinum/rhodium family is preferred. Step-by-Step Solution: List typical ranges: J (~0 to 750–800 °C), K (~−200 to 1250 °C), T (~−200 to 350 °C), S/R (~0 to 1600 °C), B (~600 to 1700 °C).Compare upper limits: noble-metal types S/R/B have the highest.Select the family with the broadest usable span and highest top end: platinum–platinum/rhodium. Verification / Alternative check: Vendor data sheets and standards consistently show Types S, R, and B reaching temperatures beyond base-metal limits while maintaining calibration stability in oxidizing environments. Why Other Options Are Wrong: Iron–constantan: Useful but limited at high temperatures and vulnerable at low temperatures due to iron oxidation. Chromel–alumel: Very versatile but still capped below noble-metal upper limits. Copper–constantan: Excellent at low temperatures; low upper limit. Type N: Improved stability vs K, but upper limit lower than S/R/B. Common Pitfalls: Confusing accuracy with range; some base-metal types can be more sensitive at moderate temperatures but cannot withstand extreme heat like platinum-based types. Final Answer: Platinum–platinum/rhodium (Types S/R/B)

Question 19

Identifying non–variable-area (VA) flowmeters: Which of the following is not a variable area flow meter (areameter) used in process flow measurement?

Accepted Answer

Introduction / Context: Variable-area (VA) meters, also known as areameters, indicate flow by allowing the flow passage area to change until the force balance is achieved. Recognizing which devices are VA aids correct selection and troubleshooting in instrumentation diagrams and specifications. Given Data / Assumptions: VA meters include tapered tubes with floats, variable orifices, and piston-style mechanisms. Electromagnetic meters measure flow based on induced voltage proportional to velocity in a conductive fluid. All devices are considered under typical plant conditions. Concept / Approach: VA devices alter flow area with flowrate, e.g., a float rising in a tapered tube (rotameter) or a spring-loaded piston moving to change an orifice gap. Magnetic flow meters, by contrast, have a fixed cross-section and infer volumetric flow Q = velocity * area by measuring the induced voltage from a conductive fluid moving through a magnetic field. Thus, magnetic flow meters are not VA instruments. Step-by-Step Solution: Define VA principle: variable area balances fluid forces.Check each option against the VA definition.Identify electromagnetic meter as non-VA because area is fixed and measurement relies on Faraday’s law. Verification / Alternative check: Instrument catalogs classify rotameters and piston-type meters as VA, while magnetic meters are velocity-based and require conductivity. Why Other Options Are Wrong: Piston type: Classic spring-loaded VA design. Rotameter: Archetypal VA meter. Orifice and tapered plug VA meter: Area varies with plug position. Variable nozzle VA meter: Area changes with flow/position. Common Pitfalls: Assuming any device with a “taper” is VA; electromagnetic flow meters have no moving parts and fixed area. Final Answer: Magnetic flow meter (electromagnetic)

Question 20

Platinum resistance thermometry behavior: As temperature increases, how does the electrical conductivity of platinum (used in RTDs) change?

Accepted Answer

Introduction / Context: Resistance temperature detectors (RTDs) exploit the predictable change in resistance of metals with temperature. Platinum is the industry standard because of its linearity, chemical stability, and reproducibility. Understanding the direction of change of conductivity (the inverse of resistivity) is fundamental. Given Data / Assumptions: Material: high-purity platinum wire or thin film. Normal RTD operating range (e.g., −200 to 600 °C). Ohmic behavior with negligible self-heating effects at proper excitation. Concept / Approach: For metals, resistivity increases with temperature due to increased lattice vibrations scattering conduction electrons. Therefore, resistance increases and conductivity (σ = 1/ρ) decreases as temperature rises. This monotonic trend underpins the positive temperature coefficient (PTC) response of platinum RTDs. Step-by-Step Solution: Recognize platinum as a metal with positive temperature coefficient of resistance.As temperature ↑ → resistivity ↑ → conductivity ↓.Therefore, the electrical conductivity decreases with temperature. Verification / Alternative check: Standard RTD equations (e.g., Callendar–Van Dusen) show resistance increases with temperature, confirming decreasing conductivity. Why Other Options Are Wrong: Increases / increases exponentially: Opposite to metallic behavior in normal ranges. Remains constant: Not for metals; semiconductors may show opposite trends. Random changes: Platinum is prized because it is predictable, not random. Common Pitfalls: Confusing metals with semiconductors; semiconductors often show conductivity increasing with temperature, unlike metals. Final Answer: Decreases

Process Control and Instrumentation Questions