Question 1

Intake temperature and compressor capacity For a given compressor and speed, the delivered capacity (mass flow rate) will be __________ when the intake air temperature is at its lowest value.

Accepted Answer

Introduction / Context: Compressor capacity in mass terms depends directly on inlet air density. Since density is inversely related to absolute temperature at a given pressure, lowering the intake temperature increases density and thus mass flow for a fixed volumetric flow capability. Given Data / Assumptions: Same compressor geometry and rotational speed. Same inlet pressure; variable inlet temperature. Performance within surge/choke limits. Concept / Approach: Mass flow m_dot = rho * V_dot. For ideal gas at fixed pressure, rho = p / (R * T). Decreasing T increases rho, hence increases m_dot for the same volumetric throughput. Therefore, the capacity is highest when the intake air is coldest. Step-by-Step Solution: Fix volumetric flow (machine-limited) and inlet pressure.Use rho = p / (R * T): lowering T raises rho.Compute m_dot = rho * V_dot: higher rho yields higher mass flow.So capacity is highest at the lowest intake temperature. Verification / Alternative check: Corrected mass flow definitions in turbomachinery use inlet total temperature precisely to normalize such effects; cooler inlets show higher actual mass flow. Why Other Options Are Wrong: “Lowest” contradicts the density relationship; “unchanged” ignores ideal gas behavior; “indeterminate” is false because the dependence is clear and monotonic under the stated constraints. Common Pitfalls: Confusing volumetric capacity with mass capacity; volumetric flow may be similar, but mass capacity changes with density. Final Answer: highest

Question 2

Air compressors and thermodynamics: The work done by an air compressor depends upon the manner (process path) in which the air is compressed (e.g., isothermal, adiabatic, or polytropic) and on clearance and intercooling details.

Accepted Answer

Introduction / Context: Understanding what governs compressor work is fundamental in thermodynamics and gas power cycles. Designers minimize power input by choosing a suitable compression process path, staging, and cooling methods. This question probes whether compressor work is path dependent or not. Given Data / Assumptions: Single or multi-stage air compression. Common idealized paths: isothermal, adiabatic (isentropic if reversible), and polytropic with index n. Same inlet state and the same final delivery pressure are assumed for comparison. Concept / Approach: For a perfect gas, compressor work is the area under the p–v curve. Different thermodynamic paths between the same end states trace different areas, hence different work. Isothermal compression yields the minimum theoretical work. Adiabatic compression requires the maximum work among the common idealized paths. Polytropic work lies between them and can be further reduced with intercooling in multi-stage arrangements. Step-by-Step Solution: Define work input as W = integral of p dv over the compression path.For isothermal: p * v = constant → W_iso = m * R * T1 * ln(p2/p1).For adiabatic: p * v^gamma = constant → W_ad depends on gamma and shows higher value than isothermal for the same pressure ratio.For polytropic: p * v^n = constant → W_poly lies between isothermal and adiabatic depending on n.Intercooling between stages reduces the temperature before the next stage, cutting the required work further. Verification / Alternative check: Plotting p–v diagrams for the three processes with the same p1, v1 and final pressure p2 shows clearly different areas (work inputs). Experimental data on multi-stage compressors with intercoolers confirm lower power draw than single-stage adiabatic compression to the same discharge pressure. Why Other Options Are Wrong: Does not depend: Incorrect because work is path dependent. Depends only on inlet pressure: Discharge pressure and path also matter. Depends only on discharge pressure: Inlet state and process path matter as well. Common Pitfalls: Assuming fixed end pressures force identical work. Ignoring temperature rise and cooling strategies leads to wrong conclusions. Final Answer: depends

Question 3

Rocket propulsion basics: A rocket engine carries its own oxidizer; combustion does not use atmospheric air.

Accepted Answer

Introduction / Context: Rocket engines operate in near-vacuum and outer space, so they cannot depend on atmospheric oxygen. This question checks the basic concept of how rockets burn fuel independent of the environment. Given Data / Assumptions: Chemical rocket with propellants stored onboard. Combustion chamber and nozzle expel high velocity gases to produce thrust. No reliance on ambient oxygen, unlike air-breathing engines. Concept / Approach: Rocket propellants are divided into fuel and oxidizer. The oxidizer supplies the oxygen needed for combustion. Options include liquid oxygen, nitrogen tetroxide, or solid oxidizers in composite propellants. Because the oxidizer is onboard, rockets function both within the atmosphere and in space. Step-by-Step Solution: Recognize the operating environment: space has negligible oxygen.Air-breathing systems (turbojet, ramjet) require atmospheric oxygen and thus cannot operate in vacuum.Rocket principle: carry oxidizer and fuel → combustion independent of atmosphere.Therefore, the correct choice is that a rocket uses its own oxygen (oxidizer). Verification / Alternative check: Historical missions (orbital and deep space) use liquid oxygen or storable oxidizers. Ground tests also show rocket operation in evacuated chambers, reinforcing the independence from air. Why Other Options Are Wrong: Surrounding air / compressed atmospheric air: Applicable to air-breathing engines, not rockets. None of these: Incorrect because rockets explicitly carry oxidizer. Common Pitfalls: Confusing rockets with jet engines. Jets compress atmospheric air; rockets do not ingest air for combustion. Final Answer: its own oxygen

Question 4

Jet propulsion diffusers: The diverging inlet duct in a jet propulsion unit acts as a diffuser to convert incoming air kinetic energy into static pressure energy.

Accepted Answer

Introduction / Context: Air-breathing propulsion systems use inlet diffusers to condition the flow for the compressor or combustor. An efficient inlet recovers dynamic pressure (ram pressure) by diffusing the flow and raising static pressure. Given Data / Assumptions: Diverging inlet duct shape (area increasing in the flow direction). Subsonic inlet operation for typical turbojets and turbofans. Goal: deliver higher static pressure and lower Mach number to the compressor face. Concept / Approach: For subsonic flow, a diffuser converts velocity head into static pressure. The continuity and momentum relations show that expanding area slows the flow. The Bernoulli relation for adiabatic, low-loss subsonic diffusion indicates an increase in static pressure at the expense of kinetic energy. Step-by-Step Solution: Incoming air has high dynamic pressure due to flight speed.A diverging duct (diffuser) reduces velocity and increases static pressure.This pressure recovery improves compressor performance and surge margin.Therefore the statement that the diverging inlet converts kinetic energy into pressure energy is true. Verification / Alternative check: Inlet pressure recovery coefficients quantify performance; well-designed subsonic diffusers show static pressure rise and total pressure losses kept minimal. Why Other Options Are Wrong: False: Contradicts diffuser function in subsonic inlets. True, but only at zero speed: At zero speed there is little kinetic energy to recover; the diffuser benefit is evident at finite flight speed. False, it converts pressure to velocity: That is the role of a nozzle, not a diffuser. Common Pitfalls: Confusing supersonic inlets (which need shocks and area variations) with subsonic diffusers; the basic energy conversion is the same but controlled differently. Final Answer: True

Question 5

Centrifugal compressor pressure ratio: Increasing impeller tip speed and lowering inlet temperature generally increase achievable pressure ratio (within Mach and stress limits).

Accepted Answer

Introduction / Context: In centrifugal compressors, pressure rise is closely tied to blade tip speed and inlet density. Designers balance mechanical limits, surge margin, and choking constraints to reach a target pressure ratio efficiently. Given Data / Assumptions: Idealized compressor behavior with reasonable efficiency. Tip speed U2 increases with rotational speed and radius. Inlet total temperature affects inlet density and relative Mach numbers. Concept / Approach: The ideal specific head of a centrifugal compressor scales approximately with U2^2. Therefore, higher tip speed increases head and potential pressure ratio for a given efficiency. Lower inlet temperature increases density, reduces inlet Mach number for the same volumetric flow, and can allow higher pressure ratio before choking or stall occur. Step-by-Step Solution: Specific head H ~ U2^2 / g_c (conceptual proportionality).Raise U2 → raise H → higher pressure rise at similar efficiency.Lower T1 → higher rho1 for same p1 → improved compressor inlet conditions and Mach margin.Thus, increasing tip speed and lowering inlet temperature increases achievable pressure ratio, bounded by stress and surge limits. Verification / Alternative check: Compressor performance maps show higher pressure ratios at higher corrected speeds and at lower corrected inlet temperatures (after accounting for scaling), consistent with the statement. Why Other Options Are Wrong: Incorrect: Ignores fundamental speed–head relation. Correct only if speed is reduced: Contradictory. Geometry only: Geometry matters, but operating speed and inlet conditions significantly shift performance. Common Pitfalls: Overlooking limits such as tip Mach number, blade stress, and surge/choke boundaries when attempting to raise pressure ratio by speed alone. Final Answer: Correct

Question 6

Closed-cycle gas turbine layout: Identify the main components that a closed-cycle gas turbine must include for steady operation with a constant working fluid.

Accepted Answer

Introduction / Context: Closed-cycle gas turbines circulate a fixed working fluid (often helium or nitrogen) through compression, external heating, and expansion. Recognizing the essential components clarifies how the cycle sustains itself. Given Data / Assumptions: Closed loop with a constant mass of working fluid. External heat source adds energy; external cooler rejects heat. Compressor and turbine are connected by a shaft delivering net power. Concept / Approach: The compressor raises the pressure of the working fluid. The heating chamber (external heater) raises its temperature at essentially the same pressure. The turbine expands the hot fluid to produce work. The cooler then removes heat to return the fluid to a low temperature before recompression, completing the loop. Step-by-Step Solution: Compression → pressure rise in the compressor.External heating → temperature rise at high pressure in a heater or heat exchanger.Expansion → turbine produces work as the fluid pressure and temperature drop.Cooling → cooler or heat exchanger removes waste heat to restore low inlet temperature to the compressor. Verification / Alternative check: On a T–s diagram, the closed Brayton cycle shows compression, constant-pressure heat addition, expansion, and constant-pressure heat rejection, consistent with the listed components. Why Other Options Are Wrong: Choosing only one or two components breaks the closed loop. Without a cooler, compressor inlet temperature rises and work skyrockets; without a heater, there is no useful expansion. Common Pitfalls: Confusing open and closed cycles; in an open cycle, combustion replaces the external heater and the working fluid is air that is exhausted to atmosphere. Final Answer: all of these

Question 7

Gas turbine performance metric: The work ratio is defined as the ratio of net work output from the plant to the turbine work.

Accepted Answer

Introduction / Context: In gas turbines, a significant fraction of the turbine work is used to drive the compressor. The work ratio indicates how much of the turbine work is available as net useful output, and is a key cycle quality indicator. Given Data / Assumptions: Turbine work W_t, compressor work W_c, net work W_net = W_t - W_c. Steady state Brayton cycle operation. Neglect auxiliary loads for clarity. Concept / Approach: Work ratio = W_net / W_t. A higher work ratio means less of the turbine work is internally consumed by the compressor, typically associated with lower pressure ratios, effective intercooling, or better component efficiencies. However, there is a tradeoff with thermal efficiency and specific work. Step-by-Step Solution: Compute turbine work W_t from expansion across the turbine.Compute compressor work W_c from compression process.Compute net work W_net = W_t - W_c.Evaluate work ratio = W_net / W_t. Verification / Alternative check: Cycle calculations show that as pressure ratio increases, W_t rises but W_c rises too. The ratio provides a normalized measure to compare cycles and is independent of absolute scale. Why Other Options Are Wrong: Compression ratio and pressure ratio are separate geometric or thermodynamic ratios, not the requested definition. None of these is incorrect because work ratio is the accepted term. Common Pitfalls: Confusing work ratio with back work ratio (W_c / W_t). Both are useful but represent different perspectives. Final Answer: work ratio

Question 8

Applications of compressed air: Pneumatic systems commonly use compressed air to operate lifts, rams, and certain pumps (air lift and diaphragm types).

Accepted Answer

Introduction / Context: Compressed air is a versatile power medium used in industrial automation and fluid handling. This question asks whether compressed air is indeed used to operate devices such as lifts, rams, and pumps. Given Data / Assumptions: Pneumatic actuators (cylinders) convert air pressure into linear force for rams and lifts. Air lift pumps use compressed air injection to raise water via density reduction. Air driven diaphragm pumps use compressed air to flex diaphragms, moving liquids. Concept / Approach: Pneumatics relies on the pressure energy of compressed air. Control valves meter flow into actuators, generating motion or force. In pumping applications, compressed air either acts as the motive fluid (air lift) or powers a mechanical membrane that displaces liquid. Step-by-Step Solution: Compressed air is generated and regulated to a working pressure.Directional control valves feed air to pistons → motion for rams and lifts.For air lift pumps, air bubbles reduce mixture density in the riser, creating upward flow.Air driven diaphragm pumps alternately pressurize chambers to move fluid. Verification / Alternative check: Industrial catalogs and plant layouts routinely show pneumatic cylinders on lifts and rams, and air operated pumps in hazardous areas where electric motors are undesirable. Why Other Options Are Wrong: “No” contradicts widespread industrial practice. The restrictions in options “Only at very high pressure” or “Only under water” are not generally true; many systems operate at moderate plant air pressures. Common Pitfalls: Assuming hydraulics are the only option for heavy lifting. Pneumatics offer cleanliness and simplicity, though at lower force density compared to hydraulic systems. Final Answer: Yes

Question 9

Terminology: A machine specifically designed to raise the pressure of air is called a compressor.

Accepted Answer

Introduction / Context: Correct terminology helps avoid confusion among related machines in fluid and thermal engineering. This question asks for the proper name of a device that raises air pressure. Given Data / Assumptions: Working fluid is air. Device function is to increase pressure from an inlet level to a higher discharge level. Steady operation is assumed. Concept / Approach: A compressor absorbs shaft power to elevate the total pressure of a gas. Types include reciprocating, rotary screw, centrifugal, and axial compressors. Gas turbines, in contrast, produce net power by expanding hot gas, while internal combustion engines produce mechanical power by combusting fuel with air. An air motor converts compressed air energy back into shaft work. Step-by-Step Solution: Identify the function: raise pressure of air.Match function to device: this is exactly what a compressor does.Exclude other devices whose primary function is different (power generation, expansion, or combustion). Verification / Alternative check: Manufacturer datasheets and engineering texts classify machines that increase gas pressure under the category of compressors, distinct from turbines and motors. Why Other Options Are Wrong: Gas turbine: expands gas to create work, not primarily to compress air. I.C engine: produces mechanical work from combustion, not a pressure-raising device for air alone. Air motor: consumes compressed air to deliver shaft work, the reverse of a compressor. Common Pitfalls: Confusing the compressor inside a gas turbine engine with the entire engine. The compressor is a component, not the whole machine. Final Answer: compressor

Question 10

Jet propulsion and ram effect: Overall compression due to ram pressure recovery increases roughly with the square of flight speed (dynamic pressure scales with V^2), enhancing inlet total pressure.

Accepted Answer

Introduction / Context: Air-breathing jet engines benefit from flight speed through ram pressure recovery in the inlet. The relationship between speed and the available dynamic pressure informs inlet design and engine performance at various Mach numbers. Given Data / Assumptions: Subsonic to transonic flight where diffuser design provides pressure recovery. Dynamic pressure q = 0.5 * rho * V^2. Compressor itself produces its own pressure ratio, but inlet ram recovery adds to compressor face total pressure. Concept / Approach: Dynamic pressure scales with the square of speed. A well-designed inlet diffuser converts part of this kinetic energy into static pressure, increasing total pressure at the compressor face relative to static ambient. Thus, the contribution from ram effect to overall compression grows with V^2, though practical limits arise from losses, shocks, and inlet distortion at higher Mach numbers. Step-by-Step Solution: Write dynamic pressure: q = 0.5 * rho * V^2.Recognize that inlet pressure recovery converts a portion of q to increased static pressure.Therefore, the ram-induced compression effect grows roughly with V^2.Engine overall pressure ratio = inlet recovery effect * compressor pressure ratio (conceptually). Verification / Alternative check: Performance charts show increasing compressor face total pressure with increasing flight speed up to design Mach, consistent with ram pressure rise proportional to V^2, adjusted for recovery efficiency. Why Other Options Are Wrong: Incorrect: Neglects fundamental dynamic pressure scaling. Correct only for propeller aircraft: Ram effect applies to jet inlets as well. Linear with speed: Physically incorrect because kinetic energy and dynamic pressure scale with V^2. Common Pitfalls: Confusing compressor pressure ratio (largely speed and geometry dependent) with ram recovery effect due to forward speed. Both contribute but are distinct. Final Answer: Correct

Question 11

Air motor thermodynamics: An air motor operates on a cycle that is the reverse of the reciprocating air compressor cycle, expanding compressed air to produce work.

Accepted Answer

Introduction / Context: Air motors and air compressors are thermodynamic inverses. Where compressors consume shaft work to raise air pressure, air motors use stored compressed air to deliver shaft work. Recognizing the reversed indicator diagrams improves understanding of pneumatic power systems. Given Data / Assumptions: Reciprocating cylinder with valves arranged for intake of high-pressure air and exhaust of low-pressure air. Idealized processes comparable to those of reciprocating compressors but in reverse order. Friction and throttling losses exist but are secondary to the conceptual reversal. Concept / Approach: On a p–v diagram, a compressor follows a compression path from low to high pressure, rejecting heat or not depending on the process. An air motor follows the reverse: it admits high-pressure air, expands it to produce work, and exhausts at a lower pressure. Thus the air motor cycle is the time-reversed counterpart of the compressor cycle. Step-by-Step Solution: Identify compressor processes: intake at low p, compression to high p, delivery.Reverse them for the motor: admission at high p, expansion delivering work, exhaust at low p.Recognize that ideal reversibility is limited by valve timing, heat transfer, and flow losses, but the cycle relation still holds. Verification / Alternative check: Indicator diagrams from laboratory setups show mirrored loops for compressor and air motor when plotted under similar scaling, confirming the reversed nature. Why Other Options Are Wrong: Disagree and conditional statements are misleading. While real devices deviate from ideal paths, the fundamental thermodynamic relationship remains that an air motor cycle is the reverse of a compressor cycle. Common Pitfalls: Expecting identical efficiencies when reversing. Practical air motors have throttling losses and cannot exactly retrace the compressor path. Final Answer: Agree

Question 12

Gas turbines with intercooling: effect on compressor work input In a gas-turbine plant that uses multistage compression with intercooling between stages, how does the required compressor work with intercooling compare to the work with no intercoolin…

Accepted Answer

Introduction / Context: Intercooling in gas turbines is a classic method to reduce compressor work. By removing heat between compression stages, the specific volume of the air entering the next stage is lowered, which reduces the work of subsequent compression for a given overall pressure ratio. This question tests conceptual understanding of why intercooling decreases the compressor power requirement. Given Data / Assumptions: Same overall pressure ratio across the compressor with and without intercooling. Idealized discussion: negligible pressure losses in intercoolers and ducting. Working fluid treated as a perfect gas with approximately constant specific heats over the compression range. Concept / Approach: Compressor work depends on the average specific volume during compression. Cooling the air between stages brings the temperature closer to the initial value, which reduces specific volume and hence the area under the p–v diagram for compression. On a T–s diagram, for the same pressure rise, intercooling moves the path closer to isothermal, lowering the enthalpy rise per kilogram and therefore the work input. Step-by-Step Solution: Define goal: achieve the same final pressure using multiple stages.Introduce intercooling: reject heat after each stage to reduce temperature before the next stage.Effect: lower inlet temperature to each subsequent stage → lower specific volume → lower stage work.Total compressor work = sum of stage works → decreases with intercooling (for the same overall pressure ratio). Verification / Alternative check: For ideal equal pressure-ratio staging with perfect intercooling (temperature restored to the original value), the minimum total compressor work is achieved. Analytical expressions for polytropic compression confirm a reduced enthalpy rise when intermediate cooling is applied. Why Other Options Are Wrong: Equal to: contradicts thermodynamics; intercooling reduces work.More than: removing heat cannot increase ideal compression work.Cannot be predicted / depends only on combustor efficiency: compressor work is determined by compression thermodynamics, not combustor performance. Common Pitfalls: Assuming intercooling always improves overall cycle efficiency; while it cuts compressor work, it also increases heat added in the combustor because the compressed air is cooler, which can reduce thermal efficiency unless regeneration is used. Final Answer: less than the work with no intercooling

Question 13

Reciprocating air compressors: is isothermal efficiency used for all calculations? Decide whether the statement “isothermal efficiency is used for all sorts of calculations in reciprocating air compressors” is correct.

Accepted Answer

Introduction / Context: Several efficiency definitions exist for compressors: isothermal, adiabatic (isentropic), and polytropic efficiencies. Choosing the right one depends on what is being analyzed: performance mapping, stage-by-stage design, or rating comparisons. The statement in the prompt overgeneralizes a specific metric. Given Data / Assumptions: Single- or multistage reciprocating compressors. Non-ideal effects such as clearance, valve losses, and heat transfer exist. Engineers commonly use polytropic or isentropic efficiency for design and performance calculations. Concept / Approach: Isothermal efficiency compares actual work to the work of ideal isothermal compression between the same pressures. It is useful as a benchmark because isothermal compression is the theoretical minimum work. However, most detailed calculations (especially across stages) are based on polytropic or isentropic models that more realistically represent the thermodynamic path and allow combining multiple small steps consistently. Step-by-Step Solution: Define isothermal efficiency = ideal isothermal work / actual work (same mass and pressure rise).Define isentropic (adiabatic) efficiency = ideal isentropic work / actual work.Define polytropic efficiency as a small-step efficiency relating differential compression to actual behavior, convenient for multistage analysis.Identify usage: design and performance maps typically quote polytropic or isentropic efficiencies; isothermal efficiency is not used for “all sorts” of calculations. Verification / Alternative check: Manufacturer datasheets for reciprocating compressors present isentropic/polytropic efficiency and volumetric efficiency; isothermal efficiency may appear as a comparative marketing metric but is not universal for engineering calculations. Why Other Options Are Wrong: “Correct” options conflict with standard practice; limiting cases (very low speed or perfect intercooling) do not justify blanket usage. Common Pitfalls: Confusing best-case (isothermal) limits with practical modeling. Using isothermal efficiency indiscriminately can underpredict power requirements. Final Answer: Incorrect

Question 14

Definition check: perfect intercooling in multistage compression For a multistage air compressor with intercoolers, perfect intercooling means the air temperature at the inlet to each subsequent stage is brought back to the initial intake temperatur…

Accepted Answer

Introduction / Context: Intercooling removes heat between compression stages. The idealized target is perfect intercooling, a concept that appears in most textbook derivations for minimizing total compression work and for selecting optimal intermediate pressures. Given Data / Assumptions: Same overall suction and delivery pressures. Intercoolers with negligible pressure loss (idealization). “Initial temperature” refers to the first-stage inlet temperature. Concept / Approach: Perfect intercooling aims to restore the compressed air to the original intake temperature prior to entering the next stage. On a T–s diagram, each stage begins at the same temperature line, reducing the average specific volume and, consequently, the work per stage. This is the condition used to derive equal pressure-ratio staging as the minimum-work solution. Step-by-Step Solution: After stage 1 compression, air leaves at elevated temperature.Intercooler removes heat at approximately constant pressure, bringing temperature back to initial value.Stage 2 sees the same inlet temperature as stage 1 had initially.Repeat for subsequent stages to realize minimum total compressor work (with equal pressure ratios). Verification / Alternative check: Analytical expressions show that, with perfect intercooling and equal pressure ratios per stage, the total compressor work is minimized for a specified overall pressure ratio. Why Other Options Are Wrong: Limiting perfect intercooling to specific numbers of stages or requiring zero clearance is unnecessary; the definition is independent of those details. Common Pitfalls: Confusing “perfect intercooling” (temperature reset) with “regeneration” (recuperation) or aftercooling (cooling after final compression). Final Answer: Agree

Question 15

Three-stage compressor with perfect intercooling: pressure relationship for minimum work For a three-stage reciprocating air compressor with perfect intercooling and negligible intercooler pressure loss (overall pressures p1 → p4), which relationshi…

Accepted Answer

Introduction / Context: Staging reduces the work of compression, particularly when heat is removed between stages. For a fixed overall pressure ratio, there is an optimal distribution of pressure ratios among stages that minimizes total work. This is a standard design question for multistage reciprocating compressors. Given Data / Assumptions: Three compression stages with intercooling between stages. Perfect intercooling: each stage inlet temperature equals the initial intake temperature. Negligible pressure drops in intercoolers and piping. Concept / Approach: For perfect intercooling and identical polytropic behavior in each stage, the total work is minimized when the pressure ratio is the same across all stages. This equal-ratio condition distributes the enthalpy rise uniformly and produces the smallest sum of stage works for the given overall pressure ratio. Step-by-Step Solution: Let overall ratio r_total = p4 / p1.With equal staging, each stage ratio r = (r_total)^(1/3).Therefore, p2 = r p1, p3 = r p2, p4 = r p3 → p2 / p1 = p3 / p2 = p4 / p3.This condition yields minimum total compressor work for the specified p4 and p1. Verification / Alternative check: Minimization can be shown by differentiating the total work with respect to intermediate pressures and setting the derivative to zero, which leads to equal pressure ratios per stage as the optimum. Why Other Options Are Wrong: Products like p1 p2 = p3 p4 or p1 p3 = p2 p4 are not generally satisfied by equal-ratio staging for three stages and do not guarantee minimum work.Statements such as p2^2 = p1 p4 or p3^2 = p2 p4 only apply to specific two-stage relationships, not to three-stage equal ratio design. Common Pitfalls: Applying the two-stage geometric mean relation (p2^2 = p1 p3) incorrectly to three-stage problems or overlooking the assumption of perfect intercooling. Final Answer: p2 / p1 = p3 / p2 = p4 / p3

Question 16

Single-acting reciprocating air compressor (no clearance): nature of compression In a single-acting reciprocating air compressor without clearance volume, the thermodynamic path of compression can be considered as which of the following under differ…

Accepted Answer

Introduction / Context: The idealized thermodynamic path of compression in a reciprocating compressor depends on the heat transfer during the process. Recognizing the limiting and practical cases is essential for estimating power and for sizing cooling equipment. Given Data / Assumptions: No clearance volume (simplifies suction/exhaust dynamics). Same suction and discharge pressures for comparison. Variable degree of heat removal during compression. Concept / Approach: Compression can approach isothermal if heat is removed continuously and effectively (e.g., very slow compression with excellent cooling). It approaches isentropic if the compression is rapid and well insulated (negligible heat exchange). The real-world case most often lies between these extremes and is modeled as polytropic with p v^n = C, where n is between 1 (isothermal) and k (isentropic exponent). Step-by-Step Solution: Define limits: isothermal (maximum cooling) and isentropic (adiabatic, no heat transfer).Recognize practical path: polytropic with exponent 1 < n < k.Conclude: depending on operating conditions and heat removal, any of the three idealizations may be used for analysis.Select option indicating all possibilities under different cooling scenarios. Verification / Alternative check: Power expressions W_iso, W_poly, and W_isentropic show distinct values; measured indicator diagrams typically align with polytropic modeling but can approach the limits under controlled experiments. Why Other Options Are Wrong: Restricting to only one path ignores the role of heat transfer; real machines vary with speed, cooling water rate, and materials. Common Pitfalls: Assuming “adiabatic” by default. In many plant compressors with good jackets and intercooling, the effective exponent can be well below k. Final Answer: any one of these (isothermal, polytropic, or isentropic)

Question 17

Afterburning in open-cycle turbojet engines (military use) In military turbojets, fuel is sometimes burned in the exhaust (after the turbine) using an afterburner. This practice primarily increases which performance metric?

Accepted Answer

Introduction / Context: Afterburning (reheat) adds fuel downstream of the turbine to raise jet exhaust temperature before the nozzle. It is used in combat aircraft to achieve short bursts of very high thrust for takeoff, climb, or supersonic dash. Given Data / Assumptions: Open-cycle turbojet with an afterburner located between the turbine exit and nozzle. No change to compressor/turbine work with afterburner “on”. Objective: understand primary performance effect. Concept / Approach: Thrust for a pure jet depends on mass flow and jet velocity relative to flight speed. Afterburning raises exhaust temperature and therefore increases nozzle exit velocity for the same mass flow, producing more thrust. However, it achieves this at very poor propulsive and thermal efficiencies, drastically increasing specific fuel consumption and reducing range/endurance. Step-by-Step Solution: Introduce additional fuel in the tailpipe → higher exhaust stagnation temperature.Higher temperature → higher nozzle exit velocity for choked/no-choked conditions.Propulsive effect: increased momentum flux → higher thrust.Efficiency impact: more fuel for relatively modest thrust gain → lower thermal and propulsive efficiencies → reduced range. Verification / Alternative check: Flight manuals and engine data show dramatic increases in specific fuel consumption with afterburner engaged, confirming that efficiency and range decrease even as thrust rises steeply. Why Other Options Are Wrong: Thermal efficiency and range do not increase; they decrease in afterburning operation.“Specific fuel consumption only” decreasing is incorrect; SFC increases significantly. Common Pitfalls: Confusing afterburning with reheating inside the Brayton cycle between turbine stages (a different concept). Afterburners add energy after the turbine and do not help shaft work or cycle efficiency. Final Answer: thrust only

Question 18

Roots blower: trend of efficiency with pressure ratio How does the efficiency of a Roots blower vary as the delivery pressure ratio is increased (other conditions unchanged)?

Accepted Answer

Introduction / Context: Roots blowers are positive-displacement rotary machines that move nearly constant volume per revolution with internal backflow and leakage. They are often used for low pressure ratios where simplicity and robustness matter more than high efficiency. Given Data / Assumptions: Fixed blower speed and geometry. Increasing delivery pressure ratio by throttling or backpressure. Air treated as a perfect gas; qualitative efficiency trend sought. Concept / Approach: In a Roots blower, actual compression largely occurs outside the casing when the trapped pocket opens to the high-pressure side, causing sudden backflow and mixing losses. As pressure ratio increases, internal leakage and pulsation losses represent a larger fraction of the indicated work, and the temperature rise increases, all of which reduce isentropic and overall efficiencies. Step-by-Step Solution: At low pressure ratio, leakage/backflow is modest → acceptable efficiency.As pressure ratio increases, pressure difference across clearances grows → more backflow and heating.Energy dissipated as heat and pulsation noise rises → efficiency drops.Therefore, efficiency decreases with increasing pressure ratio. Verification / Alternative check: Manufacturer performance maps show recommended operating ranges with pressure ratios typically below about 1.5–2, beyond which efficiency falls rapidly and discharge temperatures become excessive. Why Other Options Are Wrong: Increasing or unchanged efficiency contradicts both physics and empirical performance curves.A peaked trend is not characteristic for Roots blowers across the usual range; the dominant trend is downward. Common Pitfalls: Assuming Roots behave like dynamic compressors. They do not; they lack internal compression up to delivery pressure and thus suffer greater losses at higher ratios. Final Answer: decreases

Question 19

Ideal cycle for a closed-cycle gas turbine A closed-cycle gas turbine (with external heat addition and rejection, using a working gas in a loop) ideally operates on which thermodynamic cycle?

Accepted Answer

Introduction / Context: Gas turbines—open or closed—are conceptually based on the Brayton (Joule) cycle, consisting of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection. The “closed” qualifier refers to how heat is added/removed and whether the working fluid is recirculated, not to the underlying cycle type. Given Data / Assumptions: Closed loop with a working gas (often helium, nitrogen, or air). External heater and cooler provide constant-pressure heat transfer. Ideal turbomachinery with isentropic compression/expansion. Concept / Approach: The hallmark of the Brayton (Joule) cycle is constant-pressure heat transfer. In a closed-cycle implementation, the same gas recirculates through compressor, heater, turbine, and cooler. Regeneration is frequently added in practice to improve thermal efficiency, but the base ideal cycle remains Brayton. Step-by-Step Solution: Identify processes: 1–2 isentropic compression, 2–3 constant-pressure heat addition, 3–4 isentropic expansion, 4–1 constant-pressure heat rejection.Open vs closed: the open cycle exhausts to atmosphere; the closed cycle recirculates through a cooler.Therefore, the ideal closed-cycle gas turbine operates on the Joule (Brayton) cycle. Verification / Alternative check: Ericsson and Stirling cycles involve isothermal processes; Rankine is a vapor cycle for steam plants; Carnot is an ideal limit with isothermal and adiabatic processes, not the practical gas-turbine basis. Why Other Options Are Wrong: Constant-pressure heating/cooling distinguishes Brayton from Ericsson/Stirling; Rankine applies to phase-change (liquid-vapor) cycles; Carnot is not used directly due to impractical isothermal compression/expansion. Common Pitfalls: Equating “closed cycle” with non-Brayton cycles; closure is about recirculation, not changing the fundamental thermodynamic processes. Final Answer: Joule (Brayton) cycle

Question 20

Effect of clearance on work and power in a single-stage, single-acting reciprocating compressor Consider a single-stage, single-acting reciprocating air compressor operating between fixed suction and delivery pressures. The presence of clearance vol…

Accepted Answer

Introduction / Context: Clearance volume—dead space that remains when the piston is at top dead center—allows trapped high-pressure air to expand during the next suction stroke. It primarily reduces volumetric efficiency, but its influence on indicated work and shaft power depends on how we define the duty (fixed speed vs fixed mass flow rate). Given Data / Assumptions: Single-stage, single-acting compressor with fixed suction and delivery pressures. Same polytropic exponent for compression and re-expansion in the clearance pocket. Comparison on the basis of delivering a specified mass flow rate of free air. Concept / Approach: For a given pressure range, the indicated work per kilogram compressed is essentially independent of clearance if compression and re-expansion follow the same index; the p–v loop area for one kilogram is unchanged. However, clearance reduces the mass inducted per cycle (volumetric efficiency drops). To deliver the same mass flow, the compressor must run at higher speed or use a larger cylinder, which increases total power. Therefore, in practical plant terms (fixed required delivery), clearance does affect the power required. Step-by-Step Solution: With clearance, a portion of discharge air remains and re-expands, displacing some of the suction volume.Net fresh charge per cycle decreases → volumetric efficiency falls.Work per kg remains approximately the same (same pressure rise and path), but delivering the same kg/s now requires higher rpm or more cylinders.Hence total shaft power to meet a given mass throughput increases due to the extra cycles needed, i.e., clearance impacts required power for a specified delivery. Verification / Alternative check: Indicator diagrams with and without clearance show similar per-kg loop areas but reduced trapped-mass throughput per cycle; plant power meters confirm higher power to achieve the same flow when clearance losses are significant. Why Other Options Are Wrong: Categorically stating “no effect” ignores the operational objective of delivering a specified mass rate; in practice, more cycles are needed and power rises. Common Pitfalls: Confusing “work per kg” (nearly unchanged) with “power for a given delivered flow” (increases because volumetric efficiency drops). Exam questions sometimes focus on the latter practical viewpoint. Final Answer: True

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