Question 1

Centrifugal compressor blade geometry: If the outlet relative flow angle from the rotor exceeds 90°, the impeller blades are termed “forward-curved.”

Accepted Answer

Introduction / Context:Impeller blade exit geometry strongly affects compressor head, efficiency, and stability. Classifying blades as backward-, radial-, or forward-curved depends on the outlet angle relative to the tangent.Given Data / Assumptions:Outlet (blade) angle measured from the tangent at the impeller tip.Typical classifications: backward-curved (β2 90°).Concept / Approach:Forward-curved blades turn the flow more in the direction of impeller rotation, increasing theoretical head but often at the cost of efficiency and surge margin compared to backward-curved designs used in modern compressors.Step-by-Step Solution:Given β2 > 90° from tangent → classification is forward-curved.Backward-curved corresponds to β2 Therefore, “forward-curved” is correct.Verification / Alternative check:Velocity triangles demonstrate that forward-curved blades yield larger whirl at exit, consistent with higher theoretical head.Why Other Options Are Wrong:They contradict the standard angle-based definitions.Common Pitfalls:Confusing blade metal angle definition with flow angles referenced to absolute vs. relative frames; here the conventional metal/relative angle convention is implied.Final Answer:forward curved

Question 2

Overall isothermal efficiency of a compressor In compressor terminology, the “overall isothermal efficiency” is defined as the ratio of the isothermal power (minimum theoretical power to compress the given mass flow between the same pressures) to th…

Accepted Answer

Introduction / Context:Compressors are assessed using several efficiencies that compare real performance with idealized limits. One widely used metric is overall isothermal efficiency. Understanding its definition helps learners connect actual shaft power consumption with the theoretical minimum power required if compression could proceed at constant temperature (isothermal), which represents the lowest possible work input for a given pressure ratio.Given Data / Assumptions:Steady operation of a compressor handling a given mass flow rate between fixed inlet and delivery pressures.Isothermal power means the theoretical power if the gas were compressed isothermally between the same pressure limits.Shaft power (brake power) is the mechanical power measured at the compressor shaft from the driving motor or engine.Concept / Approach:Overall isothermal efficiency compares a theoretical best-case work input with the real shaft power. By definition: overall isothermal efficiency = (isothermal power) / (brake power). Because real compression involves irreversibilities, heat transfer limitations, valve losses, and mechanical losses, the measured brake power is always higher than the isothermal power, making the efficiency less than 1.Step-by-Step Solution:Identify the ideal baseline: isothermal compression requires the least work for a given pressure ratio.Measure actual input: brake (shaft) power supplied to the compressor.Form the ratio: overall isothermal efficiency = isothermal power / brake power.Interpretation: the closer this ratio is to 1, the nearer the machine operates to the isothermal ideal (which is rarely achievable in practice).Verification / Alternative check:Other efficiencies exist, such as isentropic (adiabatic) and polytropic efficiencies. Their definitions use isentropic or differential reference processes in the numerator. The isothermal version specifically uses isothermal power in the numerator and brake power in the denominator, matching the present definition.Why Other Options Are Wrong:False: contradicts the standard definition used in compressor testing and textbooks.“True only at design point” and “depends on staging or intercooling” confuse definition with magnitude; the definition does not change with operating point or hardware configuration.“True only if intercooling is perfect” is irrelevant; intercooling alters power magnitudes, not the definition.Common Pitfalls:Mixing overall isothermal efficiency with isentropic or polytropic efficiencies, or mistakenly using indicated power instead of brake power in the denominator. Always pair the chosen ideal reference (isothermal) with the actual shaft input when computing the overall isothermal efficiency.Final Answer:True

Question 3

Definition of “standard air” in compressor problems Standard air refers to air at which reference state and relative humidity?

Accepted Answer

Introduction / Context:To compare compressors and air machinery consistently, engineers adopt a reference state called “standard air.” Using this common baseline allows fair comparison of volumetric flow rates, power, and performance across different locations and ambient conditions.Given Data / Assumptions:Standard air is used as a conventional reference in many textbooks and problems.Humidity is included because the presence of water vapour affects density and thermodynamic properties.Concept / Approach:In many engineering curricula and design handbooks, “standard air” for compressor problems is taken as air at 1 bar absolute pressure and 20° C with 36% relative humidity. This selection provides a convenient, repeatable baseline representative of typical temperate ambient conditions.Step-by-Step Solution:Identify the accepted reference pressure: 1 bar absolute.Identify the accepted reference temperature: 20° C.Recognize the specified relative humidity: 36%.Combine to state the standard: 1 bar and 20° C with 36% relative humidity.Verification / Alternative check:While some industries use other standards (e.g., 1.01325 bar and 15° C with specified humidity, or “standard day” in aerospace at 15° C and 0% RH), the compressor problem convention in many exam syllabi is 1 bar, 20° C, 36% RH.Why Other Options Are Wrong:0.1 bar options imply near-vacuum conditions, not a standard atmosphere.40° C options reflect hot ambient conditions, not the typical standard used in classroom compressor calculations.1 bar and 15° C with 0% RH is an alternative standard in some fields, but it is not the stated convention in the present context.Common Pitfalls:Assuming “standard” always means dry air at 15° C. Standards vary by field; read the problem statement or institutional convention carefully.Final Answer:1 bar and 20° C with 36% relative humidity

Question 4

Two-stage compression with intercooling: typical simplifying assumptions Which of the following assumptions are commonly made for analytical treatment of two-stage air compression with an intercooler?

Accepted Answer

Introduction / Context:When analyzing multistage compression with intercooling, textbooks adopt idealized assumptions so that closed-form expressions for work, temperatures, and optimal intermediate pressure can be derived. Knowing these assumptions helps students judge the applicability of results to real machines.Given Data / Assumptions:Two stages: low-pressure (LP) and high-pressure (HP) cylinders with an intercooler in between.Objective: obtain tractable formulae for work and temperature.Concept / Approach:Common idealizations are: negligible pressure loss in the intercooler and associated piping; polytropic compression in each stage to represent real heat transfer (with exponent n between 1 and k); and essentially constant suction and delivery pressures at each cylinder end, ignoring small valve losses. These assumptions allow determination of the minimum-work condition and the equal pressure-ratio rule.Step-by-Step Solution:Assume no intercooler pressure drop → simplifies pressure relationships.Assume polytropic compression → realistic modeling between isothermal and isentropic limits.Assume suction/delivery at constant pressure → simplifies indicator diagram areas and indicated work expressions.Combine to derive expressions for stage work and optimal intermediate pressure.Verification / Alternative check:Relaxing these assumptions (e.g., including pressure loss) shifts the optimum slightly and increases total work; however, the equal-ratio rule remains a good first estimate.Why Other Options Are Wrong:Selecting only some assumptions omits standard simplifications used together to build the classical solution.Common Pitfalls:Assuming perfect isothermal stages; real compressors are better represented by polytropic behavior. Also, forgetting that even “constant pressure” suction/delivery hides valve-flow irreversibilities present in practice.Final Answer:All of the above

Question 5

Compressor outlet absolute pressure: terminology What is the term used for the absolute pressure of air measured at the outlet (delivery side) of a compressor?

Accepted Answer

Introduction / Context:Clear terminology is essential when reading compressor specifications and performance curves. The pressure measured at the outlet nozzle or delivery header of a compressor is a standard data point used to define pressure ratio and duty.Given Data / Assumptions:We refer to absolute pressure at the outlet, not gauge pressure unless stated.Steady delivery into a receiver or process line.Concept / Approach:The absolute pressure at the compressor outlet is called the discharge pressure. It is paired with the inlet (suction) pressure to define the compression ratio: r = p_out / p_in. The term “back pressure” is used in different contexts (e.g., exhaust systems), and “critical pressure” relates to choked flow theory, not compressor outlet nomenclature.Step-by-Step Solution:Identify location: outlet side of compressor.Identify quantity: absolute pressure.Standard term: discharge pressure.Verification / Alternative check:Compressor datasheets list suction pressure, discharge pressure, and pressure ratio; these terms are universally used in industry standards.Why Other Options Are Wrong:Back pressure: generic term for resistance pressure downstream, not the designated outlet absolute pressure term.Critical pressure: relates to nozzle choking, not outlet measurement naming.Atmospheric or stagnation pressures are not the specific descriptor for outlet line pressure in this context.Common Pitfalls:Confusing gauge and absolute units; always check whether the specification uses bar(a) or bar(g).Final Answer:Discharge pressure

Question 6

Meaning of “air power” in compressor analysis The “air power” of a compressor refers to the theoretical power imparted to the air stream (e.g., isothermal or isentropic requirement), not the measured indicated or brake power. Which option best descr…

Accepted Answer

Introduction / Context:Different “powers” appear in compressor discussions: indicated power (from the cylinder indicator diagram), brake (shaft) power supplied by the driver, mechanical losses, and the theoretical power actually imparted to the air—often called air power. Distinguishing these terms helps avoid misinterpretation of efficiency metrics.Given Data / Assumptions:Steady compressor operation with fixed inlet and discharge conditions.Air treated as a perfect gas for ideal calculations.Concept / Approach:Air power is the minimum theoretical power required to raise the air from suction to delivery conditions, based on a chosen ideal process (commonly isentropic or isothermal). Indicated power includes thermodynamic and valve-flow losses inside the machine; brake power further includes mechanical losses in bearings, seals, and drive. Therefore, air power is not identical to indicated or brake power; it is the ideal benchmark that appears in efficiency definitions.Step-by-Step Solution:Define air power as theoretical power to compress the actual mass flow between the specified pressures.Recognize indicated power is greater than air power due to internal irreversibilities.Recognize brake power is greater than indicated power due to mechanical losses.Conclude that none of the machine-measured powers equals “air power.”Verification / Alternative check:Efficiency relations: isentropic efficiency (compressor) = air power (isentropic) / brake or indicated power, depending on convention. This highlights that air power is a distinct theoretical quantity.Why Other Options Are Wrong:Indicated/brake/frictional powers are measurement categories, not the ideal minimum theoretical requirement.“Mechanical efficiency times brake power” is not a standard definition for air power.Common Pitfalls:Equating air power with indicated power because both are “about the air.” They are related but not identical; one is theoretical, the other is measured from the cycle within the cylinder.Final Answer:None of these

Question 7

Speed comparison: rotary versus reciprocating air compressors How does the typical operating speed of rotary air compressors compare with that of reciprocating air compressors?

Accepted Answer

Introduction / Context:Compressor type strongly influences achievable speeds, flow pulsation, and size. Rotary compressors (centrifugal, axial, screw, roots) and reciprocating compressors have distinct kinematic and dynamic characteristics that dictate typical operating speed ranges.Given Data / Assumptions:Modern industrial compressors with conventional materials and bearings.Typical service ranges rather than exotic or laboratory designs.Concept / Approach:Rotary machines have continuous flow paths with rotating elements that avoid the inertia reversal and valve dynamics of pistons. This enables much higher rotational speeds, which is advantageous for compactness and for matching with high-speed drivers like gas turbines or electric motors. Reciprocating compressors are limited by mechanical balance, valve response, and vibration at high speeds, thus generally running slower.Step-by-Step Solution:Identify rotary classes (centrifugal/axial/screw) → continuous flow permits high rpm.Identify reciprocating → piston acceleration reversals and valve timing limit rpm.Conclude that rotary compressors typically operate at higher speeds than reciprocating machines.Verification / Alternative check:Manufacturer catalogs show centrifugal and axial units commonly in tens of thousands of rpm; reciprocating units are commonly in hundreds to a few thousand rpm, depending on frame size and service.Why Other Options Are Wrong:Lower or “always the same” contradicts observed practice.“Impossible to generalize” is inaccurate; while overlaps exist, the broad trend is clear.Common Pitfalls:Assuming screw compressors are “slow” because of positive displacement; in reality, they often run faster than reciprocating units due to smoother rotary motion.Final Answer:Higher for rotary compressors

Question 8

Compressor taxonomy: is a centrifugal compressor an axial-flow compressor? Decide whether the statement “A centrifugal compressor is an axial-flow compressor” is correct or incorrect.

Accepted Answer

Introduction / Context:Compressors are categorized by the direction of primary flow relative to the machine axis. Correct classification matters for predicting performance maps, surge behavior, and stage loading limits.Given Data / Assumptions:Centrifugal compressors have radial outflow through an impeller.Axial compressors have flow predominantly parallel to the shaft axis through multiple blade rows.Concept / Approach:A centrifugal compressor accepts flow near the center and imparts tangential velocity, flinging the fluid radially outward; static pressure then increases in a diffuser. An axial-flow compressor compresses the fluid while it moves axially through alternating rows of rotating and stationary blades. The flow directions and stage architectures are fundamentally different.Step-by-Step Solution:Identify radial (centrifugal) versus axial flow paths.Note that hybrid “mixed-flow” machines exist, but “centrifugal” is not “axial.”Therefore, the statement equating centrifugal with axial is incorrect.Verification / Alternative check:Standard turbomachinery texts depict velocity triangles: centrifugal has a large radial component at impeller exit, while axial maintains nearly axial absolute velocity through stages.Why Other Options Are Wrong:Conditional “correct” options attempt to blur definitions; even with vaneless diffusers or multishaft layouts, the primary flow direction in centrifugal stages remains radial, not axial.Common Pitfalls:Confusing “mixed-flow” compressors with pure axial or pure centrifugal designs.Final Answer:Incorrect

Question 9

High delivery pressure strategy: best choice of compression arrangement When very high delivery pressure is required, which arrangement is most advantageous for air compression from the viewpoints of work and temperature control?

Accepted Answer

Introduction / Context:Achieving high discharge pressures efficiently requires attention to both thermodynamics and component limits. Excessive discharge temperatures damage lubricants and valves, while high work input raises operating costs.Given Data / Assumptions:Need for high overall pressure ratio.Conventional air compressor hardware (reciprocating or rotary positive-displacement).Cooling available between stages.Concept / Approach:Splitting compression into multiple stages reduces work when intercooling is provided between stages. Intercooling removes heat, reduces specific volume before the next stage, and keeps metal and discharge temperatures within safe limits. The minimum total work occurs when pressure ratios per stage are equal and intercooling is near-perfect.Step-by-Step Solution:Break the overall pressure rise into smaller ratios across stages.Cool air between stages to lower temperature and specific volume.Result: lower total work and improved reliability at high pressure ratios.Verification / Alternative check:Analytical expressions for polytropic compression show reduced enthalpy rise per kilogram with intercooling; practical experience confirms improved valve life and lubricant stability.Why Other Options Are Wrong:Single-stage: excessive discharge temperature and high work at large pressure ratios.Multistage without intercooling: forfeits much of the work-saving benefit.Large clearance or oversized motor do not change the unfavorable thermodynamics.Common Pitfalls:Confusing aftercooling (after final stage) with intercooling (between stages); only intercooling reduces subsequent stage work.Final Answer:Multistage compression with intercooling

Question 10

Principle of propulsion: rockets versus air-breathing jets Is the basic working principle of rocket propulsion the same as that of jet propulsion (i.e., reaction thrust from high-velocity mass ejection)?

Accepted Answer

Introduction / Context:Both rockets and jet engines generate thrust by expelling mass at high velocity in the opposite direction to motion. This is a direct application of conservation of momentum and Newton’s third law.Given Data / Assumptions:Steady propulsion; thrust defined by momentum change plus pressure terms at the exit plane.Different propellant sources: jets breathe atmospheric air; rockets carry oxidizer and fuel.Concept / Approach:The thrust formula for a generic propulsion device is T = m_dot * (V_exit - V_flight) + (p_exit - p_ambient) * A_exit. Both jets and rockets increase exhaust momentum relative to the vehicle; rockets are self-contained and operate in vacuum, while jets require atmospheric oxygen and therefore cannot operate in space.Step-by-Step Solution:Identify common mechanism: reaction thrust from accelerating mass in a nozzle.Differentiate: air-breathing jets use ambient air as oxidizer; rockets carry both oxidizer and fuel.Conclude: basic principle (momentum thrust) is the same despite different propellant logistics.Verification / Alternative check:Control volume analyses for both systems yield the same thrust expressions with appropriate fluid properties and mass flow definitions.Why Other Options Are Wrong:Limiting the principle to vacuum, subsonic regimes, or afterburning misconstrues the universal momentum basis of thrust.Common Pitfalls:Confusing “requires air” (jets) with “principle of operation.” The medium differs, but the physics of reaction thrust is identical.Final Answer:Yes

Question 11

Compressor pressure ratio terminology What is the term for the ratio of discharge (delivery) pressure to inlet (suction) pressure in a compressor?

Accepted Answer

Introduction / Context:Pressure ratio is a fundamental parameter that defines the duty of a compressor, influences work requirement, discharge temperature, and determines staging in multistage designs.Given Data / Assumptions:Discharge pressure and suction pressure are absolute values unless specified otherwise.Steady operation at the stated pressures.Concept / Approach:The ratio r = p_discharge / p_suction is called the compression ratio. It is used in performance correlations and to select the number of stages and intercooling requirements. Larger ratios generally imply higher work input and higher discharge temperatures for a given inlet state.Step-by-Step Solution:Define pressures p2 (discharge) and p1 (suction).Form ratio r = p2 / p1.Recognize this as the compression ratio by standard compressor nomenclature.Verification / Alternative check:Performance maps are often plotted against pressure ratio. Gas turbine compressors likewise use overall pressure ratio across the compressor train.Why Other Options Are Wrong:Expansion ratio applies to turbines, not compressors.Efficiency terms are dimensionless performance metrics, not raw pressure ratios.Common Pitfalls:Using gauge pressures in the ratio without converting to absolute can produce large errors. Always use absolute pressures in thermodynamic calculations.Final Answer:Compression ratio

Question 12

Centrifugal compressor design: for identical diameter, blade inlet angle, and rotational speed, which blade orientation typically yields the maximum pressure rise across the stage?

Accepted Answer

Introduction / Context:In turbomachinery, the achievable pressure rise of a centrifugal compressor stage depends strongly on impeller blade orientation for a given tip speed, flow coefficient, and overall diameter. The three classic orientations are forward-curved, radial (90°), and backward-curved. Understanding how each affects the Euler head and the diffusion process is key for preliminary design and exam problems.Given Data / Assumptions:Same overall impeller and diffuser dimensions (fixed diameter and width).Same blade inlet angle and the same rotational speed.Idealized comparison at the same flow coefficient, ignoring detailed loss variations beyond the first order trend.Concept / Approach:The stage ideal head is approximated by the Euler relation: Delta h_E ≈ U_2 * V_theta2 - U_1 * V_theta1With similar inlets, the dominant term is U_2 * V_theta2. Forward-curved blades increase the whirl component at exit (V_theta2), radial blades yield an intermediate whirl, and backward-curved blades reduce the whirl at exit for the same U_2. Therefore, the pressure coefficient and pressure rise trend is typically: forward-curved > radial > backward-curved (for identical boundaries).Step-by-Step Solution:Fix U_2 (same speed and radius) and geometry.Note that changing blade exit metal angle changes V_theta2.Forward-curved → higher V_theta2 → higher Euler head → greater pressure rise.Radial → moderate V_theta2 → moderate head.Backward-curved → reduced V_theta2 → lowest head among the three for same U_2.Verification / Alternative check:Velocity-triangle sketches confirm that, at fixed U_2 and mass flow, a forward exit metal angle adds to the tangential component, raising the specific work. Backward-curved blades are popular for efficiency and stable characteristic, not for maximum theoretical pressure rise.Why Other Options Are Wrong:Backward curved blades: usually give a lower pressure rise for the same speed but are more efficient and stable.Radial blades: intermediate head; not the maximum.All orientations same: contradicts Euler head dependence on V_theta2.Mixed-flow blades: not comparable under the stated “same overall dimensions and angles”.Common Pitfalls:Confusing “maximum pressure rise” with “best efficiency.” Backward-curved blades often yield higher efficiency and a non-overloading power characteristic but not the maximum head.Final Answer:Forward curved blades

Question 13

Axial-flow compressor terminology: the ratio of pressure rise occurring in the rotor (moving) blades to the total pressure rise in one stage is called what?

Accepted Answer

Introduction / Context:Axial-flow compressor stages consist of alternating rows of rotor and stator blades. Several non-dimensional parameters describe how the pressure and energy addition are partitioned between these rows. One of the most important is the degree of reaction.Given Data / Assumptions:A single axial compressor stage with one rotor and one stator.Steady, subsonic operation where classical definitions apply.Standard definition of stage pressure/enthalpy rise.Concept / Approach:The degree of reaction (R) is defined as the fraction of the static enthalpy (or static pressure) rise that occurs in the rotor relative to the total static rise across the stage. In enthalpy form: R = (Delta h_static in rotor) / (Delta h_static in stage)This definition translates directly to a “ratio of pressure rise in rotor to total pressure rise per stage” for low-Mach, near-incompressible assumptions.Step-by-Step Solution:Identify the rotor and stator contributions to static rise.Compute R = rotor static rise / (rotor + stator static rise).Recognize this ratio as the degree of reaction.Verification / Alternative check:Velocity triangles with R ≈ 0.5 show balanced static rise between rotor and stator, a common design target for many stages.Why Other Options Are Wrong:Work factor: relates work input to blade speed; different concept.Slip factor: belongs to centrifugal compressors, quantifying reduction of tangential exit velocity.Pressure coefficient: relates pressure rise to dynamic head or blade speed squared.Flow coefficient: ratio of axial velocity to blade speed; not a pressure partition.Common Pitfalls:Equating degree of reaction with isentropic efficiency; one is a distribution metric, the other an effectiveness metric.Final Answer:Degree of reaction

Question 14

Jet propulsion unit flow path: after passing through the gas turbine, where are the combustion products discharged?

Accepted Answer

Introduction / Context:In turbojet and turbofan cores, air is compressed, mixed with fuel, burned, expanded through a turbine to drive the compressor, and finally expanded further to generate thrust. Understanding the sequence of components is foundational for propulsion studies.Given Data / Assumptions:Standard jet propulsion unit (e.g., turbojet core).Open cycle exchanging mass with the surroundings.No afterburner considered for the basic path.Concept / Approach:After the gas turbine extracts shaft work to drive the compressor, the partially expanded, still-energetic exhaust gases are accelerated through the exhaust nozzle. The nozzle converts remaining thermal and pressure energy into a high-velocity jet, producing thrust by momentum change.Step-by-Step Solution:Compressor → Combustor → Turbine (to drive compressor).Turbine exit gases retain pressure and temperature.Gases pass into the exhaust (discharge) nozzle where pressure energy converts to kinetic energy.High-speed jet issues to the atmosphere, creating thrust.Verification / Alternative check:Thrust equation uses mass flow times jet velocity relative to flight speed; the exhaust nozzle is the component setting the jet velocity.Why Other Options Are Wrong:Atmosphere (directly): gases first expand through the nozzle; the nozzle is the immediate component after the turbine.Vacuum chamber: not present in open-cycle aircraft engines.Back to compressor: would imply a closed cycle, not used in aircraft jet propulsion.Closed plenum: inconsistent with thrust generation.Common Pitfalls:Confusing “nozzle exit to atmosphere” with “discharged to atmosphere.” The immediate device is the nozzle, which shapes and accelerates the flow.Final Answer:Discharge (exhaust) nozzle

Question 15

Effect of reheating on the compressor side in a multistage gas turbine: how does reheating during expansion influence compressor work?

Accepted Answer

Introduction / Context:Reheating in gas turbines inserts heat between turbine expansion stages to increase turbine specific work (and often to maintain blade metal temperatures). Students sometimes confuse its impact on the compressor, which belongs to the compression side of the Brayton cycle.Given Data / Assumptions:Multistage expansion with a reheater between turbine stages.Compressor configuration and pressure ratio unchanged.Steady-state operation without bleed air changes.Concept / Approach:Reheating raises the turbine-inlet temperature of downstream stages, thereby increasing turbine work output for a given pressure drop. The compressor is upstream of the combustor; its required work is determined by the pressure ratio, inlet condition, and compressor efficiency. Since reheating occurs after the compressor and within the turbine train, it does not alter the compression process.Step-by-Step Solution:Identify locations: Compressor → Combustor → Turbine 1 → Reheater → Turbine 2.Reheating changes the state entering Turbine 2, not the compressor inlet or pressure ratio.Therefore, compressor work remains the same for the same pressure ratio and efficiency.Verification / Alternative check:On a T–s diagram, reheating adds a horizontal rightward segment between turbine expansions; the compression path remains unchanged.Why Other Options Are Wrong:Decrease/Increase: would require a pressure-ratio or inlet-state change on the compressor, which reheating does not cause.Reversal or zero work: physically impossible for a functioning compressor.Common Pitfalls:Assuming any turbine-side modification automatically affects the compressor load; only cycle pressure ratios, intercooling, or compressor-side heat exchange alter compressor work directly.Final Answer:Has no effect on compressor work

Question 16

Volumetric efficiency trend with compression ratio in reciprocating compressors: which statement best describes the relationship?

Accepted Answer

Introduction / Context:Volumetric efficiency (eta_v) is the ratio of the actual intake volume (converted to suction conditions) to the swept volume. It captures how clearance gas re-expansion, valve drops, heating, and leakage reduce the fresh charge admitted during the suction stroke. Its variation with compression ratio is central to compressor sizing.Given Data / Assumptions:Fixed machine geometry and clearance ratio.Comparison across different pressure (compression) ratios.Similar suction conditions, valve characteristics, and speeds.Concept / Approach:At higher compression ratios, the residual gas in the clearance volume is left at a higher discharge pressure and temperature. During the subsequent suction stroke, it expands more, occupying a larger fraction of the swept volume before cylinder pressure drops below suction pressure. Hence less fresh air is taken in, reducing eta_v. Conversely, lowering the compression ratio reduces this effect, increasing eta_v.Step-by-Step Solution:Recognize clearance gas at end of delivery has p ≈ p_discharge.Higher compression ratio → higher p_discharge → greater re-expansion volume.Greater re-expansion → less swept volume left for fresh intake → lower eta_v.Therefore, eta_v increases when compression ratio decreases.Verification / Alternative check:Simplified correlations show eta_v ≈ 1 + C - C*(p_dis/p_suc)^(1/n), demonstrating a drop with increasing ratio for given clearance C and polytropic index n.Why Other Options Are Wrong:Options (b) and (c) invert the observed trend.(d) is partially true but incomplete without stating the opposite condition; option (a) states the positive direction clearly.(e) ignores strong dependence on pressure ratio and clearance.Common Pitfalls:Neglecting valve pressure losses and heating, which further depress volumetric efficiency at high ratios.Final Answer:Increases with decrease in compression ratio

Question 17

Reciprocating compressor terminology: what do we call the geometric volume swept by the piston (i.e., the volume of air drawn in during the suction stroke)?

Accepted Answer

Introduction / Context:Multiple volumetric terms are used in compressor practice: swept volume, free air delivery, and capacity. Distinguishing these avoids confusion when reading datasheets and selecting equipment.Given Data / Assumptions:Piston-cylinder compressor with defined bore and stroke.Negligible leakage for the basic geometric definition.No correction to standard conditions unless explicitly stated.Concept / Approach:The swept volume (also called displacement) is purely geometric: area of piston * stroke (per cycle) multiplied by the number of cylinders and cycles per unit time when expressing as a rate. It is the volume traversed by the piston, i.e., the nominal volume of air a cylinder would draw during suction absent re-expansion and losses. By contrast, Free Air Delivery (FAD) is the delivered volume converted to standard conditions, and “capacity” is often used synonymously with FAD on a standardized basis.Step-by-Step Solution:Compute swept volume V_s = (pi/4) * D^2 * L for one stroke.Recognize this is the volume the piston sweeps, unrelated to standard condition corrections.Therefore, the correct term for “volume of air sucked during suction stroke” is swept volume (displacement).Verification / Alternative check:Manufacturer literature lists both displacement (geometric) and FAD (corrected to standard conditions) to distinguish ideal from delivered performance.Why Other Options Are Wrong:Free air delivery: standardized delivered volume, not geometric sweep.Compressor capacity: commonly synonymous with FAD or standardized delivered volume.Standard flow rate: general term; lacks the geometric meaning.Receiver volume: storage tank volume, unrelated to piston sweep.Common Pitfalls:Using displacement to size downstream equipment; always use standardized delivered flow for piping and tool sizing.Final Answer:Swept volume (displacement)

Question 18

Supercharging of internal combustion engines: which compressor type is most commonly used (mechanically driven) for supercharging?

Accepted Answer

Introduction / Context:Supercharging raises the intake manifold pressure above ambient to increase engine power density. Historically and in many present applications, mechanically driven superchargers use positive-displacement machines for instantaneous boost and strong low-speed torque.Given Data / Assumptions:Mechanically driven supercharger (crankshaft-driven), not exhaust-driven turbocharger.Automotive and stationary engine context.Focus on common, widely adopted hardware.Concept / Approach:The Roots blower is a positive-displacement rotary machine delivering nearly fixed displacement per revolution. It provides immediate boost and simple control, making it the classic choice for belt-driven superchargers. While centrifugal compressors are used in turbochargers (exhaust-driven) and in some belt-driven “centrifugal superchargers,” the most commonly referenced mechanically driven supercharger type in fundamentals is the Roots blower.Step-by-Step Solution:Identify mechanically driven superchargers: Roots, screw (Lysholm), and occasionally centrifugal via belt.Among these, Roots is historically prevalent and widely taught in textbooks as the standard example.Therefore, the correct answer is Roots blower.Verification / Alternative check:Supercharger kits and OEM applications often specify “Roots-type” or “twin-rotor” positive-displacement units for immediate response.Why Other Options Are Wrong:Radial-flow compressor: more typical for exhaust-driven turbochargers.Axial-flow: unsuitable for small engine supercharging due to geometry and surge behavior.Reciprocating: impractical for high-speed continuous boost on engines.Scroll: uncommon for engine supercharging.Common Pitfalls:Confusing turbocharging (centrifugal compressor driven by turbine) with mechanically driven supercharging (Roots/screw).Final Answer:Roots blower (positive displacement)

Question 19

Definition check: “Free air delivery is simply the volume of air that a compressor can deliver freely.” Is this statement correct?

Accepted Answer

Introduction / Context:“Free air delivery” (FAD) is a standardized term essential for comparing compressors. It is often misstated as just the raw delivered volume, which causes confusion in selection and performance assessment.Given Data / Assumptions:Industrial air compressor context.Standard reference state (e.g., 1.013 bar and 15°C or as specified).Delivered flow measured and then corrected to the standard state.Concept / Approach:FAD is the volume flow rate of air delivered by the compressor, converted back to “free air” conditions (a defined standard temperature and pressure). It is not the raw volume at discharge conditions, nor simply “as is” volume. The correction uses the ideal gas relation to reference different operating sites and discharge pressures to a common basis.Step-by-Step Solution:Measure mass flow m_dot leaving the compressor.Convert to standardized volume: V_FAD_dot = m_dot * R * T_std / p_std.Report this standardized volumetric flow as FAD.Verification / Alternative check:Datasheets list SCFM or m^3/h (free air) at named reference conditions; on-site measurements require correction for local temperature and pressure.Why Other Options Are Wrong:“True”: ignores the essential correction to standard conditions.Conditional “true” answers (sea level, oil-free, filter status) do not change the definition.Common Pitfalls:Using discharge volumetric flow directly for comparison; always convert to the agreed standard state to compare machines.Final Answer:False

Question 20

Gas turbine heat recovery: does adding a regenerator (recuperator) increase the thermal efficiency of a basic Brayton cycle?

Accepted Answer

Introduction / Context:A regenerator (recuperator) transfers heat from the hot turbine exhaust to the compressed air before combustion. This reduces the fuel required to achieve a given turbine inlet temperature, improving thermal efficiency in many Brayton-cycle applications.Given Data / Assumptions:Simple gas turbine (compressor–combustor–turbine) augmented with a regenerator.Moderate pressure ratio and non-ideal component efficiencies.Exhaust temperature above compressor exit temperature so that heat exchange is possible.Concept / Approach:Thermal efficiency = net work output / heat supplied. With regeneration, part of the required heat input is supplied internally by exhaust energy. If the temperature of turbine exhaust exceeds the compressor outlet temperature, effective fuel heat input decreases for the same net work, increasing efficiency.Step-by-Step Solution:Baseline: determine T_comp_out and T_turb_out without regeneration.If T_turb_out > T_comp_out, add a regenerator to preheat compressed air.Combustor fuel input drops to reach target turbine inlet temperature.Net work remains similar; heat supplied decreases → efficiency rises.Verification / Alternative check:T–s or h–s diagrams with a regenerator show reduced external heat addition area for the same cycle work rectangle/loop.Why Other Options Are Wrong:“Incorrect”: contradicts Brayton analysis under typical conditions.Other conditional choices are irrelevant or physically inconsistent.Common Pitfalls:At very high pressure ratios, T_comp_out can approach or exceed T_turb_out, limiting regenerator effectiveness; the statement remains broadly correct for suitable ratios.Final Answer:Correct

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