Question 1

Prime mover requirement: Must a compressor be driven by an external prime mover to operate under normal industrial conditions?

Accepted Answer

Introduction / Context: A compressor is an energy conversion device. It does not create energy; it consumes shaft power and converts it into a higher enthalpy/pressure state of a working fluid. Recognizing the need for a prime mover is basic to power-train design and plant layout. Given Data / Assumptions: Conventional compressors (reciprocating, screw, centrifugal, axial). Industrial setting requiring continuous, controllable operation. External prime mover options: electric motor, internal combustion engine, steam or gas turbine. Concept / Approach: From the First Law, the increase in fluid energy (primarily enthalpy for compressible flow) must be supplied by shaft work. Therefore, a compressor requires mechanical input from a prime mover. Self-acting “compressors” without external power are actually pressure boosters driven by another pressurized source (which itself required a prime mover upstream). Step-by-Step Solution: Identify energy requirement: raise pressure → add work.Provide work via a prime mover coupled to compressor shaft.Acknowledge rare exceptions are not truly stand-alone compressors (e.g., ejectors).Hence, statement stands: a compressor must be driven. Verification / Alternative check: Equipment nameplates list motor kW or engine hp; process simulators compute shaft input aligning with enthalpy rise and efficiency assumptions. Why Other Options Are Wrong: “Disagree” would violate energy conservation unless another hidden prime mover exists in the system boundary. Common Pitfalls: Confusing fluid-powered boosters or ejectors with true compressors; ignoring electrical power as the prime mover via motors. Final Answer: Agree

Question 2

Ideal Brayton (gas turbine) cycle — overall thermal efficiency vs. pressure ratio For an ideal gas turbine plant operating on the Brayton cycle with isentropic compressor and turbine, the overall thermal efficiency (eta_th) can be expressed purely a…

Accepted Answer

Introduction / Context: The Brayton (Joule) cycle models the ideal gas turbine. Its thermal efficiency relates closely to the compressor pressure ratio r and the specific heat ratio gamma for an ideal gas with isentropic compression/expansion and constant-pressure heat addition and rejection. Understanding this dependence helps with preliminary cycle sizing and estimating benefits of increasing pressure ratio. Given Data / Assumptions: Ideal gas with constant gamma. Isentropic compressor and turbine. Heat addition and rejection at constant pressure. Negligible pressure losses in combustor, ducts, and nozzle. Concept / Approach: For an ideal Brayton cycle, temperature ratios across isentropic devices depend only on pressure ratio and gamma. The compressor exit to inlet temperature ratio is T2/T1 = r^((gamma - 1)/gamma) and the turbine exit to inlet temperature ratio is its reciprocal for the same r. The thermal efficiency simplifies to eta_th = 1 - (T4 - T1)/(T3 - T2). With the isentropic relations and equal pressure ratios, this reduces to a function of r and gamma alone. Step-by-Step Solution: Use isentropic relation: T2/T1 = r^((gamma - 1)/gamma).For the matched turbine: T3/T4 = r^((gamma - 1)/gamma) → T4/T3 = 1 / r^((gamma - 1)/gamma).Ideal Brayton efficiency simplifies to eta_th = 1 - (T1/T2) = 1 - 1 / r^((gamma - 1)/gamma).Therefore the correct expression is eta_th = 1 - 1 / r^((gamma - 1)/gamma). Verification / Alternative check: As r increases, r^((gamma - 1)/gamma) increases, making 1 / r^((gamma - 1)/gamma) smaller; hence efficiency rises, which matches known Brayton behavior (up to metal temperature limits). Why Other Options Are Wrong: (b) and (d) do not include gamma and are dimensionally and physically inconsistent. (c) would predict negative efficiency for r > 1. (e) represents the loss term alone, not 1 minus that term. Common Pitfalls: Confusing r^((gamma - 1)/gamma) with r^(gamma - 1), or forgetting the reciprocal in the final expression. Final Answer: eta_th = 1 - 1 / r^((gamma - 1)/gamma)

Question 3

Air compressors — what does “free air delivery (FAD)” actually mean? In compressor testing and selection, the term free air delivery refers to which of the following definitions?

Accepted Answer

Introduction / Context: Manufacturers specify compressor capacity using standardized terms so that users can compare across different machines. “Free air delivery (FAD)” is a widely used capacity metric that normalizes the delivered air volume to standard conditions (often 1.013 bar and 15 °C or as otherwise stated). Given Data / Assumptions: Steady compressor operation. Standard reference conditions are clearly defined by the test code (e.g., ISO or CAGI). We are seeking the definition, not a numerical calculation. Concept / Approach: Because gas volume varies with pressure and temperature, a direct volumetric reading at discharge cannot be compared between machines. FAD converts the delivered mass flow to an equivalent volume at standard temperature and pressure so capacities can be compared on an equal basis. Step-by-Step Solution: Measure delivered mass flow or discharge volume with known P, T.Convert to equivalent volume at standard P_std and T_std using ideal-gas relations.Report this normalized volume as the compressor’s FAD. Verification / Alternative check: Handbooks and standards define FAD as the volume of air delivered when reduced to standard conditions, confirming option (a). Why Other Options Are Wrong: (b) lacks normalization; (c) is intake swept volume, not delivered after losses; (d) ignores clearance/slip; (e) is a mass-based expression, not the FAD definition. Common Pitfalls: Not checking which “standard conditions” are used—values vary by region and standard, so always cite the reference. Final Answer: The actual volume of air delivered, referred back to standard (normal) temperature and pressure conditions

Question 4

Compressor behavior — how does volumetric efficiency vary with compression ratio? For a reciprocating air compressor, the volumetric efficiency typically __________ with an increase in overall compression ratio (all else equal).

Accepted Answer

Introduction / Context: Volumetric efficiency (eta_v) indicates how effectively the compressor cylinder fills with fresh charge. It is reduced by clearance volume and by backflow of hot residual gas. Understanding how eta_v changes with compression ratio is important for predicting capacity at higher pressures. Given Data / Assumptions: Positive-displacement reciprocating compressor with nonzero clearance. Compression and expansion approximately polytropic. Comparisons made at similar inlet conditions except for delivery pressure. Concept / Approach: A standard expression is eta_v = 1 + C - C * (p2/p1)^(1/n), where C is clearance ratio, p2/p1 is compression ratio, and n is the polytropic index. As p2/p1 increases, the term (p2/p1)^(1/n) increases, reducing eta_v. Step-by-Step Solution: Start from eta_v = 1 + C - C * (p2/p1)^(1/n).Differentiate conceptually: increasing p2/p1 increases the subtracted term.Therefore, eta_v decreases as compression ratio rises. Verification / Alternative check: Indicator diagrams show increased re-expansion of trapped clearance gas at higher delivery pressures, displacing more of the fresh charge, confirming the decrease. Why Other Options Are Wrong: (b) contradicts the formula; (c) ignores clearance effect; (d) typical machines do not show a rise then fall solely from compression ratio; (e) while C matters, the trend with higher p2/p1 is still a decrease for any C > 0. Common Pitfalls: Confusing isentropic efficiency (a loss measure) with volumetric efficiency (a capacity measure). Final Answer: decreases

Question 5

Selecting a compressor type — identify the correct statement Which of the following statements about reciprocating air compressors and clearance effects is correct?

Accepted Answer

Introduction / Context: Different compressor families suit different pressure and flow ranges. Reciprocating machines excel at high pressures and modest flows, while dynamic compressors (centrifugal/axial) excel at large flows and moderate pressures. Clearance effects also matter for capacity and power predictions. Given Data / Assumptions: Idealized indicator diagram assumptions for power. Finite clearance ratio in positive-displacement compressors. Same delivery pressure and suction conditions used in comparisons. Concept / Approach: (a) Reciprocating units can achieve very high discharge pressures because the trapped gas is compressed in a closed cylinder; volumetric throughput is limited, fitting low-volume tasks. (b) In the ideal cycle without leakage, the indicated work per kg depends mainly on inlet/outlet states and polytropic index; clearance alters capacity (eta_v) but has negligible effect on indicated work per unit mass, so for a fixed mass delivery the power change is small in the ideal model. Step-by-Step Solution: Recognize application domains: high pressure → reciprocating; high flow → dynamic.Note that clearance reduces volumetric efficiency, not the ideal work per kg compressed.Thus statements (a) and (b) are both correct → choose (c). Verification / Alternative check: Textbook indicator diagrams show identical compression/expansion lines irrespective of clearance for the same end pressures, confirming negligible power change per kg. Why Other Options Are Wrong: (d) contradicts fundamentals; (e) reverses typical selection (centrifugal are for higher flows, not the highest pressures at tiny flows). Common Pitfalls: Equating reduced capacity from clearance with reduced power per kg—these are distinct. Final Answer: Both (a) and (b) are correct

Question 6

Identify compressor type from flow direction If the flow of air through a compressor is predominantly parallel to the machine axis throughout, the compressor is classified as which type?

Accepted Answer

Introduction / Context: Compressor families are classified by the direction of the main flow path. Recognizing the flow orientation helps in quickly identifying machine types and their appropriate applications. Given Data / Assumptions: Steady operation and conventional designs. “Parallel to the axis” refers to the absolute flow path through the rotor-stator stages. Concept / Approach: In axial-flow compressors, the air progresses along the machine axis through alternating rows of rotating and stationary blades, gradually building pressure over many stages. Centrifugal compressors turn the flow radially outward in the impeller; reciprocating compressors are positive-displacement piston machines without a continuous axial flow path. Step-by-Step Solution: Map flow direction to machine family: axial → axial-flow; radial → centrifugal; oscillatory piston → reciprocating.Since the flow is parallel to the axis, the correct classification is axial-flow compressor. Verification / Alternative check: Any schematic of gas-turbine cores shows multistage axial compressors with annular flow strictly along the axis. Why Other Options Are Wrong: (a) Reciprocating has no continuous axial flow corridor; (b) flow is primarily radial; (d) mixed-flow has combined radial and axial components; (e) Roots is a positive-displacement blower. Common Pitfalls: Confusing axial-flow compressors with axial turbines—direction is the same but function differs. Final Answer: Axial-flow compressor

Question 7

Multi-stage air compression — conditions for minimum total work For compressing and delivering a given mass of air using multi-stage compression with intercooling, which set of conditions minimizes the total work input?

Accepted Answer

Introduction / Context: Staging and intercooling are used to reduce work input and discharge temperature in air compression. There is a classic optimal design point that distributes the compression across stages to minimize total power for a given overall pressure ratio. Given Data / Assumptions: N-stage compression with identical polytropic behavior per stage. Intercooling available between stages with negligible pressure loss. Objective: minimize total compressor work for a fixed overall ratio. Concept / Approach: With perfect intercooling (air returned to intake temperature), the minimum work condition occurs when the pressure ratio is the same in every stage. At this point, each stage performs the same work, which naturally follows from equal ratios and identical thermodynamics per stage. Step-by-Step Solution: Let overall ratio be R = p_out/p_in.For N stages, set stage ratio r_s so that r_s^N = R → r_s = R^(1/N).Under perfect intercooling, the temperature entering each stage is equal, making equal work per stage and minimizing the total. Verification / Alternative check: Calculus-based minimization of total polytropic work with respect to intermediate pressures yields equal stage ratios, confirming the condition. Why Other Options Are Wrong: Each of (a), (b), and (c) is correct individually, so selecting anything other than “All of the above” would omit valid requirements for minimum work. Common Pitfalls: Forgetting to account for pressure losses in real intercoolers, which slightly shift the true optimum in practice. Final Answer: All of the above

Question 8

Why turboprops instead of turbojets — primary advantage A turboprop aircraft engine is generally preferred over a pure turbojet for subsonic flight primarily because it offers:

Accepted Answer

Introduction / Context: Turboprops couple a gas-turbine core to a propeller via a power turbine and reduction gearbox. They excel in regional and utility aviation, where cruise speeds are typically below about 700 km/h and runway performance matters. Given Data / Assumptions: Comparison at subsonic flight regimes. Similar core technologies and materials. Focus on propulsive (not thermal) efficiency. Concept / Approach: Propulsive efficiency improves when the exhaust jet velocity approaches the flight speed. Propellers accelerate a large mass of air by a small amount, yielding very high propulsive efficiency at low to moderate speeds, which is where turboprops operate best. Turbojets accelerate a smaller mass flow to much higher jet velocities, which is less efficient at these speeds. Step-by-Step Solution: Identify operating regime: subsonic and relatively low Mach.Recognize propellers provide large mass flow, small delta-V → high propulsive efficiency.Conclude the primary advantage is higher propulsive efficiency at these speeds. Verification / Alternative check: Performance charts show turboprops achieving lower specific fuel consumption than turbojets at typical regional cruise speeds (~0.3–0.6 Mach). Why Other Options Are Wrong: (b) Turboprops are not for supersonic flight; (c) core OPR is not the defining advantage; (d) frontal area claim is not generally true; (e) turboprops do require reduction gearboxes. Common Pitfalls: Confusing thermal efficiency of the core with propulsive efficiency of the propulsor. Final Answer: Higher propulsive efficiency at low to moderate subsonic speeds

Question 9

Reciprocating compressor — volumetric efficiency with clearance ratio If the clearance ratio (fraction of clearance volume to swept volume) of a single-stage reciprocating air compressor is K, the ideal volumetric efficiency (eta_v) is given by whic…

Accepted Answer

Introduction / Context: Clearance volume traps a portion of compressed air that re-expands during the suction stroke, displacing part of the incoming fresh charge and reducing volumetric efficiency. A standard formula captures this effect for ideal valves and polytropic compression/expansion. Given Data / Assumptions: Single-stage, single-acting reciprocating compressor. Clearance ratio K = V_c / V_s. Compression and re-expansion are polytropic with the same index n. Concept / Approach: The ideal volumetric efficiency is derived from the pressure at which the re-expanded clearance gas falls to suction pressure, determining when the suction valve actually opens. The result is commonly written as eta_v = 1 + K - K * (p2/p1)^(1/n), which is equivalent to eta_v = 1 - K * ((p2/p1)^(1/n) - 1). Step-by-Step Solution: Let r = p2/p1 and assume equal n for compression and expansion.Re-expansion volume fraction = K * r^(1/n).Net fresh charge fraction = 1 + K - K * r^(1/n).Therefore eta_v = 1 + K - K * (p2/p1)^(1/n). Verification / Alternative check: As r → 1, eta_v → 1, which is reasonable; as r increases, eta_v decreases, matching observed behavior. Why Other Options Are Wrong: (c) and (d) have incorrect dependence on r; (e) ignores clearance and predicts zero eta_v at high ratios, which is unrealistic. Common Pitfalls: Confusing K with clearance volume percentage; K is a fraction of swept volume, not of total cylinder volume. Final Answer: eta_v = 1 + K - K * (p2/p1)^(1/n)

Question 10

Compressor classes by delivery pressure — identify the high-pressure range For air compressors, which delivery pressure range typically characterizes a “high-pressure” compressor?

Accepted Answer

Introduction / Context: Air compressors are often grouped by delivery pressure: low-, medium-, and high-pressure. While exact cutoffs vary by source, industrial practice commonly considers double-digit bar levels as high-pressure for general-purpose air delivery. Given Data / Assumptions: Gauge pressures typical of plant compressed air systems. Not referring to specialized ultra-high-pressure compressors (> 200 bar). Concept / Approach: General classifications: low (up to a few bar), medium (about 5–10 bar), and high (10 bar and above). Among the presented options, the band that clearly lies in the high-pressure category is 10 to 15 bar. Step-by-Step Solution: Compare listed ranges to conventional categories.Identify the only clearly high-pressure range among the choices: 10–15 bar.Select 10 to 15 bar. Verification / Alternative check: Many factory systems run at 6–8 bar (medium). Specialty tools and processes use 10–15 bar lines (high) before moving to booster or hydraulic solutions for higher pressures. Why Other Options Are Wrong: (a), (b), and (c) correspond to low to medium ranges; (e) is near atmospheric and not representative of a standard delivery category. Common Pitfalls: Confusing absolute and gauge pressure; the industry shorthand usually references gauge values. Final Answer: 10 to 15 bar

Question 11

Work comparison for single-stage compression (no clearance) In a single-stage, single-acting reciprocating air compressor without clearance volume, which compression path results in the maximum indicated work input between the same inlet and deliver…

Accepted Answer

Introduction / Context: The work required for gas compression depends on the thermodynamic path between the initial and final states. For a given inlet state and discharge pressure, different idealized paths (isothermal, polytropic, isentropic) yield different areas under the p–v curve, i.e., different work inputs. Given Data / Assumptions: No clearance volume and ideal valves. Same inlet pressure and temperature; same discharge pressure. Ideal, quasi-static processes for comparison. Concept / Approach: On a p–v diagram, the isothermal curve lies below the polytropic (n between 1 and gamma), which lies below the isentropic curve (n = gamma). Therefore, for the same end pressures, the isentropic path has the largest area under the curve (highest work), and the isothermal path has the least. Step-by-Step Solution: Isothermal: pv = constant → minimum work for ideal gas compression.Polytropic: pv^n = constant, 1 < n < gamma → intermediate work.Isentropic: n = gamma → maximum work among the listed realistic paths.Thus the maximum indicated work is for isentropic compression. Verification / Alternative check: Analytical expressions show W_isothermal = mRT1ln(p2/p1), W_isentropic = (mRT1/(gamma - 1))(r^((gamma - 1)/gamma) - 1), and W_polytropic lies between them for 1 < n < gamma. Why Other Options Are Wrong: (a) gives minimum work; (c) intermediate; (d) incorrect—work depends on the path; (e) isobaric compression does not connect the specified end pressures for a compressor. Common Pitfalls: Assuming “adiabatic” means “no losses therefore least work.” For compression, adiabatic actually requires more work than isothermal because temperature rises. Final Answer: Isentropic (reversible adiabatic) compression

Question 12

Air compressors: In industry, a “medium-capacity” air compressor typically delivers between 0.15 m^3/s and 5 m^3/s of free air at standard conditions (per unit time).

Accepted Answer

Introduction / Context: Compressor sizing is often communicated by volumetric delivery at standard conditions. Understanding the typical bands that classify small, medium, and large compressors helps with selection and preliminary design. Given Data / Assumptions: Classification is based on free air delivery per unit time at normal temperature and pressure (standard intake conditions). Only an order-of-magnitude selection is required; exact manufacturer ratings vary. Concept / Approach: Common practice divides compressors roughly into small (up to about 0.15 m^3/s), medium (about 0.15 to 5 m^3/s), and large (above 5 m^3/s). These brackets cover the typical ranges encountered in plants, construction, and process utilities. Step-by-Step Solution: Identify the definition sought: “medium-capacity” free air delivery band.Recall typical brackets used in handbooks and vendor catalogs.Select the band that matches medium capacity: 0.15 to 5 m^3/s. Verification / Alternative check: Surveying vendor datasheets shows portable and workshop units below 0.15 m^3/s; plant utility compressors often sit between 0.15 and 5 m^3/s; multi-megawatt process machines exceed 5 m^3/s. Why Other Options Are Wrong: 0.1 to 1.2 m^3/s: Too narrow; excludes many medium plant units above 1.2 m^3/s. Above 5 m^3/s: This is large-capacity territory. None of these: Incorrect because 0.15 to 5 m^3/s is a recognized medium range. Common Pitfalls: Confusing “delivered at standard conditions” with actual discharge conditions; always normalize to compare between compressors. Final Answer: 0.15 to 5 m^3/s

Question 13

Jet propulsion basics: A simple turbojet is essentially a gas turbine engine fitted with an inlet diffuser and a propulsive (exhaust) nozzle to produce thrust.

Accepted Answer

Introduction / Context: A simple turbojet is the foundational air-breathing jet engine architecture used to generate propulsive thrust from a continuous gas turbine cycle. Given Data / Assumptions: Core components: inlet diffuser, compressor, combustor, turbine, and exhaust nozzle. “Simple” indicates no afterburner, no bypass (unlike turbofans), and no mechanical power takeoff (unlike turboshafts). Concept / Approach: The gas turbine core raises the total temperature and pressure of air. The inlet diffuser slows and pressurizes the incoming air (static pressure rise), the compressor further raises pressure, the combustor adds heat at near-constant pressure, the turbine extracts work to drive the compressor, and the exhaust nozzle expands the hot gas to high velocity, creating thrust. Step-by-Step Solution: Recognize the gas turbine core: compressor + combustor + turbine.Add an inlet diffuser to convert flight kinetic energy into pressure for the compressor.Add a propulsive nozzle to expand exhaust and produce high jet velocity for thrust.Therefore, a simple turbojet is a gas turbine with diffuser and nozzle for propulsion. Verification / Alternative check: Cutaway schematics of classic turbojets (e.g., early military engines) show precisely this layout without bypass streams or afterburners. Why Other Options Are Wrong: Disagree: Contradicts the standard definition. Agree, but only with afterburning: Afterburners are optional add-ons and not required for a “simple” turbojet. Disagree, because a turbojet has no turbine: False; the turbine is essential to drive the compressor. Common Pitfalls: Confusing turbojets with turbofans (which have a fan and bypass) or turboshafts (which deliver shaft power instead of pure jet thrust). Final Answer: Agree

Question 14

Rocket performance: The propulsive (thrust) power of a rocket equals thrust multiplied by flight speed. With mass flow rate m_dot, jet speed v1, and aircraft speed v2, the useful propulsive power is P = m_dot * (v1 - v2) * v2.

Accepted Answer

Introduction / Context: Propulsive (useful) power in flight is the rate at which the propulsion system does work on the vehicle to increase or maintain its kinetic energy against drag. For rockets or pure jets, this equals thrust times the flight speed. Given Data / Assumptions: m_dot is the exhaust mass flow rate (propellant for rockets). v1 is the jet exhaust speed relative to the vehicle. v2 is the aircraft (vehicle) speed relative to the air/space reference. Ideal momentum theory; pressure thrust term neglected for simplicity. Concept / Approach: Thrust T from momentum balance in 1-D is T = m_dot * (v1 - v2) for a generic momentum jet (with v2 representing incoming stream speed). The useful propulsive power is the power delivered to the vehicle, P = T * v2. Combining gives P = m_dot * (v1 - v2) * v2. Step-by-Step Solution: Write thrust: T = m_dot * (v1 - v2).Write propulsive power: P = T * v2.Substitute: P = m_dot * (v1 - v2) * v2.Interpretation: The term (v1 - v2) is the jet velocity rise relative to flight, and multiplying by v2 gives useful power at vehicle speed. Verification / Alternative check: Propulsive efficiency η_p = useful power / jet power = [m_dot * (v1 - v2) * v2] / [0.5 * m_dot * (v1 - v2)^2] = 2 v2 / (v1 - v2). This standard relationship is consistent with the derived power expression (for idealized cases). Why Other Options Are Wrong: P = m_dot * v1^2 / 2: This is the exhaust kinetic power, not the useful propulsive power to the vehicle. P = m_dot * v2^2 / 2: Relates to vehicle kinetic energy rate only in a special acceleration case, not general propulsion power expression. P = (v1 + v2) / 2: Dimensionally incorrect and not a power. Common Pitfalls: Confusing jet power with propulsive power; only the portion of jet energy that goes into pushing the vehicle forward at speed v2 counts as useful propulsive power. Final Answer: P = m_dot * (v1 - v2) * v2

Question 15

Two-stage compression with perfect intercooling: If n1 and n2 are the polytropic indices in stage-1 and stage-2, then the work ratio with equal pressure ratios is W1/W2 = [n1/(n1 − 1)] / [n2/(n2 − 1)].

Accepted Answer

Introduction / Context: In multi-stage air compression with perfect intercooling and equal pressure ratios per stage, each stage can follow a different polytropic index n. Comparing stage works helps in assessing valve timing, cooling, and stage matching. Given Data / Assumptions: Two stages with polytropic indices n1 (stage-1) and n2 (stage-2). Perfect intercooling restores the interstage temperature to the initial suction temperature. Equal pressure ratios per stage. Ideal gas behavior with constant specific heats. Concept / Approach: For polytropic compression p * v^n = constant, the specific work (per unit mass) is proportional to n/(n − 1) times a function of the pressure ratio raised to (n − 1)/n. With equal pressure ratios and identical inlet temperature to each stage (due to perfect intercooling), the ratio of works reduces to the ratio of n/(n − 1) factors. Step-by-Step Solution: For a stage: w = [n/(n − 1)] * R * T_in * [(r)^((n − 1)/n) − 1].With equal r and same T_in for both stages, the bracketed term is equal for each.Therefore, W1/W2 = [n1/(n1 − 1)] / [n2/(n2 − 1)].This compares only the polytropic factors, since other terms cancel. Verification / Alternative check: If n1 = n2, the ratio becomes 1, matching the expectation that both stages do equal work under perfect intercooling with equal pressure ratios. Why Other Options Are Wrong: Inverse ratio: Swaps the stage roles incorrectly. (n1 − 1)/(n2 − 1): Omits the n terms; not dimensionally consistent with polytropic work dependence. n2/n1: Also incorrect; polytropic work does not scale simply as n. Common Pitfalls: Assuming stage work equality without checking n values; perfect intercooling equalizes temperatures, but differing n values still change the polytropic factor. Final Answer: W1/W2 = [n1/(n1 − 1)] / [n2/(n2 − 1)]

Question 16

Effect of altitude on compressor power: For the same machine and similar operating conditions, an air compressor at high altitude generally requires less shaft power due to lower inlet density and reduced mass flow.

Accepted Answer

Introduction / Context: Altitude changes ambient pressure and density, which affects the mass flow and power required by compressors and blowers. This question focuses on the qualitative trend for the same machine operated at higher elevation. Given Data / Assumptions: Same compressor geometry and speed. Similar pressure ratio target relative to local ambient. Lower ambient pressure and density at altitude; temperature may also be lower but is a secondary factor here. Concept / Approach: Compressor power roughly scales with mass flow and with the specific work per unit mass. At higher altitude, the inlet density is lower, reducing mass flow for the same volumetric displacement. Even if the pressure ratio is maintained, the reduced m_dot lowers total shaft power. Step-by-Step Solution: m_dot = rho_in * V_dot; at altitude, rho_in decreases → m_dot decreases.Power ~ m_dot * specific work; for similar pressure ratios, specific work is comparable.Therefore, overall power decreases primarily because m_dot is smaller.Conclusion: The compressor requires less power at high altitude. Verification / Alternative check: Aircraft and mountain-site installations derate compressor mass throughput and power with altitude; vendor correction curves confirm the trend. Why Other Options Are Wrong: Same: Ignores strong density effect on mass flow. More: Opposite of the usual trend. Depends only on temperature: Pressure/density changes dominate. Common Pitfalls: Confusing pressure ratio referenced to sea level with pressure ratio relative to local ambient; always specify the operating basis. Final Answer: less

Question 17

Air motors vs. compressors: A reciprocating air motor runs on the thermodynamic cycle that is the reverse of a reciprocating air compressor, not the same process sequence.

Accepted Answer

Introduction / Context: Reciprocating air motors and compressors are thermodynamic counterparts. Where a compressor consumes work to raise air pressure, an air motor expands compressed air to produce work. Given Data / Assumptions: Idealized cycles to illustrate the relationship. Neglect small losses and throttling for the conceptual comparison. Concept / Approach: On a p–v diagram, a compressor traces a loop representing intake at low pressure, compression, and discharge at high pressure. An air motor traces a reversed loop: admission at high pressure, expansion delivering work, and exhaust at low pressure. Hence the operation is not “similar” in process direction; it is the reverse. Step-by-Step Solution: Compressor: intake → compression → delivery; work input required.Air motor: admission → expansion → exhaust; work output delivered.Thus, the statement “operation is similar” is false in a thermodynamic sense; it is reversed. Verification / Alternative check: Indicator diagrams from lab rigs show the compressor and air motor loops mirrored about an axis, confirming the reversal. Why Other Options Are Wrong: Any “True/only if” variants misrepresent the fundamental reversal; specific heat transfer modes do not change that. Common Pitfalls: Equating mechanical construction similarity (cylinders, pistons, valves) with thermodynamic process similarity; the hardware may look alike, but the cycle direction differs. Final Answer: False

Question 18

Air compressor piping: Moisture separators are typically installed immediately after the intercooler to remove condensed water before the next compression stage.

Accepted Answer

Introduction / Context: Intercoolers drop the temperature of compressed air between stages, causing water vapor to condense. Proper placement of moisture separators protects downstream stages and equipment. Given Data / Assumptions: Multi-stage compressor with intercooling and (often) an aftercooler before storage. Cooling the air below its dew point condenses water that must be removed. Concept / Approach: Because most condensation occurs where temperature is reduced sharply, the separator is placed right after the intercooler. This removes liquid water before the air enters the next compression stage. A second separator is commonly used after the aftercooler before the receiver, but the primary, definitive location is after the intercooler. Step-by-Step Solution: Compression raises temperature and reduces relative humidity.Intercooling reduces temperature; water condenses.Install separator immediately after the intercooler to capture condensate.Dryer or aftercooler and a final separator may follow before storage. Verification / Alternative check: P&IDs for typical compressor packages show knock-out pots/separators downstream of each cooler. Why Other Options Are Wrong: Before intercooler: Little to no condensation yet; ineffective. Between aftercooler and receiver: Often used as an additional separator, but the question asks generally—first essential location is after the intercooler. Before first stage suction: Unrelated to condensation removal from compressed air. Common Pitfalls: Assuming a single separator is sufficient; multi-stage systems usually need separators after each cooler. Final Answer: after the intercooler

Question 19

Definitions check: “Mean effective pressure” (MEP) for a compressor is the hypothetical constant pressure that, acting on the swept volume, would produce the same work per cycle; it is not a volumetric quantity.

Accepted Answer

Introduction / Context: Terminology matters: volumetric performance and work indicators are different concepts in compressor engineering. Mean effective pressure (MEP) is a work proxy, not a flow definition. Given Data / Assumptions: Compressor cycle on a p–v diagram. Swept (displacement) volume V_s and indicated work per cycle W_ind. Concept / Approach: MEP is defined so that W_ind = MEP * V_s. It allows comparison of different machines independent of size. Volumetric quantities like “actual volume delivered at standard conditions” are instead Free Air Delivery (FAD) or relate to volumetric efficiency—not MEP. Step-by-Step Solution: Define MEP: MEP = W_ind / V_s.Observe that none of the listed options describe a pressure or work-based metric.Therefore, the correct choice is “none of the above.” Verification / Alternative check: Handbooks present MEP as a notional constant pressure creating the same area (work) under the indicator diagram over the stroke volume. Why Other Options Are Wrong: Actual volume delivered at STP: This is FAD. Volume delivered or sucked: Raw volumetric measures; neither is a pressure nor work term. Common Pitfalls: Equating volumetric efficiency or FAD with MEP; they measure different aspects—flow vs. work. Final Answer: none of the above

Question 20

Axial-flow compressor kinematics: In an axial compressor stage, the bulk flow of air proceeds essentially parallel to the machine axis (aside from small swirl components).

Accepted Answer

Introduction / Context: Axial-flow compressors are widely used in gas turbines due to their high mass flow capability and compact geometry. Understanding the predominant flow direction helps with velocity triangle analysis. Given Data / Assumptions: Multi-row rotor–stator blade rows. Design point, subsonic to transonic relative velocities. Concept / Approach: While rotors impart swirl and stators remove it, the through-flow (meridional component) is arranged to be nearly parallel to the axis to minimize diffusion losses and maintain steady blade incidence. Velocity triangles are constructed about this axial mean component. Step-by-Step Solution: Identify the mean flow direction: axial (parallel to shaft).Rotors add swirl (tangential velocity), stators deswirl, but the meridional flow remains axial.Therefore the statement is correct. Verification / Alternative check: Stage analyses and CFD show small radial components for endwall effects, but the dominant component is axial by design. Why Other Options Are Wrong: “Incorrect” contradicts the definition; “only at stall” or “only in stators” are misunderstandings—stall disrupts axial uniformity, and both blade rows share the axial through-flow path. Common Pitfalls: Confusing swirl (tangential) with axial through-flow; both coexist but describe different components. Final Answer: Correct

Compressors, Gas Dynamics and Gas Turbines Questions