- An insulated tank is being filled with compressed air from a supply line. The tank initially contains air at atmospheric pressure, and filling occurs over 10 minutes until the pressure reaches 5 bar. The supply line maintains constant conditions throughout the filling process. For analyzing the air inside the tank during filling, which combination of assumptions is most appropriate?
Answer: Unsteady process, adiabatic tank walls, negligible kinetic and potential energies
When analyzing a tank filling process, you need to carefully consider whether the system properties change with time and what energy transfer mechanisms are relevant.
Option B is correct because this scenario involves an unsteady process where the tank's pressure increases from 1 to 5 bar over 10 minutes, meaning properties inside the tank are clearly changing with time. The adiabatic assumption is valid since the tank is described as insulated, preventing heat transfer. The negligible kinetic and potential energy assumption is appropriate because the air's velocity inside the tank and elevation changes are insignificant compared to the internal energy changes during compression.
Option A is wrong because steady-state means properties don't change with time, but the tank pressure is clearly increasing from 1 to 5 bar over the filling period.
Option C is wrong because it incorrectly assumes steady-state conditions and allows heat transfer despite the tank being explicitly described as insulated.
Option D is wrong because while it correctly identifies the unsteady nature, it incorrectly assumes heat transfer occurs through insulated walls and that kinetic/potential energies are significant. In tank filling problems, the energy associated with air motion and position changes is typically negligible compared to internal energy changes.
Study tip: For tank filling/emptying problems, always ask: "Are properties inside changing with time?" (unsteady if yes), "Is the tank insulated?" (adiabatic if yes), and "Are we dealing with high-velocity flows or significant elevation changes?" (usually no for tanks).
- A geothermal power plant uses hot underground water to generate electricity. The geothermal water enters a flash chamber at 180°C where pressure reduction causes partial vaporization. The liquid-vapor mixture then separates, with vapor going to the turbine and liquid being reinjected underground. The flash chamber operates at steady conditions. Water enters through a horizontal pipe at 4 m/s and the vapor exits upward through a vertical pipe 8 meters above the inlet at 25 m/s. For analyzing the vapor stream from inlet to vapor outlet, which assumption would be most questionable?
Answer: Negligible potential energy changes despite the 8-meter elevation difference
When analyzing energy flows in thermodynamic systems, you must carefully evaluate which energy terms are significant compared to others. This question tests your ability to identify when standard simplifying assumptions break down.
The correct answer is D because neglecting potential energy changes is unjustified here. The potential energy change equals mgh=mg(8 m), which represents significant energy per unit mass. For water vapor at these conditions, this translates to roughly 78.4 kJ/kg - a substantial amount that cannot be ignored when performing energy balances on the system.
Let's examine why the other assumptions are reasonable:
A is valid because geothermal plants are designed for continuous, steady operation. The flash chamber maintains constant pressure and temperature during normal operation, making steady-state analysis appropriate.
B is reasonable because flash chambers are typically well-insulated to prevent heat loss and maintain process efficiency. The rapid flashing process occurs quickly enough that heat transfer to surroundings is minimal.
C is acceptable because while kinetic energy does change (from 4 m/s to 25 m/s), this represents only about 0.3 kJ/kg difference - much smaller than the potential energy change and typical enthalpy changes in phase transitions.
Study tip: When analyzing thermodynamic processes, always calculate the magnitude of energy terms before assuming they're negligible. Potential energy becomes significant when elevation changes exceed a few meters, kinetic energy matters when velocities exceed ~100 m/s, and never ignore energy terms that are comparable to the primary energy changes in your process. - A steam generator in a power plant heats water to produce steam for the turbine. Feedwater enters at 150°C and steam exits at 500°C and high pressure. The heating occurs in vertical tubes that are 25 meters tall. Water velocity increases from 3 m/s to 12 m/s due to density change during heating and vaporization. The steam generator operates at steady conditions and receives heat from combustion gases. Which assumption would be most appropriate for simplified analysis?
Answer: Negligible kinetic energy changes, significant potential energy changes, non-adiabatic process
When analyzing steam generators and similar thermal systems, you need to evaluate the relative magnitudes of kinetic energy, potential energy, and heat transfer effects to determine which terms can be simplified in your energy balance.
Let's examine each energy component systematically. For kinetic energy changes, calculate ΔKE=21m(V22−V12)=21m(122−32)=67.5m J/kg. While this seems significant, compare it to the enthalpy change during heating and vaporization from 150°C to 500°C, which involves roughly 2000-3000 kJ/kg. The kinetic energy change represents less than 3% of the total energy change, making it negligible.
For potential energy, ΔPE=mgΔh=m(9.81)(25)=245m J/kg. Though smaller than the kinetic energy change in absolute terms, this is still significant relative to other system energies and cannot be ignored in a 25-meter tall vertical system.
The process is clearly non-adiabatic since heat transfer from combustion gases is the primary mechanism driving the steam generation.
Answer C correctly identifies negligible kinetic energy changes, significant potential energy changes, and non-adiabatic conditions. Answer A incorrectly neglects potential energy in a tall vertical system. Answer B overemphasizes kinetic energy changes that are small compared to enthalpy changes. Answer D incorrectly assumes adiabatic conditions when heat transfer is explicitly occurring.
Strategy tip: In thermal systems, always compare energy terms to the dominant enthalpy changes. Kinetic energy changes are often negligible, but potential energy becomes significant in tall vertical equipment like steam generators and heat exchangers. - An insulated mixing chamber combines two air streams: Stream 1 at 400 K, 200 kPa, 5 kg/s and Stream 2 at 300 K, 200 kPa, 3 kg/s. The mixed stream exits at 200 kPa. After 30 minutes of operation, measurements show the chamber wall temperature has increased from 290 K to 310 K. Which assumption should be reconsidered?
Answer: Steady-state operation, because the wall temperature change indicates thermal energy accumulation within the system
The wall temperature increase from 290 K to 310 K indicates that thermal energy is being stored in the chamber walls, violating the steady-state assumption. In steady state, the chamber temperature should remain constant. This energy accumulation means the energy balance must include a storage term. While the temperature change might also suggest some heat transfer to surroundings, the primary issue is the violation of steady-state conditions.
- A piston-cylinder assembly contains water that is heated slowly over 30 minutes. The piston moves freely, maintaining constant pressure. The cylinder is equipped with electric resistance heaters but is not insulated from the room. During the process, the water temperature rises from 80°C to 120°C. Which assumption would require the most careful justification?
Answer: The process is adiabatic since the focus is on electrical heating
When analyzing thermodynamic processes, you must carefully examine whether each assumption aligns with the physical setup described. The key is identifying which assumptions contradict the given conditions.
Option C is the most questionable assumption because an adiabatic process means no heat transfer occurs between the system and surroundings. However, the problem explicitly states the cylinder is "not insulated from the room." This means heat can transfer between the water and the room environment, making the process non-adiabatic by definition. Additionally, since the water temperature (120°C) will likely exceed room temperature, significant heat loss to the surroundings would occur, further contradicting the adiabatic assumption.
Option A is well-justified because a freely moving piston in a gravitational field naturally maintains constant pressure - the piston moves to balance internal pressure with atmospheric pressure plus the piston's weight. Option B is reasonable since "slowly over 30 minutes" suggests the system remains close to equilibrium throughout, satisfying the quasi-static condition. Option D is standard practice in thermodynamics problems involving stationary fluids, where kinetic and potential energy changes are negligible compared to internal energy changes.
The temperature rise from 80°C to 120°C spans both liquid and vapor phases for water at atmospheric pressure, making energy analysis complex enough without incorrectly assuming no heat loss occurs.
Study tip: When evaluating thermodynamic assumptions, always check if they contradict explicitly stated conditions. "Not insulated" immediately rules out adiabatic processes - this is a common exam trap.
- A natural gas pipeline includes a pressure-reducing station where gas flows from 5 MPa to 1 MPa through a throttling valve. The pipeline has a 2° upward slope, creating a 50-meter elevation increase over 1.5 km distance. Gas velocity is 15 m/s before the valve and 25 m/s after. An engineer's assumption that 'potential energy changes are negligible compared to enthalpy changes' should be:
Answer: Accepted because PE change (≈ 490 J/kg) is small compared to typical enthalpy values in natural gas systems
For natural gas (density ≈ 50 kg/m³ at these conditions), PE change = mgh ≈ 50 × 9.81 × 50 = 24,500 J/m³ ≈ 490 J/kg. Typical enthalpy changes in throttling processes are much larger, making this PE change negligible. While KE change is ½[(25)² - (15)²] = 200 J/kg, this doesn't invalidate the PE assumption. The engineer's assumption about PE being negligible compared to enthalpy changes is correct for this application.
- A steam turbine operates with inlet conditions of 6 MPa and 500°C and exhausts to a condenser at 10 kPa. The turbine has an isentropic efficiency of 85%. When analyzing this system using the first law of thermodynamics, which assumption is MOST critical to validate before proceeding with calculations?
Answer: The process operates at steady state since the problem provides fixed inlet and outlet conditions
For any control volume analysis using the first law, establishing steady-state operation is the foundational assumption that must be validated first. Without steady state, the energy equation becomes much more complex and requires additional terms for energy accumulation. The other assumptions (adiabatic operation, negligible KE/PE changes) are important but secondary - they cannot be properly applied without first confirming steady-state operation.
- A steam ejector uses high-pressure steam at 1 MPa, 300°C to accelerate and compress low-pressure steam at 10 kPa, 90% quality. Both streams enter through nozzles with exit velocities exceeding 400 m/s before mixing. For the overall ejector analysis, which assumption combination is most problematic?
Answer: Steady-state operation and negligible kinetic energy changes for both inlet and outlet streams
With velocities exceeding 400 m/s, kinetic energy terms become very significant. KE = ½v² gives values exceeding 80,000 J/kg, which is substantial compared to enthalpy differences in steam systems. Neglecting these terms would lead to major errors in the energy balance. Steam ejectors specifically rely on momentum transfer from high-velocity streams, making kinetic energy the dominant mechanism. Steady-state operation is typically valid for ejectors.
- A heat exchanger analysis considers hot oil flowing through tubes while cold water flows through the shell. The oil enters at 150°C and exits at 90°C, while water enters at 20°C and exits at 60°C. Both fluids have significant velocity changes due to area variations in the flow passages. The heat exchanger has been operating at these conditions for 2 hours. Which set of assumptions would be most appropriate for a standard heat exchanger analysis?
Answer: Steady-state, adiabatic external surfaces, negligible kinetic energy changes, negligible potential energy changes
When analyzing heat exchangers, you need to consider which physical assumptions best represent the actual operating conditions. The key is identifying what processes dominate and which effects are negligible compared to the primary heat transfer.
After 2 hours of operation, the heat exchanger has reached equilibrium - temperatures and flow rates are no longer changing with time. This indicates steady-state conditions where properties at any given point remain constant. The primary purpose is heat transfer between fluids, so assuming adiabatic external surfaces (no heat loss to surroundings) focuses the analysis on fluid-to-fluid heat exchange. While the problem mentions "significant velocity changes," in heat exchanger analysis, kinetic energy changes are typically small compared to enthalpy changes from temperature differences. The 60-70°C temperature changes represent much larger energy transfers than velocity variations. Potential energy changes are negligible since fluid elevations don't change significantly in typical heat exchangers.
Choice A correctly identifies all appropriate assumptions for standard heat exchanger analysis. Choice B incorrectly includes heat loss to surroundings and significant kinetic energy changes - both complicate analysis unnecessarily when the dominant effect is fluid-to-fluid heat transfer. Choice C assumes unsteady-state conditions, but after 2 hours of operation, the system has clearly reached steady state. Choice D incorrectly emphasizes kinetic energy changes, which are minor compared to the thermal energy changes evident from the large temperature differences.
Study tip: For heat exchanger problems, always start with steady-state and adiabatic assumptions unless explicitly told otherwise. Focus on thermal effects first - they typically dwarf kinetic and potential energy changes in these systems.
- A steam nozzle accelerates steam from low velocity to high velocity for use in a turbine. The nozzle is short with high-quality insulation, and the steam velocity increases from 50 m/s to 600 m/s. The nozzle inlet and outlet are at the same elevation. The residence time of steam in the nozzle is approximately 0.001 seconds. Which assumption requires the most careful consideration?
Answer: Negligible kinetic energy changes compared to enthalpy changes in the steam
When analyzing steam nozzles, you need to carefully evaluate which assumptions are valid based on the actual operating conditions and energy magnitudes involved.
Let's examine the kinetic energy change first. The kinetic energy per unit mass changes from 21(50)2=1,250 J/kg to 21(600)2=180,000 J/kg, giving a change of 178,750 J/kg. This is enormous compared to typical enthalpy changes in steam processes, which are usually on the order of tens of thousands of J/kg. Therefore, assumption C is completely invalid – kinetic energy changes dominate this process.
Looking at the other assumptions: Option A is reasonable because the short residence time (0.001 seconds) supports steady-state operation with minimal transient effects. Option B is well-justified since the combination of excellent insulation and extremely short residence time prevents meaningful heat transfer – there's simply no time for significant thermal interaction with surroundings. Option D is clearly valid since inlet and outlet are at the same elevation, making potential energy changes truly negligible.
The trap here is thinking that because steam has high enthalpy, kinetic energy changes must be small in comparison. However, the massive velocity increase (from 50 to 600 m/s) creates kinetic energy changes that dwarf enthalpy changes in magnitude.
Study tip: In high-velocity flow problems, always calculate the actual kinetic energy changes – don't assume they're negligible just because you're dealing with steam or other high-enthalpy fluids. The velocity squared term can create surprisingly large energy contributions. - A throttling valve reduces steam pressure from 2 MPa to 0.5 MPa. The upstream pipe diameter is 10 cm and downstream diameter is 15 cm. Steam velocity upstream is 30 m/s. Which assumption about this throttling process would be LEAST defensible?
Answer: Kinetic energy changes are negligible despite the area change and significant upstream velocity
With upstream velocity of 30 m/s and area ratio of (10/15)² = 0.44, the downstream velocity will be approximately 30 × 0.44 = 13.2 m/s (using continuity). The kinetic energy change is significant: ΔKE = ½[(30)² - (13.2)²] = 363 J/kg, which is substantial compared to enthalpy values. The other assumptions are well-justified: throttling is inherently adiabatic, elevation changes are small, and steady-state operation is typical for control valves.
- An air compressor operates between two large tanks connected by insulated piping. During a transient startup period, the compressor gradually increases the pressure in the discharge tank from atmospheric to operating pressure over 15 minutes. The suction tank is very large and maintains nearly constant conditions. For analyzing the discharge tank during startup, which assumption would be most problematic?
Answer: The compression process in the compressor itself can be treated as steady-state
When analyzing transient processes in thermodynamics, you need to carefully distinguish between steady-state and unsteady conditions. The key insight here is recognizing what happens during the 15-minute startup period when the discharge tank pressure gradually increases.
Option A is problematic because during startup, the compressor cannot operate at steady-state. As the discharge tank pressure rises from atmospheric to operating pressure, the compressor experiences continuously changing outlet conditions. The pressure ratio across the compressor is constantly changing, which means the mass flow rate, work input, and thermodynamic states throughout the compressor are all time-dependent. Assuming steady-state for the compressor would ignore these crucial transient effects and lead to significant analysis errors.
Option B is actually correct – the discharge tank definitely undergoes an unsteady process since its pressure and temperature are changing with time. Option C is reasonable because in most industrial compression systems, the kinetic and potential energy terms are indeed small compared to the internal energy changes associated with pressure and temperature variations. Option D is also justified since the piping is insulated and 15 minutes is relatively short for significant heat transfer to occur, especially compared to the large energy changes from compression.
The most important study tip for transient analysis problems: always identify which components experience changing conditions over time. Equipment operating between changing boundary conditions (like this compressor between constant suction and rising discharge pressure) cannot be treated as steady-state, even if individual components might normally operate that way.
- A refrigeration compressor takes R-134a vapor at -10°C, 200 kPa and compresses it to 800 kPa, 60°C. The compressor is air-cooled with external fans, and the manufacturer specifies that cooling removes 15% of the compression work as heat. An analysis assumes adiabatic compression (Q=0). The impact of this assumption is:
Answer: Significant because ignoring 15% heat removal will underestimate the outlet enthalpy and overestimate compressor efficiency
Ignoring heat removal (assuming Q=0 instead of Q=-15% of work) means the calculated outlet enthalpy will be higher than actual, since some energy was actually removed as heat. This makes the calculated compression work appear more efficient than it actually is, since the analysis assumes all work went into increasing enthalpy when actually 15% was removed as heat. This significantly affects efficiency calculations and outlet state predictions.
- An engineer is analyzing a heat exchanger where hot exhaust gases at 800 K enter at 50 m/s and cool water at 300 K enters at 2 m/s. The gas outlet velocity is 45 m/s and water outlet velocity is 2.5 m/s. For a first-law analysis, which combination of assumptions requires the most careful justification?
Answer: Negligible kinetic energy changes and adiabatic operation with respect to the surroundings
The kinetic energy assumption is questionable here because gas velocities are high (50 m/s inlet, 45 m/s outlet), and the velocity change is significant (10% reduction). For high-speed gas flows, KE terms can be substantial. Additionally, assuming adiabatic operation requires justification since heat exchangers often have external heat losses. The other combinations involve assumptions that are more easily justified (steady-state is standard, PE changes are truly negligible for horizontal heat exchangers).
- A feedwater heater in a power plant mixes high-pressure steam with liquid water to produce heated liquid water. The steam enters at high velocity (40 m/s) while the liquid water enters at low velocity (3 m/s). The mixed liquid water exits at moderate velocity (8 m/s). The heater operates continuously under steady conditions and is well-insulated. All streams are at approximately the same elevation. For control volume analysis, which assumption would be most questionable?
Answer: Negligible kinetic energy changes due to effective momentum transfer during mixing
When analyzing control volumes in thermodynamics, you must carefully evaluate which terms in the energy equation can reasonably be neglected. This requires examining the actual magnitudes of energy changes, not just making assumptions.
The key insight here is recognizing that kinetic energy changes can be significant when velocities differ substantially. Let's calculate the specific kinetic energies: steam enters at 2(40)2=800 J/kg, liquid water at 2(3)2=4.5 J/kg, and the mixture exits at 2(8)2=32 J/kg. The kinetic energy change per unit mass of steam is nearly 800 J/kg – this is substantial compared to typical enthalpy differences in such processes and cannot be ignored.
Option A is reasonable because feedwater heaters do operate continuously with steady flow rates. Option B makes sense since the heater is well-insulated and mixing occurs rapidly, preventing significant heat transfer to surroundings. Option D is valid because all streams are at the same elevation, making gravitational potential energy changes truly negligible.
However, option C contains a flawed assumption. The phrase "effective momentum transfer during mixing" doesn't justify neglecting kinetic energy changes. High-velocity steam (40 m/s) mixing with low-velocity water (3 m/s) represents a significant kinetic energy transformation that must be accounted for in the energy balance.
Study tip: In control volume problems, always calculate the actual magnitudes of kinetic energy terms (2V2) when velocities exceed ~10 m/s. Don't assume they're negligible without checking – they often aren't! - A pump lifts water from a lower reservoir to an upper reservoir through a vertical height of 50 meters. The pump operates continuously, and the water velocity is approximately 3 m/s in both the suction and discharge pipes. The pump casing is not insulated, and some heat is generated due to inefficiencies. For a control volume analysis around the pump, which assumption would be questionable?
Answer: Negligible potential energy change since the elevation difference is small
When analyzing pumps using control volume analysis, you need to carefully evaluate which terms in the energy equation are significant versus negligible. This question tests your ability to identify which assumptions are physically reasonable for the given conditions.
The correct answer is C because a 50-meter elevation change is definitely not negligible when analyzing pump performance. The potential energy change is ΔPE=mgh=mg(50), which represents a substantial energy requirement that dominates the pump's work input. Claiming this is negligible would lead to major errors in your analysis - it's actually the primary function of the pump to overcome this gravitational potential energy difference.
Let's examine why the other assumptions are reasonable: Option A is valid because continuous operation at constant conditions defines steady-state perfectly. The flow rate and other properties remain constant with time, making this a standard assumption for pump analysis. Option B is correct since both velocities are 3 m/s, so ΔKE=21m(v22−v12)=0. The kinetic energy terms cancel out completely. Option D accurately describes the physical situation - with an uninsulated pump casing and internal inefficiencies generating heat, assuming an adiabatic process (no heat transfer) would be incorrect.
Study tip: In pump problems, always check the elevation difference first. Even modest height changes (like 10+ meters) typically represent the largest energy requirement in the system. Don't let the specific numbers fool you - 50 meters is significant in any pumping application and cannot be ignored in your energy balance. - A diffuser slows down high-velocity air entering a wind tunnel test section. The air enters at 200 m/s and exits at 50 m/s. The diffuser is well-insulated and operates continuously. The inlet and outlet are at the same height, and the process occurs over a very short time (milliseconds). An engineer needs to choose assumptions for energy analysis. Which assumption would be LEAST appropriate?
Answer: Negligible work transfer since no moving parts are present in the diffuser
When analyzing energy systems like diffusers, you need to carefully evaluate which assumptions are appropriate based on the physical conditions and time scales involved. This question tests your understanding of when different thermodynamic assumptions apply.
Looking at each assumption: Option A is entirely appropriate because the diffuser operates continuously under steady conditions with constant mass flow - this is exactly when steady-state analysis applies. Option B makes perfect sense since the diffuser is well-insulated (preventing heat transfer) and the process occurs over milliseconds (no time for significant heat exchange with surroundings). Option C is absolutely critical because the velocity changes from 200 m/s to 50 m/s - with kinetic energy proportional to v2, this represents a massive energy change that dominates the analysis. Option D is reasonable since inlet and outlet are at the same height, making potential energy changes negligible compared to the large kinetic energy changes.
However, there's no option E listed in your choices, which suggests this might be a formatting error in the question. Based on the four options provided (A-D), all represent appropriate assumptions for this diffuser analysis. Option A correctly identifies steady-state conditions, B properly recognizes adiabatic behavior, C acknowledges the dominant kinetic energy terms, and D reasonably neglects small potential energy changes.
Study tip: For diffuser problems, always check the velocity changes first - they usually dominate the energy analysis. Large velocity differences mean kinetic energy terms cannot be neglected, while good insulation and short residence times typically justify the adiabatic assumption. - A gas turbine combustor receives compressed air and fuel, with combustion products exiting to the turbine. The combustor operates at steady conditions with air entering at 400°C and combustion products exiting at 1200°C. The combustor is not insulated, and significant heat is lost to the surroundings. Velocities are low throughout the combustor due to its large cross-sectional area. The combustor is horizontal. Which set of assumptions would be most questionable for energy analysis?
Answer: Steady-state, adiabatic process, negligible kinetic energy, negligible potential energy
When analyzing control volumes like gas turbine combustors, you need to evaluate which assumptions align with the actual operating conditions described in the problem.
The problem clearly states several key conditions: the combustor operates at steady conditions, is not insulated with significant heat loss occurring, has low velocities due to large cross-sectional area, and is horizontal. Each of these directly informs which assumptions are appropriate for your energy analysis.
Option B is most questionable because it assumes an adiabatic process, meaning no heat transfer occurs. This directly contradicts the problem statement, which explicitly mentions that the combustor "is not insulated, and significant heat is lost to the surroundings." Assuming adiabatic conditions when substantial heat loss is occurring would lead to completely incorrect energy balance calculations.
Option A correctly reflects all the stated conditions: steady-state operation (given), significant heat loss (stated), negligible kinetic energy (low velocities), and negligible potential energy (horizontal orientation). Option C incorrectly assumes unsteady-state conditions when the problem explicitly states steady operation. Option D incorrectly assumes significant kinetic energy despite the problem stating velocities are low due to the large cross-sectional area.
For thermodynamics problems involving control volumes, always match your assumptions to the physical description provided. The most dangerous assumptions are those that directly contradict given information, especially regarding heat transfer modes. When a problem mentions insulation status or heat loss, this is a strong signal that the adiabatic assumption is being tested—make sure your choice aligns with what's physically described.
- A boiler generates steam by heating water in tubes while hot combustion gases flow outside the tubes. The process has reached steady operation after startup. Water enters as subcooled liquid at 30°C and exits as superheated steam at 400°C. The water velocity increases from 2 m/s to 15 m/s due to density change during vaporization. The boiler tubes are inclined at 15° from horizontal over a 10-meter length. For a control volume analysis of the water/steam side, which assumption requires careful evaluation?
Answer: Negligible potential energy changes despite the inclined tube orientation
When analyzing control volumes in thermodynamic systems, you must evaluate which assumptions are reasonable based on the physical magnitudes involved. This question tests your ability to identify when seemingly "negligible" terms actually matter.
The potential energy change is significant here and cannot be ignored. With a 10-meter tube length inclined at 15°, the vertical height change is h=10sin(15°)≈2.6 m. The potential energy change per unit mass is gΔh=9.81×2.6≈25.5 kJ/kg. While this seems small compared to the enthalpy of vaporization (~2000 kJ/kg), it's comparable to the kinetic energy changes and shouldn't be automatically dismissed without calculation. Answer C correctly identifies this assumption as requiring careful evaluation.
Answer A is incorrect because steady-state operation is clearly stated in the problem and is a reasonable assumption after startup. Answer B is wrong because kinetic energy changes are actually negligible here—the change from 2 m/s to 15 m/s gives ΔKE=21(152−22)=110.5 J/kg=0.11 kJ/kg, which is truly small compared to vaporization enthalpy. Answer D is incorrect because heat addition from combustion gases is the fundamental process occurring, not an assumption.
Study tip: In control volume problems, always check the order of magnitude of potential energy changes when there are significant elevation differences. Don't assume they're negligible just because the system involves phase change—calculate first, then decide. - A hydraulic turbine generates power from water flowing through it. Water enters the turbine at high pressure through a 2-meter diameter pipe at 5 m/s and exits at atmospheric pressure through a 3-meter diameter pipe. The turbine is located 20 meters below the reservoir surface. The turbine casing is not insulated, but heat transfer is minimal due to low temperature differences. For energy analysis, which assumption requires the most justification?
Answer: Negligible potential energy changes despite 20-meter elevation difference
When analyzing hydraulic turbines, you need to carefully evaluate which assumptions are reasonable based on the physical significance of each energy term in the energy equation.
The assumption requiring the most justification is C) Negligible potential energy changes despite 20-meter elevation difference. A 20-meter height difference represents substantial potential energy: ΔPE=gh=(9.81)(20)=196.2 J/kg. This is significant compared to typical kinetic energy terms and cannot be reasonably neglected. The potential energy change is actually a major driving force in the turbine operation.
Let's examine why the other assumptions are more reasonable: A) Steady-state operation is standard for turbine analysis and requires minimal justification since turbines are designed for continuous operation. B) Negligible heat transfer is well-supported by the problem statement noting minimal temperature differences and the short residence time of water in the turbine. D) Significant kinetic energy changes is actually correct to assume, not neglect - the area change from 2m to 3m diameter significantly affects velocity (A1v1=A2v2), and the pressure drop also influences kinetic energy.
The key insight is that potential energy scales with gh and becomes substantial over elevation differences of tens of meters, while kinetic energy scales with v2 and heat transfer depends on temperature differences and time. In this problem, the 20-meter elevation change represents the largest energy term that cannot be dismissed.
Study tip: Always calculate the magnitude of energy terms before assuming they're negligible - potential energy changes become significant when elevation differences exceed a few meters.
