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Practice Exam
Question 1. Which assumption is most appropriate when modeling a rapid gas release that occurs faster than heat can be transferred to the surroundings? A) Isothermal flow B) Isentropic flow C) Polytropic flow with n = 1. D) Steady‑state incompressible flow Answer: B Explanation: A rapid release is assumed adiabatic and reversible, leading to constant entropy (isentropic) conditions. Question 2. In a control‑volume analysis of a vessel blowdown, which of the following balances is NOT required? A) Mass balance B) Energy balance C) Momentum balance D) Charge balance Answer: D Explanation: Charge balance is irrelevant to fluid flow; mass, energy, and momentum balances are essential. Question 3. The discharge coefficient (C_d) for a sharp‑edged orifice is typically closest to which value? A) 0. B) 0. C) 0. D) 0. Answer: C
Practice Exam
Explanation: Sharp‑edged orifices usually have C_d ≈ 0.60, accounting for vena‑vena effects. Question 4. Bernoulli’s equation is most accurate for which type of flow? A) Highly compressible gas at Mach > 0. B) Incompressible liquid with negligible friction losses C) Supersonic flow through a nozzle D) Transient flow in a pipe surge Answer: B Explanation: Bernoulli’s equation assumes incompressible, inviscid, steady flow; thus it best applies to liquids under those conditions. Question 5. For an ideal gas, the critical pressure ratio (P_c/P_0) that marks the onset of choked flow is given by: A) (2/(γ+1))^(γ/(γ‑1)) B) (γ‑1)/γ C) (γ+1)/2γ D) (γ/(γ‑1))^(γ‑1) Answer: A Explanation: Derivation from isentropic flow theory yields P_c/P_0 = [2/(γ+1)]^(γ/(γ‑1)). Question 6. If the upstream stagnation pressure is 2 MPa, temperature 300 K, γ = 1.4, molecular weight 28 kg kmol⁻¹, and C_d = 0.95, which equation provides the choked mass flow rate (ṁ) through an orifice of area A? A) ṁ = C_d A P_0 √(γ/(R T_0)) (2/(γ+1))^((γ+1)/(2(γ‑1))) B) ṁ = C_d A √(2 ρ ΔP) C) ṁ = C_d A P_0/(√(R T_0))
Practice Exam
B) Vessel pressure and atmospheric pressure C) Vapor pressure and critical pressure D) Vessel pressure and liquid hydrostatic head Answer: B Explanation: The net pressure forcing the liquid out is the excess of vessel pressure over ambient (atmospheric) pressure. Question 10. A liquid stored at 120 °C with a normal boiling point of 80 °C is released to the atmosphere. Which phenomenon occurs? A) Subcooled liquid jet B) Flashing, with a portion instantly vaporizing C) Condensation of ambient vapor onto the jet D) No phase change because the pressure is high enough Answer: B Explanation: Since the storage temperature exceeds the boiling point at atmospheric pressure, the liquid flashes to vapor on release. Question 11. The flashing fraction (f) for a liquid release is calculated using which of the following relationships? A) f = (P_0 – P_atm)/(P_0) B) f = ( h_v – h_l )/( h_g – h_l ) C) f = ( T_0 – T_b )/( T_0 ) D) f = C_d · A · √(2 g h) / ṁ_total Answer: B Explanation: Flashing fraction is the ratio of enthalpy difference between the saturated vapor and liquid to the total enthalpy change from the initial state to saturated vapor.
Practice Exam
Question 12. In the Homogeneous Equilibrium Model (HEM) for two‑phase flow, which assumption is made? A) Liquid and vapor travel at different velocities (slip) B) Phases are not in thermodynamic equilibrium C) Both phases have the same velocity and are in equilibrium D) Only vapor phase contributes to momentum Answer: C Explanation: HEM assumes no slip; liquid and vapor share the same velocity and are thermodynamically equilibrated. Question 13. The quality (x) of a two‑phase mixture is defined as: A) Mass of liquid / total mass B) Volume of vapor / total volume C) Mass of vapor / total mass D) Ratio of specific heats (γ) of vapor to liquid Answer: C Explanation: Quality (x) = m_vapor / (m_vapor + m_liquid), representing the vapor mass fraction. Question 14. Which of the following best describes slip in two‑phase flow? A) The difference in temperature between phases B) The relative velocity between liquid and vapor phases C) The pressure drop due to friction in each phase D) The change in composition due to mixing Answer: B Explanation: Slip refers to the velocity difference between vapor and liquid phases.
Practice Exam
Explanation: Vessel wall thickness is relevant for structural integrity, not for calculating release rates. Question 18. For a compressible gas flowing through a long pipe before discharge, the major pressure loss is calculated using: A) Bernoulli’s equation without friction term B) Darcy‑Weisbach equation with friction factor f C) Torricelli’s law D) Ideal gas law only Answer: B Explanation: The Darcy‑Weisbach equation accounts for frictional losses in pipe flow of gases. Question 19. The uncertainty introduced by the discharge coefficient (C_d) is mainly due to: A) Variations in ambient temperature B) Geometry of the orifice and flow regime C) Changes in molecular weight of the gas D) Errors in pressure transducer calibration Answer: B Explanation: C_d depends on the shape of the opening and whether the flow is laminar, turbulent, choked, etc. Question 20. In a worst‑case release scenario defined by many regulations, which parameter is typically maximized? A) Release duration B) Ambient humidity C) Downwind wind speed
Practice Exam
D) Elevation of the source above ground Answer: A Explanation: Worst‑case scenarios often assume the longest possible release duration to maximize emitted mass. Question 21. Which of the following statements about choked flow is correct? A) Mass flow rate continues to increase as downstream pressure drops below critical pressure. B) Flow becomes sonic at the throat, and mass flow rate reaches a maximum independent of downstream pressure. C) Choked flow only occurs for liquids. D) The critical pressure ratio is always 0.5 for any gas. Answer: B Explanation: In choked conditions, the flow reaches Mach 1 at the restriction and cannot increase further despite lower downstream pressure. Question 22. The speed of sound in an ideal gas is given by: A) a = √(γ R T) B) a = √(R T/γ) C) a = γ R T D) a = R / (γ T) Answer: A Explanation: The sonic velocity a = √(γ R T) where γ is specific heat ratio, R specific gas constant, T absolute temperature. Question 23. For a subsonic (non‑choked) gas release, which equation best estimates the mass flow rate? A) ṁ = C_d A P_0 √(2γ/(R T_0)(P_a/P_0)^{2/γ} – (P_a/P_0)^{(γ+1)/γ})
Practice Exam
Question 26. The term “static head” in liquid release calculations refers to: A) The pressure due to the liquid column height above the orifice. B) The pressure generated by pump suction. C) The dynamic pressure from fluid velocity. D) The atmospheric pressure acting on the liquid surface. Answer: A Explanation: Static head is the hydrostatic pressure from the liquid height, driving the flow through an opening. Question 27. When a liquid is released from a pressurized tank and the liquid level drops, the driving pressure: A) Remains constant because pressure is dictated by the gas phase. B) Increases as the liquid level falls. C) Decreases proportionally to the reduction in liquid head. D) Becomes zero once the tank is empty. Answer: C Explanation: As the liquid level drops, the hydrostatic head reduces, lowering the pressure driving the flow. Question 28. The term “flash point” of a liquid is defined as: A) The temperature at which the liquid boils at atmospheric pressure. B) The lowest temperature at which the liquid can form an ignitable mixture with air. C) The temperature at which the liquid’s viscosity reaches a minimum. D) The temperature at which the liquid solidifies. Answer: B
Practice Exam
Explanation: Flash point is the minimum temperature at which sufficient vapor is produced to ignite. Question 29. In two‑phase flow modeling, the “critical flow” condition is reached when: A) The vapor phase reaches Mach 1 at the orifice. B) The liquid phase reaches Mach 1. C) Both phases reach Mach 0.5. D) The mixture density equals the liquid density. Answer: A Explanation: Critical (choked) flow for two‑phase mixtures occurs when the vapor (or gas) phase velocity reaches the local speed of sound. Question 30. Which of the following best describes the effect of pipe length on the mass flow rate of a gas discharge? A) Longer pipe always increases mass flow rate. B) Longer pipe reduces mass flow rate due to frictional pressure drop. C) Pipe length has no effect if the flow is choked. D) Pipe length only affects liquid, not gas flow. Answer: B Explanation: Frictional losses increase with pipe length, reducing the available pressure drop and thus the mass flow rate. Question 31. For a gas with γ = 1.3, what is the approximate critical pressure ratio (P_c/P_0)? A) 0. B) 0. C) 0.
Practice Exam
B) Maximum possible inventory, pressure, and temperature. C) Average operating conditions. D) Zero wind speed and high humidity. Answer: B Explanation: Worst‑case analyses use the most hazardous combination of inventory, pressure, and temperature to bound potential impacts. Question 35. Which thermodynamic property is most critical for calculating the flashing fraction of a liquid? A) Specific heat capacity at constant pressure (Cp) B) Vapor pressure curve C) Surface tension D) Viscosity Answer: B Explanation: The vapor pressure curve determines the saturation conditions and thus the amount of liquid that flashes to vapor. Question 36. A vessel containing a saturated liquid at 150 kPa and 350 K ruptures to atmospheric pressure (101 kPa). Which flow regime is expected at the orifice? A) Subsonic liquid jet only B) Choked vapor flow with flashing C) Non‑choked gas flow D) No flow because pressure is below saturation Answer: B Explanation: The liquid is above its boiling point at atmospheric pressure, causing flashing; the vapor phase may become choked.
Practice Exam
Question 37. Which of the following statements about the “specific heat ratio” (γ) is true? A) γ = Cp/Cv and is always greater than 1 for gases. B) γ = Cv/Cp and is less than 1 for gases. C) γ is equal to the gas constant R. D) γ does not affect choked flow calculations. Answer: A Explanation: γ is the ratio of specific heats at constant pressure and volume; for gases it is > 1 and directly influences choked flow. Question 38. In a transient release, the total released mass is obtained by: A) Multiplying the initial mass flow rate by the release duration. B) Integrating the time‑varying mass flow rate over the release period. C) Using the steady‑state mass flow rate only. D) Assuming constant pressure throughout the release. Answer: B Explanation: Transient releases have variable flow rates; total mass requires time integration of ṁ(t). Question 39. Which of the following is NOT a typical assumption in the Homogeneous Equilibrium Model? A) No slip between phases. B) Instantaneous thermodynamic equilibrium. C) Separate temperature fields for each phase. D) Single‑phase density used for momentum calculations. Answer: C
Practice Exam
D) Vapor generated by a downstream heater. Answer: B Explanation: Flash vapor is the portion of liquid that instantly vaporizes due to a rapid pressure drop. Question 43. Which equation best predicts the mass flow rate of a liquid through a short pipe with friction factor f? A) ṁ = C_d A √(2 g h – f L v²/2D) B) ṁ = C_d A √(2 ΔP/ρ – f L v²/2D) C) ṁ = C_d A √(2 ΔP/ρ) · (1 – f L/D) D) ṁ = C_d A √(2 g h) · (1 – f L/D) Answer: B Explanation: The Bernoulli equation with Darcy‑Weisbach friction term gives ΔP – f L v²/2D as the effective pressure drop. Question 44. For a gas release where the downstream pressure is higher than the critical pressure ratio, the flow will be: A) Choked, with Mach = 1 at the throat. B) Subsonic, with Mach < 1 throughout. C) Supersonic, with Mach > 1 downstream. D) Stagnant, with zero mass flow. Answer: B Explanation: If downstream pressure is above the critical ratio, the flow remains subsonic (non‑choked). Question 45. Which of the following best describes the effect of ambient temperature on the mass flow rate of a gas release?
Practice Exam
A) Higher ambient temperature always increases mass flow rate. B) Higher ambient temperature reduces gas density, potentially increasing volumetric flow but decreasing mass flow. C) Ambient temperature has no effect because the release is isentropic. D) Ambient temperature only affects liquid releases. Answer: B Explanation: Increased temperature lowers density; for a given pressure differential, volumetric flow may rise, but mass flow (ρ · v) can decrease. Question 46. In a vessel blowdown, the pressure drop over time can be approximated by: A) An exponential decay if the flow is choked. B) A linear decrease regardless of flow regime. C) A logarithmic function of time. D) A sinusoidal variation due to acoustic oscillations. Answer: A Explanation: Choked blowdown leads to an exponential pressure decay as mass flow rate is proportional to pressure. Question 47. The term “static pressure” in the context of a pressurized liquid release refers to: A) The pressure due to fluid velocity. B) The pressure exerted by the liquid column at the orifice depth. C) The atmospheric pressure acting on the liquid surface. D) The pressure drop caused by pipe friction. Answer: B Explanation: Static pressure is the hydrostatic pressure from the liquid height above the opening.
Practice Exam
Answer: B Explanation: Release duration is the interval over which the source actively emits material. Question 51. Which fluid property is essential for calculating the speed of sound in a vapor? A) Viscosity B) Specific heat ratio (γ) and temperature C) Surface tension D) Vapor pressure Answer: B Explanation: Speed of sound a = √(γ R T) depends on γ and temperature (via the gas constant R). Question 52. The “critical flow coefficient” (C_c) differs from the discharge coefficient (C_d) in that C_c: A) Is used only for liquid flow. B) Accounts for choked conditions and is typically lower than C_d. C) Is always equal to 1.0 for gases. D) Represents the ratio of actual to ideal mass flow for subsonic flow. Answer: B Explanation: C_c corrects for deviations in choked flow; it is generally less than the nominal C_d. Question 53. Which of the following best describes the impact of a high molecular weight gas on choked flow mass rate, assuming all other conditions equal? A) Increases mass flow because of higher density. B) Decreases mass flow because of lower speed of sound. C) Has no effect; only temperature matters.
Practice Exam
D) Causes the flow to become subsonic. Answer: B Explanation: Higher molecular weight reduces the specific gas constant R, lowering the speed of sound and thus the choked mass flow rate. Question 54. During a vapor release, the “expansion factor” (often denoted as Y) is used to account for: A) Temperature rise due to compression. B) Deviation from ideal gas behavior during expansion. C) The increase in kinetic energy of the jet. D) The effect of pipe roughness on flow. Answer: B Explanation: The expansion factor corrects mass flow for real‑gas effects during isentropic expansion. Question 55. In a two‑phase HEM calculation, the mixture density (ρ_m) is obtained by: A) ρ_m = x ρ_v + (1 – x) ρ_l B) ρ_m = (ρ_v · ρ_l)/(x ρ_l + (1 – x) ρ_v) C) ρ_m = √(ρ_v · ρ_l) D) ρ_m = ρ_v / ρ_l Answer: A Explanation: Mixture density is the mass‑weighted average of vapor and liquid densities using quality x. Question 56. Which of the following is a primary reason for using a “worst‑case” release scenario in regulatory compliance? A) To minimize the cost of safety equipment.
