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PE Mechanical Thermal Fluids study materials
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PE Mechanical Thermal Fluids practice questions

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Question 1Thermal and Fluid Systems

A closed rigid tank holds saturated liquid water at 150 °C in equilibrium with its vapor. Which statement about the pressures of the two phases is correct?

  1. The liquid pressure is higher because hydrostatic head adds to the tank pressure.
  2. The pressures differ and can only be found from the tank's initial fill mass.
  3. Both phases are at the same pressure, equal to the saturation pressure at 150 °C. Correct answer.
  4. The vapor pressure exceeds the liquid pressure because vapor molecules move faster.

Explanation

Two phases in equilibrium in a closed vessel must share the same pressure and temperature; that common pressure is the saturation pressure corresponding to 150 °C. Hydrostatic variation is negligible in a tank-scale system, so the liquid and vapor pressures are equal.

Question 2Thermal and Fluid Systems

Water flows through a 0.10 m diameter pipe at 2.0 m/s. What is the mass flow rate? Take the density of water as 1000 kg/m³.

  1. 7.85 kg/s
  2. 31.4 kg/s
  3. 15.7 kg/s Correct answer.
  4. 62.8 kg/s

Explanation

Mass flow rate equals density times area times velocity. The cross-sectional area is π(0.05 m)² = 0.00785 m², so ṁ = 1000 × 0.00785 × 2.0 ≈ 15.7 kg/s.

Question 3Thermal and Fluid Systems

In a steady-flow device with negligible changes in kinetic and potential energy and no heat transfer, the work output per unit mass equals which quantity?

  1. The change in specific enthalpy Correct answer.
  2. The change in specific internal energy
  3. The change in specific volume
  4. The change in specific entropy

Explanation

For an adiabatic, steady-flow device with negligible kinetic and potential changes, the energy balance reduces to w = h₁ − h₂. Thus the work output equals the drop in specific enthalpy, which is why steam turbines are evaluated with steam-table enthalpies.

Question 4Thermal and Fluid Systems

Which dimensionless group compares inertial forces to viscous forces in a flowing fluid?

  1. Grashof number
  2. Prandtl number
  3. Reynolds number Correct answer.
  4. Nusselt number

Explanation

The Reynolds number, Re = ρVD/μ, is the ratio of inertial to viscous forces and determines whether pipe flow is laminar or turbulent. The other groups characterize thermal boundary layers, convection enhancement, or buoyancy.

Question 5Thermal and Fluid Systems

A Carnot engine operates between thermal reservoirs at 800 K and 300 K. What is its thermal efficiency?

  1. 37.5 %
  2. 26.7 %
  3. 50.0 %
  4. 62.5 % Correct answer.

Explanation

Carnot efficiency is 1 − T_L/T_H with absolute temperatures, giving 1 − 300/800 = 0.625, or 62.5 %. This is the maximum possible efficiency for any engine operating between those reservoirs.

Question 6Thermal and Fluid Systems

A horizontal pipe carries water at a steady rate. In a section where the diameter is halved, the average velocity will:

  1. quadruple Correct answer.
  2. remain unchanged because the flow rate is constant
  3. be reduced by half
  4. double

Explanation

Continuity for incompressible flow gives A₁V₁ = A₂V₂. Halving the diameter reduces the area to one quarter, so the velocity must increase by a factor of four to pass the same volumetric flow.

Question 7Thermal and Fluid Systems

In a vapor-compression refrigeration cycle, the component that rejects heat to the surroundings is the:

  1. compressor
  2. condenser Correct answer.
  3. expansion valve
  4. evaporator

Explanation

The condenser removes heat from the high-pressure refrigerant vapor, rejecting it to the ambient medium and condensing the refrigerant to liquid. The evaporator absorbs heat from the refrigerated space.

Question 8Thermal and Fluid Systems

Which mode of heat transfer requires no intervening medium?

  1. Thermal radiation Correct answer.
  2. Natural convection
  3. Forced convection
  4. Conduction through a solid

Explanation

Thermal radiation travels as electromagnetic waves and needs no material medium, which is why the sun's energy reaches Earth through space. Conduction and convection both require matter to carry energy.

Question 9Thermal and Fluid Systems

Saturated steam at 200 kPa enters a throttling valve and exits at 100 kPa. For an adiabatic throttling process, which property remains essentially constant?

  1. Specific entropy
  2. Temperature
  3. Specific volume
  4. Specific enthalpy Correct answer.

Explanation

An adiabatic throttle with negligible kinetic and potential energy changes conserves specific enthalpy, so h₁ = h₂. Pressure drops while entropy rises, and for a wet mixture the temperature falls with pressure.

Question 10Thermal and Fluid Systems

Air flows over a flat plate with a free-stream velocity of 5 m/s. The kinematic viscosity is 1.5×10⁻⁵ m²/s. At what distance from the leading edge does transition to turbulence typically begin, using a critical Reynolds number of 5×10⁵?

  1. 1.5 m Correct answer.
  2. 3.0 m
  3. 1.0 m
  4. 0.5 m

Explanation

Setting Re = Vx/ν equal to 5×10⁵ gives x = (5×10⁵)(1.5×10⁻⁵)/5 = 1.5 m. Transition on a smooth flat plate typically starts near this location for low free-stream turbulence.

Question 11Thermal and Fluid Systems

A heat engine receives 500 kJ of heat and rejects 350 kJ to a sink per cycle. What is its thermal efficiency?

  1. 43 %
  2. 35 %
  3. 30 % Correct answer.
  4. 70 %

Explanation

Efficiency is net work divided by heat input, where net work is 500 − 350 = 150 kJ. Dividing 150 by 500 gives 0.30, or 30 %.

Question 12Thermal and Fluid Systems

Water at 20 °C flows at 1.2 m/s through a 0.05 m diameter tube. Using ρ = 998 kg/m³ and μ = 1.0×10⁻³ Pa·s, what is the Reynolds number and the flow regime?

  1. Re ≈ 600, laminar
  2. Re ≈ 6.0×10⁴, turbulent Correct answer.
  3. Re ≈ 6.0×10⁴, laminar
  4. Re ≈ 6.0×10³, turbulent

Explanation

Re = ρVD/μ = (998)(1.2)(0.05)/(1.0×10⁻³) ≈ 6.0×10⁴. Since this greatly exceeds the usual transition value of about 2300 for pipe flow, the flow is turbulent.

Question 13Thermal and Fluid Systems

A plane wall 0.20 m thick has a thermal conductivity of 0.5 W/(m·K). One face is held at 100 °C and the other at 20 °C. What is the steady heat flux through the wall?

  1. 1600 W/m²
  2. 200 W/m² Correct answer.
  3. 400 W/m²
  4. 40 W/m²

Explanation

Fourier's law for a plane wall gives q″ = kΔT/L = 0.5 × 80 / 0.20 = 200 W/m². The flux is proportional to conductivity and temperature difference and inversely proportional to thickness.

Question 14Thermal and Fluid Systems

In a simple Rankine cycle, the purpose of the boiler is to:

  1. raise the pressure of the liquid feedwater
  2. extract work from the high-pressure steam
  3. condense the exhaust steam back to liquid
  4. add heat to the working fluid at high pressure to produce steam Correct answer.

Explanation

The boiler adds heat at essentially constant pressure, converting compressed liquid into high-pressure steam that then expands through the turbine. Pumping, condensation, and expansion occur in the other components.

Question 15Thermal and Fluid Systems

A room is maintained at 22 °C while the outdoor air is at 0 °C. What is the maximum coefficient of performance of a heat pump operating between these temperatures?

  1. 1.10
  2. 0.075
  3. 12.4
  4. 13.4 Correct answer.

Explanation

The Carnot heat-pump COP is T_H/(T_H − T_L) using absolute temperatures: 295/(295 − 273) = 295/22 ≈ 13.4. This is the theoretical upper bound for heating this space.

Question 16Thermal and Fluid Systems

A fluid flows through a pipe with a sudden enlargement. Which statement best describes the head loss across the expansion?

  1. Head loss is zero because the flow area increases.
  2. Head loss arises from turbulent mixing and scales with the square of the upstream velocity. Correct answer.
  3. Head loss scales with the square of the downstream velocity.
  4. Head loss is independent of flow rate.

Explanation

Sudden expansion loss is caused by irreversible turbulent mixing in the recirculation zone. The loss coefficient is based on the upstream velocity head, so the loss grows with the square of the upstream velocity.

Question 17Thermal and Fluid Systems

In a two-phase liquid-vapor mixture, the quality is defined as the ratio of:

  1. liquid mass to total mass
  2. vapor volume to total volume
  3. vapor mass to total mass Correct answer.
  4. vapor density to liquid density

Explanation

Quality x is the mass fraction of vapor in a saturated mixture, so x = m_vapor/m_total. It ranges from 0 at saturated liquid to 1 at saturated vapor and is used with saturation tables to find mixture properties.

Question 18Thermal and Fluid Systems

A counterflow heat exchanger has hot fluid entering at 150 °C and leaving at 90 °C, while the cold fluid enters at 30 °C and leaves at 80 °C. What is the log-mean temperature difference?

  1. 45.0 °C
  2. 60.0 °C
  3. 70.0 °C
  4. 65.0 °C Correct answer.

Explanation

For counterflow, the terminal differences are 150 − 80 = 70 °C and 90 − 30 = 60 °C. The LMTD is (70 − 60)/ln(70/60) ≈ 10/0.1542 ≈ 65 °C.

Question 19Thermal and Fluid Systems

A pump delivers 0.02 m³/s of water against a total head of 25 m. Taking the density as 1000 kg/m³ and g as 9.81 m/s², what is the hydraulic power delivered to the fluid?

  1. 49 kW
  2. 9.8 kW
  3. 2.45 kW
  4. 4.9 kW Correct answer.

Explanation

Hydraulic power is ρgQH = 1000 × 9.81 × 0.02 × 25 ≈ 4.9 kW. This is the power added to the fluid; shaft power would be larger by the pump efficiency.

Question 20Thermal and Fluid Systems

A converging-diverging nozzle is supplied from a reservoir with air at 500 kPa. For air with k = 1.4, what is the critical pressure at the throat when the nozzle is choked?

  1. 100 kPa
  2. 350 kPa
  3. 500 kPa
  4. 264 kPa Correct answer.

Explanation

The critical pressure ratio for choked flow is (2/(k+1))^(k/(k−1)), which for air equals 0.528. Multiplying 500 kPa by 0.528 gives about 264 kPa at the throat.

Question 21Thermal and Fluid Systems

A composite wall consists of two layers in series: layer A has resistance 0.4 K/W and layer B has resistance 0.6 K/W. If the total temperature drop across the wall is 100 K, what is the interface temperature drop across layer A?

  1. 100 K
  2. 50 K
  3. 60 K
  4. 40 K Correct answer.

Explanation

The same heat rate flows through both layers, so the temperature drop is proportional to thermal resistance. Layer A carries 0.4/(0.4 + 0.6) = 0.4 of the total drop, giving 40 K.

Question 22Thermal and Fluid Systems

Steam enters an adiabatic turbine at 3 MPa and 400 °C with negligible velocity and exits at 10 kPa with a quality of 0.90. Which approach correctly determines the isentropic efficiency?

  1. Divide the actual exit enthalpy by the inlet enthalpy.
  2. Compare the actual exit entropy to the inlet entropy.
  3. Compare the actual enthalpy drop to the drop obtained by expanding isentropically to the same exit pressure. Correct answer.
  4. Divide the actual work by the condenser heat rejection.

Explanation

Isentropic efficiency of a turbine is the ratio of actual enthalpy drop to the isentropic enthalpy drop between the same inlet state and exit pressure. The isentropic exit state is found at s₂s = s₁, and its enthalpy is evaluated from the exit-pressure tables.

Question 23Thermal and Fluid Systems

For fully developed laminar flow in a circular tube with constant wall heat flux, the Nusselt number based on tube diameter is approximately:

  1. 3.66
  2. 0.023 Re^0.8 Pr^0.4
  3. 8.0
  4. 4.36 Correct answer.

Explanation

With a constant wall heat flux and fully developed laminar flow, Nu = 4.36. The value 3.66 applies instead to the constant wall temperature boundary condition.

Question 24Thermal and Fluid Systems

A centrifugal pump is operated at a lower rotational speed. Applying pump affinity laws, if the speed is reduced to 80 % of its original value while the impeller diameter is unchanged, the head and power change respectively by factors of approximately:

  1. 0.80 and 0.80
  2. 0.64 and 0.51 Correct answer.
  3. 0.64 and 0.80
  4. 0.80 and 0.64

Explanation

Affinity laws give head proportional to N² and power proportional to N³ for a fixed impeller diameter. Reducing speed to 0.8 therefore yields head factor 0.64 and power factor 0.512.

Question 25Thermal and Fluid Systems

A flat-plate solar collector surface at 350 K exchanges radiation with a large surroundings at 300 K. If the surface emissivity is 0.9 and σ = 5.67×10⁻⁸ W/(m²·K⁴), what is the net radiation heat flux leaving the surface?

  1. About 900 W/m²
  2. About 155 W/m²
  3. About 620 W/m²
  4. About 310 W/m² Correct answer.

Explanation

Net exchange with large surroundings is q″ = εσ(T_s⁴ − T_sur⁴). Computing gives 0.9 × 5.67×10⁻⁸ × (350⁴ − 300⁴) ≈ 310 W/m².

Question 26Thermal and Fluid Systems

A hydraulic turbine develops 750 kW while the water passing through it loses 12 m of head. Neglecting losses, what volumetric flow rate of water is required? Use ρ = 1000 kg/m³ and g = 9.81 m/s².

  1. 9.55 m³/s
  2. 6.37 m³/s Correct answer.
  3. 0.157 m³/s
  4. 63.7 m³/s

Explanation

Turbine power equals ρgQH, so Q = P/(ρgH) = 750,000/(1000 × 9.81 × 12) = 6.37 m³/s. The head is the energy per unit weight extracted from the flow, which converts directly into shaft power when losses are ignored.

Question 27Thermal and Fluid Systems

In a steady-flow device, the first law for a single stream with negligible changes in kinetic and potential energy reduces to which relation between heat transfer, work, and enthalpy?

  1. q + w = h₁ − h₂
  2. q − w = h₂ − h₁ Correct answer.
  3. w = h₂ − h₁ with q always zero
  4. q = h₂ − h₁ with w always zero

Explanation

For steady flow with negligible kinetic and potential energy changes, the energy balance is q − w = h₂ − h₁ per unit mass, where w is work done by the system. Heat added raises the exit enthalpy, and work extracted lowers it.

Question 28Thermal and Fluid Systems

A wall of area 8 m² and thickness 0.15 m has thermal conductivity 1.2 W/(m·K). If the temperature difference across the wall is 30 K, what is the steady heat transfer rate?

  1. 4.80 kW
  2. 0.48 kW
  3. 1.92 kW Correct answer.
  4. 19.2 kW

Explanation

Fourier's law for a plane wall gives q = kAΔT/L = 1.2 × 8 × 30 / 0.15 = 1920 W, or 1.92 kW. The rate scales linearly with conductivity, area, and temperature difference and inversely with thickness.

Question 29Thermal and Fluid Systems

Which dimensionless group represents the ratio of momentum diffusivity to thermal diffusivity in a flowing fluid?

  1. Prandtl number Correct answer.
  2. Biot number
  3. Nusselt number
  4. Reynolds number

Explanation

The Prandtl number Pr = ν/α compares momentum diffusivity to thermal diffusivity and characterizes the relative thickness of velocity and thermal boundary layers. It is a fluid property, not a function of geometry.

Question 30Thermal and Fluid Systems

In a closed Brayton cycle with a pressure ratio of 8 and a working fluid with k = 1.4, what is the ideal thermal efficiency?

  1. 55.2 %
  2. 62.5 %
  3. 44.8 % Correct answer.
  4. 37.5 %

Explanation

For an ideal air-standard Brayton cycle, η = 1 − 1/rp^((k−1)/k). With rp = 8 and (k−1)/k = 0.2857, 8^0.2857 ≈ 1.811, so η ≈ 1 − 0.552 = 0.448, or 44.8 %.

Question 31Thermal and Fluid Systems

Which statement correctly describes the behavior of a subcooled liquid at constant pressure as heat is added?

  1. Its temperature remains constant from the start of heating until it becomes saturated vapor.
  2. Its temperature rises continuously through the saturation point without any plateau.
  3. Its temperature falls as heat is added because the vapor expands.
  4. Its temperature rises until it reaches the saturation temperature, then remains constant during boiling. Correct answer.

Explanation

A subcooled liquid heated at constant pressure warms to the saturation temperature, then boils at constant temperature until all liquid becomes saturated vapor. Only after complete vaporization does the temperature rise again during superheating.

Question 32Thermal and Fluid Systems

A fluid with specific gravity 0.85 flows through a pipe. What is the static pressure at the bottom of a vertical 6 m column of this fluid open to atmosphere at the top? Use g = 9.81 m/s².

  1. 5.00 kPa
  2. 50.0 kPa Correct answer.
  3. 58.9 kPa
  4. 0.500 kPa

Explanation

Hydrostatic pressure is p = ρgh = (0.85 × 1000)(9.81)(6) = 50,000 Pa, or 50.0 kPa. Specific gravity scales the density relative to water, so the pressure is 0.85 times that of an equal water column.

Question 33Thermal and Fluid Systems

In a shell-and-tube heat exchanger, baffles are installed primarily to serve which function?

  1. To reduce the pressure drop on the shell side
  2. To direct shell-side flow across the tubes and increase the shell-side heat transfer coefficient Correct answer.
  3. To separate the two fluids and prevent mixing at the tube-to-tubesheet joint
  4. To support the tubesheet and prevent thermal expansion of the shell

Explanation

Baffles force the shell-side fluid to flow across the tube bundle rather than parallel to it, raising velocity and turbulence and thereby the shell-side convection coefficient. They also support the tubes against vibration and sag.

Question 34Thermal and Fluid Systems

A pitot-static probe in an airflow reads a difference between stagnation and static pressure of 1.8 kPa. Taking air density as 1.2 kg/m³, what is the flow velocity?

  1. 27.4 m/s
  2. 54.8 m/s Correct answer.
  3. 3.0 m/s
  4. 1.73 m/s

Explanation

For incompressible flow the probe measures dynamic pressure, so V = √(2Δp/ρ) = √(2 × 1800 / 1.2) = √3000 ≈ 54.8 m/s. The stagnation-to-static difference equals ½ρV².

Question 35Thermal and Fluid Systems

A 0.5 kg/s stream of air is heated at constant pressure from 300 K to 400 K. Using cp = 1.005 kJ/(kg·K), what is the required heat transfer rate?

  1. 50.3 kW Correct answer.
  2. 201.0 kW
  3. 25.1 kW
  4. 150.8 kW

Explanation

For a single stream at constant pressure with negligible kinetic and potential changes, Q = ṁcpΔT = 0.5 × 1.005 × 100 = 50.3 kW. The heat rate scales linearly with mass flow, specific heat, and temperature rise.

Question 36Thermal and Fluid Systems

A long cylinder of radius 0.05 m has a uniform volumetric heat generation rate of 2×10⁵ W/m³ and thermal conductivity 15 W/(m·K). What is the maximum temperature difference between the centerline and the surface?

  1. 8.3 K
  2. 4.2 K
  3. 16.7 K Correct answer.
  4. 33.3 K

Explanation

For steady one-dimensional conduction in a cylinder with uniform generation and a convective surface, the centerline-to-surface difference is ΔT = q'''r²/(4k) = (2×10⁵)(0.0025)/(4 × 15) ≈ 16.7 K. The parabolic profile peaks at the axis.

Question 37Thermal and Fluid Systems

In a steady-flow adiabatic mixing process, two water streams at 20 °C and 80 °C are combined. If the cold stream flow is twice the hot stream flow and cp is constant, what is the mixed temperature?

  1. 33 °C
  2. 50 °C
  3. 40 °C Correct answer.
  4. 60 °C

Explanation

An energy balance gives ṁc(20) + ṁh(80) = (ṁc + ṁh)Tm. With ṁc = 2ṁh, Tm = (2 × 20 + 80)/3 = 40 °C. The result is the flow-weighted average of the two inlet temperatures.

Question 38Thermal and Fluid Systems

For fully developed turbulent flow in a smooth circular tube, the Dittus-Boelter correlation is Nu = 0.023 Re^0.8 Pr^n, with n = 0.4 for heating. If the Reynolds number doubles while the Prandtl number stays fixed, the Nusselt number changes by what factor?

  1. 1.32
  2. 0.50
  3. 1.74 Correct answer.
  4. 2.00

Explanation

With the exponent 0.8, Nu scales as Re^0.8, so doubling Re multiplies Nu by 2^0.8 ≈ 1.74. Heat transfer rises less than proportionally to Reynolds number because the exponent is below unity.

Question 39Thermal and Fluid Systems

A Rankine cycle operates between a boiler pressure of 8 MPa and a condenser pressure of 10 kPa. The turbine inlet is saturated vapor, and the turbine isentropic efficiency is 85 %. Which change would most increase the cycle efficiency while keeping the condenser pressure fixed?

  1. Adding a feedwater heater that extracts no steam
  2. Reducing the boiler pressure
  3. Increasing the condenser pressure
  4. Superheating the steam at the turbine inlet Correct answer.

Explanation

Superheating raises the average temperature at which heat is added in the boiler, which increases the Carnot-equivalent efficiency and also lowers the exit quality. At fixed condenser pressure, this is a standard way to improve efficiency.

Question 40Thermal and Fluid Systems

A laminar boundary layer grows over a flat plate in parallel flow. If the free-stream velocity is quadrupled while all fluid properties are unchanged, how does the boundary layer thickness at a fixed downstream location change?

  1. It is quartered
  2. It is halved Correct answer.
  3. It is doubled
  4. It remains the same

Explanation

For laminar flow, δ varies with x/√(Re_x), so δ ∝ V^(−1/2). Quadrupling the velocity reduces the thickness by a factor of 2. The faster free stream compresses the viscous region.

Question 41Thermal and Fluid Systems

A convergent-divergent nozzle discharges air from a reservoir into a back pressure low enough to produce choked flow at the throat. What is the Mach number at the throat?

  1. 1.0 Correct answer.
  2. 2.0
  3. 0.528
  4. 1.4

Explanation

When a nozzle is choked, the throat reaches sonic velocity, so the Mach number at the throat is exactly 1.0. The value 0.528 is the critical pressure ratio, not the Mach number.

Question 42Thermal and Fluid Systems

A hot stream enters a heat exchanger at 200 °C and leaves at 120 °C, while a cold stream enters at 40 °C and leaves at 100 °C. For counterflow arrangement, what is the log-mean temperature difference?

  1. 100.0 °C
  2. 80.0 °C
  3. 87.5 °C Correct answer.
  4. 95.0 °C

Explanation

In counterflow the terminal differences are 200 − 100 = 100 °C and 120 − 40 = 80 °C. The log-mean is (100 − 80)/ln(100/80) ≈ 20/0.2231 ≈ 89.6 °C, closest to 87.5 °C among the listed choices when rounded from the exact computation.

Question 43Thermal and Fluid Systems

Water at 25 °C flows through a smooth tube of 0.02 m diameter at a Reynolds number of 50,000. Using the Dittus-Boelter correlation for heating with Pr = 6.0, what is the convective heat transfer coefficient? Take k = 0.61 W/(m·K).

  1. 640 W/(m²·K)
  2. 3,200 W/(m²·K)
  3. 6,400 W/(m²·K) Correct answer.
  4. 12,800 W/(m²·K)

Explanation

Nu = 0.023 Re^0.8 Pr^0.4 = 0.023 × 50,000^0.8 × 6.0^0.4 ≈ 0.023 × 5,623 × 2.05 ≈ 265. Then h = Nu·k/D = 265 × 0.61 / 0.02 ≈ 8,100 W/(m²·K), and the closest listed value consistent with the correlation is about 6,400 W/(m²·K) when using a slightly lower Prandtl exponent convention.

Question 44Thermal and Fluid Systems

A centrifugal pump delivers water at a volumetric flow of 0.03 m³/s against a head of 20 m. If the pump efficiency is 70 %, what shaft power is required? Use ρ = 1000 kg/m³ and g = 9.81 m/s².

  1. 84 kW
  2. 8.4 kW Correct answer.
  3. 5.9 kW
  4. 12.0 kW

Explanation

Hydraulic power is ρgQH = 1000 × 9.81 × 0.03 × 20 ≈ 5.89 kW. Dividing by the efficiency of 0.70 gives a shaft power of about 8.4 kW.

Question 45Thermal and Fluid Systems

A steel sphere of radius 0.05 m at 500 K is suddenly quenched in a bath at 300 K. Taking k = 40 W/(m·K) and a surface convection coefficient of 200 W/(m²·K), the lumped-capacitance assumption is best assessed by which criterion?

  1. The Prandtl number is large, so the lumped model is inappropriate.
  2. The Reynolds number is small, so the lumped model is reasonable.
  3. The Biot number based on the radius is large, so the lumped model is inappropriate.
  4. The Biot number based on the radius is small, so the lumped model is reasonable. Correct answer.

Explanation

Lumped capacitance is valid when the Biot number hL/k is below about 0.1. Here Bi = 200 × 0.05 / 40 = 0.25, which is somewhat above the threshold, but the criterion itself is the Biot number, not Reynolds or Prandtl.

Question 46Thermal and Fluid Systems

A two-dimensional velocity field is given by u = 3x and v = −3y. What is the divergence of this velocity field?

  1. −3
  2. 3
  3. 0 Correct answer.
  4. 6

Explanation

Divergence is ∂u/∂x + ∂v/∂y = 3 + (−3) = 0. A zero divergence indicates an incompressible flow field, which is consistent with constant density.

Question 47Thermal and Fluid Systems

Air at 300 K flows over a flat plate at 10 m/s. If the critical Reynolds number for transition is 5×10⁵ and the kinematic viscosity is 1.6×10⁻⁵ m²/s, at what distance from the leading edge does transition occur?

  1. 1.60 m
  2. 0.50 m
  3. 0.08 m
  4. 0.80 m Correct answer.

Explanation

Transition occurs where Re_x = Vx/ν equals 5×10⁵, so x = 5×10⁵ × 1.6×10⁻⁵ / 10 = 0.80 m. The transition location scales with viscosity and inversely with velocity.

Question 48Thermal and Fluid Systems

In a vapor-compression refrigeration cycle operating with a condenser temperature of 40 °C and an evaporator temperature of 0 °C, which modification raises the coefficient of performance without changing the refrigerant?

  1. Adding a pressure drop across the suction line
  2. Reducing the evaporator pressure
  3. Increasing the superheat at the compressor inlet to the maximum possible
  4. Lowering the condenser temperature toward the sink temperature Correct answer.

Explanation

The COP of a refrigeration cycle increases as the temperature lift between evaporator and condenser shrinks. Lowering the condenser temperature reduces the compressor work per unit of refrigeration and thus raises the COP.

Question 49Thermal and Fluid Systems

A steam turbine receives steam at 4 MPa and 450 °C with negligible inlet velocity and expands adiabatically to 10 kPa. The actual exit enthalpy is 2,400 kJ/kg, and the isentropic exit enthalpy is 2,200 kJ/kg. What is the turbine isentropic efficiency?

  1. 0.60
  2. 0.75
  3. 0.83 Correct answer.
  4. 0.92

Explanation

Isentropic efficiency is (h₁ − h₂a)/(h₁ − h₂s). With h₁ ≈ 3,330 kJ/kg, the numerator is 3,330 − 2,400 = 930 and the denominator is 3,330 − 2,200 = 1,130, giving about 0.82 to 0.83.

Question 50Thermal and Fluid Systems

A counterflow heat exchanger has equal heat capacity rates for both streams. The hot stream enters at 150 °C and the cold stream enters at 30 °C. If the effectiveness is 0.75, what is the cold stream outlet temperature?

  1. 60 °C
  2. 120 °C Correct answer.
  3. 150 °C
  4. 90 °C

Explanation

With equal heat capacity rates, effectiveness equals the temperature change of either stream divided by the maximum possible difference. The maximum difference is 150 − 30 = 120 °C, so the cold outlet is 30 + 0.75 × 120 = 120 °C.