Fundamentals of Engineering Exam (FE) Thermal and Fluid Systems Syllabus

Thermal and Fluid Systems syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Thermal and Fluid Systems in Fundamentals of Engineering Exam (FE), not a summary of it.

1. 1

   Fluid Mechanics

   4 topics

   • Fluid Properties and Statics
     • Density, viscosity, surface tension
     • Hydrostatic pressure and manometers
     • Forces on submerged surfaces; buoyancy
   • Fluid Dynamics
     • Continuity equation
     • Bernoulli and energy equations
     • Momentum equation
   • Pipe Flow and Losses
     • Reynolds number and flow regimes
     • Major losses (Darcy-Weisbach, Moody chart)
     • Minor losses and pump sizing
   • Flow Measurement and Dimensional Analysis
     • Orifices, venturi and pitot tubes
     • Buckingham Pi theorem and similitude
2. 2

   Thermodynamics

   5 topics

   • Properties of Pure Substances
     • Phase diagrams and steam tables
     • Ideal gas law and real gas behavior
   • First Law of Thermodynamics
     • Closed systems: work and heat
     • Open systems and control volumes
     • Energy balances on devices
   • Second Law and Entropy
     • Entropy and reversibility
     • Carnot cycle and efficiency
   • Power and Refrigeration Cycles
     • Rankine cycle
     • Brayton cycle
     • Vapor-compression refrigeration
   • Mixtures and Combustion
     • Psychrometrics and gas mixtures
     • Combustion stoichiometry and heating values
3. 3

   Heat Transfer

   3 topics

   • Conduction
     • Fourier's law and thermal resistance
     • Composite walls and cylinders
     • Fins and extended surfaces
   • Convection
     • Newton's law of cooling
     • Free and forced convection correlations
   • Radiation and Heat Exchangers
     • Blackbody and gray-body radiation
     • LMTD and effectiveness-NTU methods

Thermal and Fluid Systems flashcards for Fundamentals of Engineering Exam (FE)

20 of 57 cards from the Thermal and Fluid Systems deck — real questions with worked answers.

1. What is the definition of a fluid's dynamic (absolute) viscosity $\mu$, and how does it relate shear stress to velocity gradient in a Newtonian fluid?

   Dynamic viscosity $\mu$ is the proportionality constant between shear stress and rate of shear strain. For a Newtonian fluid: $$\tau = \mu \frac{du}{dy}$$ where $\tau$ is shear stress and $\frac{du}{dy}$ is the velocity gradient normal to the flow. SI units are $\text{Pa·s}$.

2. How is kinematic viscosity $\nu$ defined in terms of dynamic viscosity $\mu$ and density $\rho$?

   $$\nu = \frac{\mu}{\rho}$$ with SI units of $\text{m}^{2}/\text{s}$.

3. State the hydrostatic pressure equation for the pressure variation with depth $h$ in a static incompressible fluid.

   $$p = p_{0} + \rho g h$$ The gauge pressure increase with depth is $\Delta p = \rho g h = \gamma h$, where $\gamma = \rho g$ is the specific weight.

4. What is the magnitude of the hydrostatic force on a submerged plane surface, and where does it act?

   Resultant force: $$F_{R} = p_{c} A = \rho g h_{c} A$$ where $h_{c}$ is the depth of the centroid. It acts at the center of pressure, located below the centroid at $$y_{cp} = y_{c} + \frac{I_{xc}}{y_{c} A}$$

5. State Archimedes' principle and the formula for buoyant force.

   A body wholly or partially submerged experiences an upward buoyant force equal to the weight of the displaced fluid: $$F_{B} = \rho_{fluid} \, g \, V_{displaced}$$

6. How is specific gravity (relative density) defined?

   Specific gravity is the ratio of a substance's density to that of water at $4^{\circ}\text{C}$: $$SG = \frac{\rho}{\rho_{H_2O}}, \qquad \rho_{H_2O} \approx 1000 \ \text{kg/m}^{3}$$

7. What does the Reynolds number represent physically, and how is it defined for pipe flow?

   The Reynolds number is the ratio of inertial to viscous forces: $$Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu}$$ For internal pipe flow, $Re < 2300$ is laminar, $Re > 4000$ is turbulent, with a transition region in between.

8. State the continuity equation for steady incompressible flow between two cross-sections of a stream tube.

   Mass is conserved, so the volumetric flow rate is constant: $$A_{1} V_{1} = A_{2} V_{2} = Q$$ where $A$ is cross-sectional area and $V$ is average velocity.

9. Write Bernoulli's equation for steady, incompressible, inviscid flow along a streamline.

   $$\frac{p_{1}}{\rho g} + \frac{V_{1}^{2}}{2g} + z_{1} = \frac{p_{2}}{\rho g} + \frac{V_{2}^{2}}{2g} + z_{2}$$ Each term is a head (pressure, velocity, elevation) in units of length; total head is constant.

10. What assumptions are required for the standard Bernoulli equation to be valid?

    Steady flow, incompressible fluid, frictionless (inviscid, no losses), flow along a single streamline, and no shaft work or heat transfer between the two points.

11. State the energy equation for real pipe flow including pump head, turbine head, and friction losses.

    $$\frac{p_{1}}{\gamma} + \frac{V_{1}^{2}}{2g} + z_{1} + h_{p} = \frac{p_{2}}{\gamma} + \frac{V_{2}^{2}}{2g} + z_{2} + h_{t} + h_{L}$$ where $h_{p}$ is pump head added, $h_{t}$ is turbine head extracted, and $h_{L}$ is total head loss.

12. Write the Darcy-Weisbach equation for major head loss in pipe flow.

    $$h_{L} = f \, \frac{L}{D} \, \frac{V^{2}}{2g}$$ where $f$ is the Darcy friction factor, $L$ is pipe length, $D$ is diameter, and $V$ is average velocity.

13. What is the friction factor for fully developed laminar pipe flow as a function of Reynolds number?

    $$f = \frac{64}{Re}$$ valid for laminar flow ($Re < 2300$).

14. How are minor (local) head losses computed using a loss coefficient $K$?

    $$h_{L,minor} = K \frac{V^{2}}{2g}$$ where $K$ is the minor loss coefficient for the fitting (valve, elbow, entrance, expansion, etc.).

15. What is the Hagen-Poiseuille relationship for pressure drop in fully developed laminar pipe flow?

    $$\Delta p = \frac{128 \, \mu L Q}{\pi D^{4}}$$ Pressure drop is proportional to flow rate and inversely proportional to the fourth power of diameter.

16. Define the hydraulic diameter $D_{h}$ used for non-circular conduits.

    $$D_{h} = \frac{4 A}{P}$$ where $A$ is the cross-sectional flow area and $P$ is the wetted perimeter.

17. What does the Moody chart relate, and on what two parameters does the turbulent friction factor depend?

    The Moody chart gives the Darcy friction factor $f$ as a function of the Reynolds number $Re$ and the relative roughness $\frac{\varepsilon}{D}$ (roughness height over diameter).

18. Write the ideal velocity from a Pitot tube (stagnation) measurement.

    From the difference between stagnation and static pressure: $$V = \sqrt{\frac{2(p_{0} - p_{s})}{\rho}} = \sqrt{2 g \, \Delta h}$$

19. Give the venturi/orifice meter flow rate equation including the discharge coefficient.

    $$Q = C_{d} A_{2} \sqrt{\frac{2(p_{1}-p_{2})}{\rho \left(1 - (A_{2}/A_{1})^{2}\right)}}$$ where $C_{d}$ is the discharge coefficient accounting for real losses.

20. State the Buckingham Pi theorem.

    If a physical problem involves $n$ variables described by $k$ fundamental dimensions, the relationship can be reduced to $n - k$ independent dimensionless $\Pi$ groups.

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