A 13-section interactive reference guide covering the core NCEES PE Mechanical exam topics. Includes thermodynamics laws and steam tables, fluid mechanics with Bernoulli and Darcy-Weisbach, heat transfer with LMTD and NTU methods, machine element fatigue (Modified Goodman), dynamics and vibration, HVAC and refrigeration cycles, pressure vessel ASME code, turbomachinery affinity laws, controls instrumentation, and engineering economics.
All three PE Mechanical discipline areas are covered: Thermal & Fluid Systems (thermodynamics laws, steam tables, Rankine cycle, Bernoulli equation, Darcy-Weisbach pipe losses, pump affinity laws, centrifugal pump NPSH, heat exchanger LMTD method, pressure vessel hoop stress per ASME VIII); Mechanical Systems & Materials (Modified Goodman fatigue criterion, Shigley bearing life, spur gear Lewis stress, belt drive power, shaft dynamics, natural frequency, vibration transmissibility, elastic moduli, thermal stress); and HVAC & Refrigeration (vapor compression cycle enthalpy analysis, COP formulas, psychrometric processes, sensible/latent heat load formulas, ton of refrigeration equivalents, PID control, thermocouple selection).
Use the Prev / Next buttons at the bottom, or press the arrow keys on your keyboard. Click the ☰ menu button in the top-right corner to open the table of contents and jump directly to any of the 13 sections. The gold progress bar at the top tracks your position through all sections. Scroll the mouse wheel to advance or go back.
The NCEES PE Mechanical exam is open-book with NCEES-approved references only. Bring tabbed copies of Shigley's Mechanical Engineering Design (machine elements, fatigue), ASHRAE Handbook of Fundamentals (psychrometrics, heat transfer coefficients), Machinery's Handbook (gear and screw thread data), and steam tables. The NCEES PE Reference Handbook is provided on-screen during the exam. Tab and annotate your references before exam day — time spent hunting for formulas is time lost on problems.
All formulas in this guide use US Customary units consistent with the NCEES PE Mechanical exam. Key conversions to memorize: 1 HP = 550 ft·lbf/s = 2,545 Btu/hr; 1 ton cooling = 12,000 Btu/hr; 1 ft H₂O = 0.4335 psi; 1 ft³/s = 449 GPM. For heat transfer problems, always identify whether the resistance is dominated by convection (low h) or conduction (low k/L) before selecting your approach. For fatigue problems, always check whether you need Modified Goodman (combined alternating + mean stress) or simple endurance limit comparison (fully reversed loading only).
The PE Mechanical exam has 80 questions covering three discipline areas: HVAC & Refrigeration (25–35%), Mechanical Systems & Materials (25–35%), and Thermal & Fluid Systems (35–45%). Key subjects include thermodynamics, fluid mechanics, heat transfer, machine elements, dynamics, materials science, HVAC systems, pressure vessel design, and turbomachinery.
Carnot efficiency η = 1 - T_L/T_H where temperatures are in absolute units (°R or K). This is the maximum possible efficiency for any heat engine operating between two temperature reservoirs. For a steam plant with 700°F (1160°R) steam and 80°F (540°R) condenser: η_max = 1 - 540/1160 = 53.4%. Real Rankine cycle plants achieve roughly 30–40% due to irreversibilities.
The pump affinity laws relate changes in speed (N) or impeller diameter (D) to performance changes: flow Q ∝ N, head H ∝ N², and power P ∝ N³. For example, reducing pump speed by 20% (to 80% of original) reduces flow by 20%, head by 36%, and power by 49%. This is the basis for VFD (variable frequency drive) energy savings — a modest speed reduction produces a dramatic power reduction due to the cubic relationship.
Modified Goodman: σ_a/S_e + σ_m/S_ut = 1/n, where σ_a is alternating stress amplitude, σ_m is mean stress, S_e is endurance limit (≈ 0.5×S_ut for steel ≤ 200 ksi after Marin factor corrections), S_ut is ultimate tensile strength, and n is safety factor. If the operating stress point falls below the Goodman line (1/n < 1), the part has infinite fatigue life; above it predicts finite life or imminent failure. For fully reversed loading (σ_m = 0), the criterion simplifies to n = S_e/σ_a.