Elastic stiffness — slope of the stress-strain line

Stress where permanent (plastic) deformation begins

Maximum stress the material can carry

How much it deforms plastically before fracture

Resistance to indentation; correlates with strength

What are the three PE Mechanical depth exams?

Candidates choose one of three depth exams: HVAC & Refrigeration; Machine Design & Materials; or Thermal & Fluids Systems. All three sit on the same shared mechanical-engineering core, but you take only the depth that matches your practice.

What is the passing score on the PE Mechanical exam?

The PE Mechanical is reported as pass or fail with no fixed percentage. NCEES uses a criterion-referenced cut score set by panels of licensed engineers through a formal standard-setting process, so the bar reflects minimum competency for safe practice rather than a curve.

What reference can I use on the PE Mechanical exam?

The only reference allowed is the searchable NCEES PE Mechanical Reference Handbook, shown on-screen during the computer-based exam. Practicing with the handbook so you can quickly locate equations, property tables, and charts is essential, because the exam is closed-book otherwise.

How long should I study for the PE Mechanical exam?

Most candidates spend roughly 200 to 300 hours over three to four months. Build fluency with the NCEES Reference Handbook, master the shared core (thermodynamics, fluids, heat transfer, machine design), then go deep on your chosen depth with full-length, timed practice.

How should I use this PE Mechanical study guide?

Work through the six core modules first, taking each checkpoint quiz to find gaps, then study the depth exam you plan to sit. Drill weak areas with our free practice questions and flashcards, and rehearse the full timing with practice tests before exam day.

Is this PE Mechanical study guide free?

Yes — the full guide, the checkpoints, the glossary, the practice questions, and the flashcards are 100% free with no account required.

How hard is the PE Mechanical exam?

It is demanding: an 8-hour exam of multi-step, calculation-heavy problems where endurance and time management matter as much as knowledge. Fluency with the NCEES Reference Handbook and disciplined, timed practice are what separate a pass from a fail.

What is the first law of thermodynamics?

The first law is conservation of energy: energy is neither created nor destroyed, only converted. For a closed system, the change in internal energy equals heat added minus work done by the system: ΔU = Q − W. For an open (control-volume) system it becomes the steady-flow energy equation. On the PE Mechanical exam you most often apply the steady-flow energy equation across a device (turbine, pump, heat exchanger), tracking enthalpy, kinetic, and potential energy plus heat and work. Sign convention matters: heat into the system is positive, and work done by the system is positive.

What is the second law of thermodynamics?

The second law states that the entropy of an isolated system never decreases and that heat flows spontaneously from hot to cold. It sets the maximum possible efficiency of any heat engine — the Carnot efficiency — and explains why no real cycle can convert all heat into work. Carnot efficiency η = 1 − T_cold / T_hot, with temperatures in absolute units (K or °R), is the ceiling no real engine can exceed. Irreversibilities (friction, unrestrained expansion, finite temperature differences) generate entropy and reduce real efficiency below the Carnot limit.

What is the coefficient of performance (COP)?

COP measures a refrigeration or heat-pump cycle's efficiency: the useful heat moved divided by the work input. For cooling, COP = Q_L / W_in; for heating, COP = Q_H / W_in. A higher COP means more cooling or heating per unit of compressor work, and COP is always greater than zero. The ideal (Carnot) cooling limit is COP = T_cold / (T_hot − T_cold) in absolute temperature; real vapor-compression cycles fall below it. Heating and cooling COP for the same machine differ by 1: COP_heating = COP_cooling + 1.

How does the vapor-compression refrigeration cycle work?

Refrigerant cycles through four components: a compressor raises the vapor's pressure and temperature; a condenser rejects heat and condenses it to liquid; an expansion valve drops the pressure (constant enthalpy); and an evaporator absorbs heat from the conditioned space, boiling the refrigerant back to vapor. The cooling effect is the evaporator heat absorbed, Q_L; the compressor work, W_in, is what you pay for, so COP = Q_L / W_in. On a pressure-enthalpy (P-h) diagram the cycle is a rectangle, which makes the enthalpy differences easy to read for load and COP calculations.

What is psychrometrics?

Psychrometrics is the study of moist air — the relationships among dry-bulb temperature, wet-bulb temperature, humidity ratio, relative humidity, enthalpy, and dew point. HVAC engineers use the psychrometric chart to size cooling and heating loads and to design dehumidification and humidification processes. Dry-bulb temperature is the horizontal axis and humidity ratio the vertical axis; relative-humidity curves and enthalpy lines cross the chart. Sensible heat changes dry-bulb temperature; latent heat changes moisture content. Total load is the sum of both.

What is Bernoulli's equation?

Bernoulli's equation is conservation of energy for an ideal, incompressible, frictionless fluid along a streamline: pressure head plus velocity head plus elevation head is constant. Written as P/ρg + V²/2g + z = constant. It shows that where velocity rises, pressure falls. Real piping adds a head-loss term, so the engineering form is P₁/ρg + V₁²/2g + z₁ = P₂/ρg + V₂²/2g + z₂ + h_L. It assumes steady flow, no heat or shaft work between the two points, and constant density.

What is the Reynolds number?

The Reynolds number is the dimensionless ratio of inertial to viscous forces in a flow: Re = ρVD/μ = VD/ν. It predicts whether flow is laminar or turbulent. In a pipe, flow is generally laminar below about Re = 2300 and turbulent above roughly Re = 4000. ρ is density, V velocity, D the characteristic length (pipe diameter), μ dynamic viscosity, and ν kinematic viscosity. The flow regime determines which friction-factor correlation you use for head-loss calculations.

How do you calculate head loss in a pipe?

The Darcy-Weisbach equation gives major friction head loss: h_L = f (L/D)(V²/2g), where f is the Darcy friction factor, L the pipe length, D the diameter, V the velocity, and g gravity. The friction factor comes from the Moody chart using Reynolds number and relative roughness. In laminar flow the factor is simply f = 64/Re; in turbulent flow it depends on both Re and ε/D. Minor losses from fittings, valves, and bends are added with loss coefficients: h_minor = K (V²/2g).

What is Fourier's law of heat conduction?

Fourier's law states that conductive heat flow is proportional to the temperature gradient and the area, and flows from hot to cold: q = −kA(dT/dx). Here k is the material's thermal conductivity, A the cross-sectional area, and dT/dx the temperature gradient. The minus sign shows heat moves down the gradient. For a plane wall it simplifies to q = kA·ΔT / L, equivalent to a thermal resistance R = L/(kA). Series and parallel resistance networks let you combine conduction and convection like an electrical circuit.

What is the difference between conduction, convection, and radiation?

Conduction transfers heat through a solid or still fluid by molecular contact (q = −kA dT/dx). Convection transfers heat between a surface and a moving fluid (q = hA·ΔT, Newton's law of cooling). Radiation transfers heat as electromagnetic waves, with no medium needed (q = εσA·T⁴). Convection is natural (buoyancy-driven) or forced (a fan or pump drives the flow), which changes the heat-transfer coefficient h. Radiation matters most at high absolute temperatures because it scales with the fourth power of temperature.

What is bending stress and how do you calculate it?

Bending stress is the normal stress in a beam caused by a bending moment: σ = Mc/I, where M is the bending moment, c the distance from the neutral axis to the outer fiber, and I the area moment of inertia. The stress is maximum at the outer fibers and zero at the neutral axis. The section modulus S = I/c packages the geometry, giving σ = M/S — handy for comparing beam shapes. Designers size beams so the maximum bending stress stays below the allowable stress with an adequate factor of safety.

What is a factor of safety?

The factor of safety (FoS) is the ratio of a material's strength to the actual stress it carries: FoS = strength / applied stress. A value above 1 means the part can withstand more than the expected load. Engineers choose it to cover uncertainty in loads, materials, and analysis. Static design often uses the yield strength; for cyclic loading the endurance limit is used instead. Higher factors apply where failure is catastrophic or loads are poorly known; lower factors where weight and cost matter and loads are well characterized.

What is fatigue failure and the endurance limit?

Fatigue is failure from repeated (cyclic) loading at stresses below the static strength; tiny cracks initiate and grow until the part breaks. The endurance limit is the stress amplitude below which a material (notably steel) can endure essentially infinite cycles without fatigue failure. An S-N (stress vs cycles) curve shows fatigue life; for steels it flattens to a horizontal endurance limit. Mean-stress effects are handled with the Goodman or Soderberg criteria, which combine alternating and mean stresses.

What is the difference between ductile and brittle materials?

A ductile material (like mild steel or aluminum) deforms plastically and absorbs significant energy before fracturing, giving warning through visible yielding and necking. A brittle material (like cast iron or ceramic) fractures suddenly with little plastic deformation and weak warning, often failing in tension. On a stress-strain curve, ductile materials show a long plastic region; brittle materials fracture near the elastic limit. Ductile parts are typically analyzed with the distortion-energy (von Mises) or maximum-shear criteria; brittle parts with maximum-normal-stress theory.

What is the natural frequency of a vibrating system?

Natural frequency is the rate at which a system oscillates freely after a disturbance, with no continuing force. For a single-degree-of-freedom mass-spring system it is ωn = √(k/m) in radians per second, where k is stiffness and m is mass. Heavier mass lowers it; stiffer springs raise it. In hertz, f_n = ωn / (2π). Resonance occurs when a forcing frequency matches the natural frequency, causing large amplitudes. Damping reduces amplitude and slightly lowers the damped natural frequency; engineers detune machinery away from resonance.

What is the ideal gas law?

The ideal gas law relates pressure, volume, temperature, and amount of a gas: PV = mRT, where P is absolute pressure, V volume, m mass, R the specific gas constant, and T absolute temperature. It models gases well at low pressure and high temperature, away from condensation. It also appears as PV = nR̄T using moles and the universal gas constant R̄ = 8.314 J/(mol·K). Always use absolute pressure and absolute temperature (K or °R) in the equation.

What is the Rankine cycle?

The Rankine cycle is the ideal steam power cycle: a pump raises liquid pressure, a boiler adds heat to make superheated steam, a turbine expands the steam to produce work, and a condenser rejects heat to close the loop. Thermal efficiency is net work divided by heat added, η = W_net / Q_in. Superheating, reheating, and regenerative feedwater heating raise efficiency by increasing the average temperature of heat addition. It is the thermodynamic backbone of most fossil and nuclear power plants and a core Thermal & Fluids depth topic.

What is pump head and how do you find pump power?

Pump head is the energy a pump adds per unit weight of fluid, expressed in length (feet or meters). Hydraulic (fluid) power is P = ρgQH, where Q is the volumetric flow rate and H the head. Dividing by pump efficiency gives the required shaft (brake) power. The system curve (static lift plus friction losses) and the pump curve intersect at the operating point. Net positive suction head available (NPSH_a) must exceed the pump's required NPSH to avoid cavitation.

First law of thermodynamics

Conservation of energy: energy is neither created nor destroyed. For a closed system, ΔU = Q − W (heat added minus work done by the system). For a control volume it becomes the steady-flow energy equation.

Second law of thermodynamics

Heat flows spontaneously from hot to cold and the entropy of an isolated system never decreases. It sets the maximum efficiency of any heat engine (the Carnot limit).

A property measuring a system's disorder or unavailable energy. It increases in any real (irreversible) process and stays constant in an ideal reversible (isentropic) one.

A property equal to internal energy plus pressure times volume, h = u + Pv. It is the natural energy term for flow processes and is read directly from steam and refrigerant tables.

PV = mRT — relating absolute pressure, volume, mass, the specific gas constant, and absolute temperature. Accurate for gases at low pressure and high temperature.

The maximum thermal efficiency of a heat engine operating between two temperatures: η = 1 − T_cold / T_hot, in absolute temperature. No real cycle can exceed it.

The study of moist air — relating dry-bulb temperature, wet-bulb temperature, humidity ratio, relative humidity, enthalpy, and dew point on the psychrometric chart.

Heat that changes a substance's temperature without changing its phase. In HVAC, it is the part of a load that changes dry-bulb temperature.

Heat that changes a substance's phase at constant temperature, such as condensing water vapor. In HVAC it is the moisture (humidity) part of the load.

Energy conservation for ideal incompressible flow along a streamline: P/ρg + V²/2g + z = constant. Where velocity rises, pressure falls.

Conservation of mass: for incompressible flow A₁V₁ = A₂V₂, so a smaller area means a higher velocity. Mass flow rate ṁ = ρAV.

The dimensionless ratio of inertial to viscous forces, Re = ρVD/μ. It predicts laminar (Re ~4000) pipe flow.

Darcy-Weisbach equation

Major friction head loss in a pipe: h_L = f (L/D)(V²/2g), with f the Darcy friction factor from the Moody chart.

A plot of the Darcy friction factor against Reynolds number and relative roughness ε/D, used to find friction factor for turbulent pipe flow.

Net positive suction head (NPSH)

The suction-side pressure margin above the fluid's vapor pressure. NPSH available must exceed NPSH required, or the pump cavitates.

Conductive heat transfer: q = −kA(dT/dx). Heat flows down the temperature gradient, proportional to conductivity k and area A.

Newton's law of cooling

Convective heat transfer between a surface and a fluid: q = hA·ΔT, where h is the convection coefficient and ΔT the surface-to-fluid temperature difference.

An electrical analogy for heat flow: conduction R = L/(kA), convection R = 1/(hA). Series resistances add, so q = ΔT / R_total.

Log-mean temperature difference (LMTD)

The effective temperature driving force in a heat exchanger, used as q = UA·LMTD to size or rate it.

FREE PE Mechanical Study Guide 2026 + Readiness Score

This free PE Mechanical study guide teaches to the NCEES Principles and Practice of Engineering (PE) Mechanical exam— the licensure exam that, with your state board’s requirements, lets you stamp drawings as a Professional Engineer.^[1] It covers the shared mechanical-engineering core that every candidate must master, then explains all three depth exams so you can prepare the one you choose.

And it’s interactive, not a wall of text: every module has a built-in checkpoint quiz, hover-able glossary terms, worked formulas, and labeled diagrams, so you learn by doing.

Read it module by module, test yourself at each checkpoint, then round out your free PE Mechanical prep with our practice questions and flashcards.

PE Mechanical Exam Snapshot

PE Mechanical exam at a glance (2026)
Detail	PE Mechanical (each depth exam)
Questions	80 questions (computer-based)
Depth exams	Choose ONE: HVAC & Refrigeration · Machine Design & Materials · Thermal & Fluids Systems
Exam time	8 hours of exam time; about a 9-hour appointment with tutorial and a 50-minute break
Passing standard	Pass/fail; criterion-referenced cut score set by NCEES (no fixed percentage)
Reference	Searchable NCEES PE Mechanical Reference Handbook only (on-screen)
Administered by	NCEES at Pearson VUE test centers (year-round)
Eligibility	Set by your state board (typically FE passed plus qualifying experience)
Cost	$400 NCEES exam fee (plus any state board fees; verify at NCEES.org)

All three depth exams share the same foundation. This guide teaches the six core areasfirst — thermodynamics, fluid mechanics, heat transfer, machine design, materials, and dynamics & vibrations — then maps each depth so you know exactly where to go deep:^[2]

One PE Mechanical license — three depth exams

Every candidate studies the same mechanical-engineering core, then chooses one of three depth exams to sit. You take only the depth you select.

Shared ME coreThermodynamics · Fluid Mechanics · Heat Transfer · Machine Design · Materials · Dynamics & Vibrations

HVAC & RefrigerationPsychrometrics, heating & cooling loads, duct & pipe distribution, the refrigeration cycle, and HVAC equipment.

Machine Design & MaterialsStress analysis, fatigue & failure, joints & fasteners, bearings, gears, springs, and material selection.

Thermal & Fluids SystemsThermodynamic cycles, energy & mass balances, fluid mechanics, heat transfer, and fluid & thermal machinery.

Pick the depth that matches your daily practice — that’s where you’ll score the most.

How the Depth Exams Are Weighted

Each depth exam draws roughly 80 questions across its published NCEES knowledge areas. The HVAC & Refrigeration depth — the most common — splits its 80 questions across four areas, with Equipment and Distribution carrying the most weight:^[2]

PE Mechanical — HVAC & Refrigeration depth weighting (2026)

HVAC Equipment & Components34% · ~27 Qs

Distribution & Systems31% · ~25 Qs

HVAC Loads & Psychrometrics25% · ~20 Qs

Supportive Knowledge10% · ~8 Qs

The Machine Design & Materials and Thermal & Fluids Systems depths weight their own knowledge areas (stress and failure analysis, joints, and materials for one; thermodynamic cycles, fluid mechanics, and heat transfer for the other). Confirm the current area weights for your chosen depth in the official NCEES exam specifications before you build your study plan.^[2]

1 · Thermodynamics

Thermodynamics is the engine of the PE Mechanical exam — it underlies every depth, especially HVAC & Refrigeration and Thermal & Fluids. Master energy balances, the property tables, and the standard cycles, and a large share of the exam falls into place.

The First & Second Laws

The is energy conservation. For a closed system, $\Delta U = Q - W$ ; for a device with flow, you apply the steady-flow energy equation, tracking enthalpy, kinetic and potential energy, heat, and shaft work.^[4] The says heat flows from hot to cold and never decreases — which caps any engine at the $\eta = 1 - \dfrac{T_{cold}}{T_{hot}}$ (absolute temperature).

Ideal Gas & Properties

The $PV = mRT$ relates pressure, volume, mass, the specific gas constant, and absolute temperature. For property-rich substances such as steam and refrigerants, you read and entropy directly from the NCEES handbook tables and charts rather than computing them.

Core thermodynamic relations
Concept	Relation
Closed-system first law	$\Delta U = Q - W$
Ideal gas law	$PV = mRT$
Carnot efficiency	$\eta = 1 - \dfrac{T_{cold}}{T_{hot}}$
Refrigeration COP (cooling)	$COP = \dfrac{Q_L}{W_{in}}$
Sensible heat	$q = \dot m \, c_p \, \Delta T$

Power & Refrigeration Cycles

Two cycles dominate. The (pump → boiler → turbine → condenser) is the steam power cycle behind Thermal & Fluids; the vapor-compression refrigeration cycle(compressor → condenser → expansion valve → evaporator) is the heart of HVAC & Refrigeration. Both close into a loop, and you analyze them with enthalpy differences from the tables.

The vapor-compression refrigeration cycle

1 → 2 CompressorLow-pressure vapor is compressed to high pressure & temperature (work in).
2 → 3 CondenserRefrigerant rejects heat to the surroundings and condenses to liquid (Q_H out).
3 → 4 Expansion valveThrottling drops pressure & temperature at constant enthalpy (isenthalpic).
4 → 1 EvaporatorRefrigerant absorbs heat from the space and evaporates (Q_L in = cooling effect).

Coefficient of performance COP = Q_L / W_in = cooling delivered ÷ compressor work. The expansion valve closes the loop back to the evaporator.

The cooling effect is the evaporator heat absorbed, and the is that cooling divided by the compressor work. The (compressor → combustor → turbine) is the gas-turbine analogue.

Psychrometrics

is the study of moist air and the single most HVAC-flavored core topic. The psychrometric chart relates dry-bulb temperature (horizontal axis), humidity ratio (vertical axis), relative humidity, wet-bulb temperature, enthalpy, and dew point. A cooling load splits into (changing temperature) and (removing moisture).

Checkpoint · Core · Thermodynamics

Question 1 of 10

On a standard psychrometric chart, which property is read along the horizontal axis?

2 · Fluid Mechanics

Fluid mechanics governs how air and water move through ducts, pipes, and equipment — central to distribution design and to the Thermal & Fluids depth. Master mass and energy balances, the flow regime, and head loss.

Fluid Statics & Continuity

Hydrostatic pressure rises with depth, $P = \rho g h$ . Mass is conserved by the : for incompressible flow $A_1 V_1 = A_2 V_2$ , so a smaller area means a higher velocity, and mass flow rate is $\dot m = \rho A V$ .

Bernoulli & Energy

is energy conservation along a streamline for ideal flow: $\dfrac{P}{\rho g} + \dfrac{V^2}{2g} + z = \text{constant}$ . Real piping adds a head-loss term, so the engineering form is $\dfrac{P_1}{\rho g} + \dfrac{V_1^2}{2g} + z_1 = \dfrac{P_2}{\rho g} + \dfrac{V_2^2}{2g} + z_2 + h_L$ .^[4]

Pipe Flow & Head Loss

The $Re = \dfrac{\rho V D}{\mu}$ sets the regime: laminar below roughly 2300, turbulent above about 4000. Major friction loss comes from the , with the friction factor read from the .

Friction factor vs Reynolds number (the Moody chart idea)

Laminar (Re < ~2300): f = 64/Re. Turbulent: read f from the Moody chart using Re and relative roughness ε/D, then head loss h_L = f (L/D)(V²/2g).

Pipe-flow relations
Concept	Relation
Reynolds number	$Re = \dfrac{\rho V D}{\mu}$
Major head loss	$h_L = f \dfrac{L}{D} \dfrac{V^2}{2g}$
Laminar friction factor	$f = \dfrac{64}{Re}$
Minor loss (fittings)	$h_{minor} = K \dfrac{V^2}{2g}$

Pumps & Fluid Machinery

A pump adds head $H$ to the fluid; hydraulic power is $P = \rho g Q H$ , and dividing by efficiency gives the shaft (brake) power.^[7] The operating point is where the pump curve meets the system curve. Watch : the available suction head must exceed the pump’s required NPSH, or the pump cavitates.

Checkpoint · Core · Fluid Mechanics

Question 1 of 10

In a direct-expansion (DX) refrigeration system, what is the primary function of the suction line connecting the evaporator to the compressor?

3 · Heat Transfer

Heat transfer connects thermodynamics to real equipment — how fast energy moves, and how to size the coils, condensers, and heat exchangers that move it. Three modes, then heat-exchanger sizing.

Conduction & Resistance

gives conduction: $q = -kA \dfrac{dT}{dx}$ ; for a plane wall it simplifies to $q = \dfrac{kA \, \Delta T}{L}$ . Treat each layer as a and add them in series like a circuit.^[4]

Heat transfer as resistances in series

T_hot fluid

ConvectionR = 1 / (h·A)

ConductionR = L / (k·A)

T_cold fluid

Total: q = ΔT / R_total, with resistances added in series. Fourier’s law q = −kA(dT/dx); Newton’s cooling q = hA·ΔT.

Convection & Radiation

handles convection: $q = hA \, \Delta T$ , where the coefficient $h$ is larger for forced flow than for natural convection. Radiation scales with the fourth power of absolute temperature, $q = \varepsilon \sigma A T^4$ , so it matters most at high temperatures.

Heat Exchangers (LMTD & NTU)

For a heat exchanger, the heat duty is $q = UA \cdot \text{LMTD}$ , where $U$ is the overall coefficient and is the effective temperature driving force. When outlet temperatures are unknown, the effectiveness-NTU method is the cleaner tool.

Heat-transfer modes
Mode	Relation
Conduction (Fourier)	$q = \dfrac{kA \, \Delta T}{L}$
Convection (Newton)	$q = hA \, \Delta T$
Radiation	$q = \varepsilon \sigma A T^4$
Heat exchanger	$q = UA \cdot \text{LMTD}$

Checkpoint · Core · Heat Transfer

Question 1 of 10

In a vapor-compression refrigeration cycle, which component raises the refrigerant pressure and temperature between the evaporator and condenser?

4 · Machine Design

Machine design is the analytical core of the Machine Design & Materials depth and appears in every depth’s supportive knowledge. It is about stress, failure, and sizing real components with an adequate margin.

Stress, Strain & Mohr’s Circle

Three load types give three : axial $\sigma = P/A$ , $\sigma = Mc/I$ , and torsion $\tau = Tr/J$ . When normal and shear stresses act together, finds the principal stresses and the maximum shear.

Normal & shear stress on a 2-D element

Axialσ = P/A

Bendingσ = Mc/I

Torsionτ = Tr/J

Mohr’s circle converts σₓ, σᵧ, and τ into the principal stresses σ₁, σ₂ and the maximum shear.

Fatigue & Failure Theories

Under repeated loading, parts fail by at stresses below the static strength. For steels, an exists below which life is effectively infinite; the and Soderberg lines combine mean and alternating stress. For static failure, ductile parts use the distortion-energy (von Mises) or maximum-shear theory; brittle parts use maximum-normal-stress.

Shafts, Bolts, Gears & Bearings

Shafts carry combined bending and torsion; bolted and welded joints are sized for shear and tension; gears transmit torque with defined ratios and tooth-bending limits; rolling-element bearings are rated by $L_{10}$ life. Power, torque, and speed are linked by $P = T \omega$ .

Key machine-design stresses
Load	Stress	Where it's used
Axial	σ = P/A	Tension/compression members, bolts
Bending	σ = Mc/I	Beams, shafts under transverse load
Torsion	τ = Tr/J	Shafts, drive couplings
Direct shear	τ = V/A	Pins, rivets, bolts in shear

Checkpoint · Core · Machine Design

Question 1 of 10

A screw compressor controls capacity at part load most commonly by which means?

5 · Materials

Material behavior decides which design equations and safety factors apply. Know the stress-strain curve cold, and the difference between ductile and brittle response.

Mechanical Properties

On the stress-strain curve, the elastic slope is $E = \sigma / \varepsilon$ (stiffness). Past the yield point the material deforms plastically; the peak is the ultimate strength. Other properties — hardness, toughness, fatigue strength, and creep — round out selection.

Mechanical properties from the stress-strain curve
Property	What it tells you
Young's modulus (E)	Elastic stiffness — slope of the stress-strain line
Yield strength	Stress where permanent (plastic) deformation begins
Ultimate strength	Maximum stress the material can carry
Ductility	How much it deforms plastically before fracture
Hardness	Resistance to indentation; correlates with strength

Material Behavior & Selection

metals (mild steel, aluminum) yield and neck, giving warning; brittle materials (cast iron, ceramics) fracture suddenly and are weak in tension. Heat treatment (annealing, quenching, tempering) trades strength against ductility, and corrosion, temperature, and cyclic loading all drive material choice.

Checkpoint · Core · Materials

Question 1 of 10

Within the supportive-knowledge area for HVAC and refrigeration engineering, what is the primary role of an engineering code of ethics regarding public welfare?

6 · Dynamics & Vibrations

Dynamics describes motion and the forces that cause it; vibrations describes how mechanical systems oscillate. Both show up in supportive knowledge and in rotating-equipment problems.

Kinematics & Kinetics

Kinematics describes motion (position, velocity, acceleration) without forces; kinetics adds Newton’s second law $F = ma$ . Energy methods — work-energy and conservation of momentum — often solve problems faster than force balances.^[5]

Free & Forced Vibration

A single-degree-of-freedom mass-spring system has a $\omega_n = \sqrt{k/m}$ . The $\zeta$ sets how oscillations decay. — large amplitudes — occurs when a forcing frequency matches the natural frequency, so engineers detune machinery away from it.

Checkpoint · Core · Dynamics & Vibrations

Question 1 of 10

In an ideal evaporative (adiabatic saturation) cooling process, which air property remains essentially constant?

7 · The Three Depth Exams

With the core in hand, choose the depth that matches your practice. You take only one of the three — here is what each emphasizes so you can study the right material.^[2]

HVAC & Refrigeration

The most-taken depth. It tests psychrometrics and heating/cooling loads, air- and water-side distribution (ducts, pipes, fans, pumps), the refrigeration cycleand equipment (chillers, cooling towers, air handlers), and a supportive-knowledge area. Its 80 questions weight Equipment & Components and Distribution & Systems most heavily.

The ideal Rankine (steam power) cycle

1 → 2 PumpLiquid is pumped to boiler pressure. Work added; small pump work.
2 → 3 BoilerHeat added at constant pressure; water becomes superheated steam (Q_in).
3 → 4 TurbineSteam expands, producing shaft work (W_out); pressure & temperature drop.
4 → 1 CondenserHeat rejected at constant pressure; steam condenses back to liquid (Q_out).

Thermal efficiency η = W_net / Q_in = (W_turbine − W_pump) / Q_in. The condenser loop closes back to the pump.

Machine Design & Materials

This depth goes deep on stress and failure analysis, fatigue, joints and fasteners, bearings, gears, springs, and shafts, kinematics of mechanisms, and material selection. If your work is mechanical components and machinery, this is your exam.

Thermal & Fluids Systems

The broadest engineering-science depth: thermodynamic cycles (Rankine, Brayton, refrigeration), energy and mass balances, fluid mechanics and piping systems, heat transfer, and fluid & thermal machinery (pumps, compressors, turbines). It rewards strong command of the core modules above.

Choosing your PE Mechanical depth exam
Depth exam	Best for engineers who…	Core emphasis
HVAC & Refrigeration	Design building mechanical & refrigeration systems	Thermo, psychrometrics, fluids, heat transfer
Machine Design & Materials	Design mechanical components & machinery	Machine design, materials, dynamics
Thermal & Fluids Systems	Work in energy, process, or power systems	Thermo, fluids, heat transfer

Checkpoint · The Three Depth Exams

Question 1 of 10

A cooling coil handles air entering at 38 BTU/lb and leaving at 25 BTU/lb at a mass flow of 30,000 lb/hr of dry air. What is the total cooling capacity?

How to Use This Study Guide

A study guide is a map, not the whole territory — use it alongside the NCEES PE Mechanical Reference Handbook and our practice tools. The single biggest skill on exam day is locating equations and property data fast in the handbook, so practice with it open, exactly as you will test.

A study loop that actually works

1
Master the core first
Work the six core modules in order: thermodynamics, fluids, heat transfer, machine design, materials, dynamics & vibrations.
2
Choose your depth
Pick the one depth exam that matches your practice, then go deep on its knowledge areas.
3
Take the checkpoints
The quick check after each module exposes what didn't stick — then drill it.
4
Drill with the handbook open
Send weak topics into the free practice questions and flashcards, always using the NCEES Reference Handbook.
5
Simulate the full clock
Rehearse a full 80-question, timed exam so the long day feels routine before test day.

PE Mechanical Concept Questions

Common PE Mechanical concepts the exam tests — across the shared engineering core and the three depths. Tap any card for a short, exam-ready answer backed by an official source (NCEES, the U.S. Department of Energy, NIST), then test yourself on them as flashcards.

PE Mechanical Glossary

Quick definitions for the terms and formulas you’ll see most across the PE Mechanical exam:

Bending stress: Normal stress from a bending moment in a beam: σ = Mc/I, maximum at the outer fiber and zero at the neutral axis.
Bernoulli's equation: Energy conservation for ideal incompressible flow along a streamline: P/ρg + V²/2g + z = constant. Where velocity rises, pressure falls.
Brayton cycle: The ideal gas-turbine cycle: compressor, combustor, turbine, with heat rejection. Efficiency rises with the pressure ratio.
Carnot efficiency: The maximum thermal efficiency of a heat engine operating between two temperatures: η = 1 − T_cold / T_hot, in absolute temperature. No real cycle can exceed it.
Coefficient of performance (COP): Useful heat moved divided by work input for a refrigeration or heat-pump cycle. Cooling COP = Q_L / W_in; heating COP = Q_H / W_in. Higher is more efficient.
Continuity equation: Conservation of mass: for incompressible flow A₁V₁ = A₂V₂, so a smaller area means a higher velocity. Mass flow rate ṁ = ρAV.
Damping ratio: A dimensionless measure of how oscillations decay. Underdamped (ζ < 1) oscillates; critically damped (ζ = 1) returns fastest without overshoot.
Darcy-Weisbach equation: Major friction head loss in a pipe: h_L = f (L/D)(V²/2g), with f the Darcy friction factor from the Moody chart.
Ductility: A material's ability to deform plastically before fracture; ductile metals neck and give warning, brittle materials fracture suddenly.
Endurance limit: The cyclic stress amplitude below which a material (notably steel) can endure essentially infinite cycles without fatigue failure.
Enthalpy: A property equal to internal energy plus pressure times volume, h = u + Pv. It is the natural energy term for flow processes and is read directly from steam and refrigerant tables.
Entropy: A property measuring a system's disorder or unavailable energy. It increases in any real (irreversible) process and stays constant in an ideal reversible (isentropic) one.
Factor of safety: The ratio of a material's strength to the applied stress, FoS = strength / stress. Above 1 means the part can carry more than the expected load.
Fatigue: Progressive cracking and failure under repeated (cyclic) loading at stresses below the static strength.
First law of thermodynamics: Conservation of energy: energy is neither created nor destroyed. For a closed system, ΔU = Q − W (heat added minus work done by the system). For a control volume it becomes the steady-flow energy equation.
Fourier's law: Conductive heat transfer: q = −kA(dT/dx). Heat flows down the temperature gradient, proportional to conductivity k and area A.
Goodman criterion: A fatigue design line that combines mean stress and alternating stress to predict safe combinations under cyclic loading.
Ideal gas law: PV = mRT — relating absolute pressure, volume, mass, the specific gas constant, and absolute temperature. Accurate for gases at low pressure and high temperature.
Isentropic efficiency: The ratio of actual to ideal (reversible, constant-entropy) work for a turbine, compressor, or pump.
Latent heat: Heat that changes a substance's phase at constant temperature, such as condensing water vapor. In HVAC it is the moisture (humidity) part of the load.
Log-mean temperature difference (LMTD): The effective temperature driving force in a heat exchanger, used as q = UA·LMTD to size or rate it.
Mohr's circle: A graphical method to find principal stresses and maximum shear stress from the stresses on a known plane (σₓ, σᵧ, τ).
Moody chart: A plot of the Darcy friction factor against Reynolds number and relative roughness ε/D, used to find friction factor for turbulent pipe flow.
Natural frequency: The frequency at which a system oscillates freely after a disturbance. For a mass-spring system, ωn = √(k/m).
Net positive suction head (NPSH): The suction-side pressure margin above the fluid's vapor pressure. NPSH available must exceed NPSH required, or the pump cavitates.
Newton's law of cooling: Convective heat transfer between a surface and a fluid: q = hA·ΔT, where h is the convection coefficient and ΔT the surface-to-fluid temperature difference.
Psychrometrics: The study of moist air — relating dry-bulb temperature, wet-bulb temperature, humidity ratio, relative humidity, enthalpy, and dew point on the psychrometric chart.
Rankine cycle: The ideal steam power cycle: pump, boiler, turbine, condenser. Thermal efficiency η = W_net / Q_in.
Resonance: The large-amplitude response that occurs when a forcing frequency matches a system's natural frequency.
Reynolds number: The dimensionless ratio of inertial to viscous forces, Re = ρVD/μ. It predicts laminar (Re < ~2300) versus turbulent (Re > ~4000) pipe flow.
Second law of thermodynamics: Heat flows spontaneously from hot to cold and the entropy of an isolated system never decreases. It sets the maximum efficiency of any heat engine (the Carnot limit).
Sensible heat: Heat that changes a substance's temperature without changing its phase. In HVAC, it is the part of a load that changes dry-bulb temperature.
Stress: Internal force per unit area. Normal stress σ acts perpendicular to a surface; shear stress τ acts parallel to it.
Thermal resistance: An electrical analogy for heat flow: conduction R = L/(kA), convection R = 1/(hA). Series resistances add, so q = ΔT / R_total.
Young's modulus: The slope of the elastic stress-strain line, E = σ/ε. It measures stiffness — how much a material deforms elastically under load.

Free PE Mechanical Study Materials & Resources

Everything you need to prepare for the PE Mechanical exam is free here — no paywall, no sign-up. This guide is the foundation; pair it with the rest of our free PE Mechanical study materials for active recall, timed practice, and last-minute review:

PE Mechanical Practice Test — exam-style questions with answer explanations.
PE Mechanical Flashcards — active-recall decks for the high-yield formulas and concepts.

PE Mechanical Study Guide FAQ

Each PE Mechanical depth exam has 80 questions. It is computer-based, delivered with 8 hours of exam time within an appointment of about 9 hours that includes a tutorial, a nondisclosure agreement, and a scheduled 50-minute break you can use whenever you like.

References

1.NCEES. “PE Mechanical Exam — Principles and Practice of Engineering.” NCEES. ↑
2.NCEES. “PE Mechanical Exam Specifications & Reference Handbook.” NCEES. ↑
3.NCEES. “Computer-Based Testing (CBT) at Pearson VUE.” NCEES. ↑
4.U.S. Department of Energy. “Thermodynamics, Heat Transfer, and Fluid Flow (DOE Fundamentals Handbook, Vol. 1–3).” U.S. Department of Energy. ↑
5.U.S. Department of Energy. “Mechanical Science (DOE Fundamentals Handbook).” U.S. Department of Energy. ↑
6.National Institute of Standards and Technology. “NIST Reference on Constants, Units, and Uncertainty.” NIST. ↑
7.U.S. Department of Energy. “Improving Pumping System Performance — A Sourcebook for Industry.” U.S. Department of Energy. ↑
8.U.S. Department of Energy. “Energy Saver — Heat Pump Systems & Central Air Conditioning.” U.S. Department of Energy. ↑

Sources for the concept answers

Every answer in the PE Mechanical concept questions above is drawn from an official primary source:

U.S. Department of Energy. “Energy Saver — Central Air Conditioning.” U.S. Department of Energy.
National Institute of Standards and Technology. “Engineering Statistics / Reference Data.” National Institute of Standards and Technology.
U.S. Department of Energy. “Thermodynamics, Heat Transfer, and Fluid Flow (DOE Fundamentals Handbook).” U.S. Department of Energy.
U.S. Department of Energy. “Thermodynamics, Heat Transfer, and Fluid Flow (DOE Fundamentals Handbook).” U.S. Department of Energy.
National Institute of Standards and Technology. “Materials Measurement Science.” National Institute of Standards and Technology.

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