Chartered Membership of IMechE (CEng MIMechE) Core Mechanical Engineering Knowledge Syllabus

State the first law of thermodynamics for a closed system.

$\Delta U = Q - W$: the change in internal energy equals heat added to the system minus work done by the system.

Write the steady-flow energy equation (SFEE) for an open system per unit mass.

$q - w = \left(h_2 - h_1\right) + \frac{1}{2}\left(v_2^{2} - v_1^{2}\right) + g\left(z_2 - z_1\right)$, where $h$ is specific enthalpy.

State the second law (Kelvin–Planck statement) and define the Carnot efficiency.

Kelvin–Planck: no cycle can convert all heat from a single reservoir into work. Carnot efficiency: $\eta_{Carnot} = 1 - \frac{T_C}{T_H}$, with temperatures in kelvin.

Define the ideal gas law and the relation between $c_p$, $c_v$, and $R$.

$pV = mRT$ (or $p = \rho R T$). For an ideal gas $c_p - c_v = R$ and $\gamma = \frac{c_p}{c_v}$.

What is entropy change for a reversible process, and what does the second law say about isolated systems?

$dS = \frac{\delta Q_{rev}}{T}$. For an isolated system $\Delta S_{total} \geq 0$ (equality only for reversible processes).

Name the four processes of the ideal Carnot cycle in order.

1) Isothermal heat addition, 2) reversible adiabatic (isentropic) expansion, 3) isothermal heat rejection, 4) reversible adiabatic (isentropic) compression.

State Fourier's law of heat conduction (1D).

$\dot{Q} = -kA\frac{dT}{dx}$, where $k$ is thermal conductivity, $A$ the area, and $\frac{dT}{dx}$ the temperature gradient (negative sign because heat flows down the gradient).

Write Newton's law of cooling for convection and define the relevant quantities.

$\dot{Q} = hA(T_s - T_\infty)$, where $h$ is the convective heat transfer coefficient, $A$ the surface area, $T_s$ the surface temperature, and $T_\infty$ the fluid temperature.

State the Stefan–Boltzmann law for radiative heat transfer from a real surface.

$\dot{Q} = \varepsilon \sigma A T^{4}$, where $\varepsilon$ is emissivity, $\sigma = 5.67\times10^{-8}\,\text{W m}^{-2}\text{K}^{-4}$, $A$ area, and $T$ absolute temperature.

Define the Reynolds, Nusselt, and Prandtl numbers used in convective heat transfer.

$Re = \frac{\rho v L}{\mu}$ (inertial/viscous), $Nu = \frac{hL}{k}$ (convective/conductive), $Pr = \frac{\mu c_p}{k} = \frac{\nu}{\alpha}$ (momentum/thermal diffusivity).

For 1D steady conduction through a plane wall, write thermal resistance and the resistance for convection.

Conduction: $R_{cond} = \frac{L}{kA}$. Convection: $R_{conv} = \frac{1}{hA}$. Heat flow: $\dot{Q} = \frac{\Delta T}{R_{total}}$ with resistances in series.

State the hydrostatic pressure relation and the equation for force on a submerged surface.

$p = \rho g h$ (gauge pressure at depth $h$). Resultant force on a plane surface: $F = \rho g \bar{h} A$, where $\bar{h}$ is the depth of the centroid.

State Archimedes' principle.

The buoyant force on a body equals the weight of the fluid it displaces: $F_B = \rho_{fluid} g V_{displaced}$.

Write the continuity equation for incompressible steady flow and Bernoulli's equation.

Continuity: $A_1 v_1 = A_2 v_2$. Bernoulli: $p + \frac{1}{2}\rho v^{2} + \rho g z = \text{constant}$ along a streamline (inviscid, incompressible).

What distinguishes laminar from turbulent pipe flow, and at what Reynolds number does transition typically occur?

Laminar flow is smooth and orderly (viscous dominated); turbulent flow is chaotic with mixing. In a pipe, transition is around $Re \approx 2300$ (laminar below, turbulent above ~4000).

Write the Darcy–Weisbach equation for head loss due to friction in a pipe.

$h_f = f\frac{L}{D}\frac{v^{2}}{2g}$, where $f$ is the Darcy friction factor, $L$ length, $D$ diameter, $v$ mean velocity.

Define the drag force equation and the dynamic viscosity (Newton's law of viscosity).

Drag: $F_D = \frac{1}{2}\rho v^{2} C_D A$. Newton's law of viscosity: $\tau = \mu\frac{du}{dy}$, where $\mu$ is dynamic viscosity and $\frac{du}{dy}$ the velocity gradient.

Compare the Otto and Diesel cycles by their heat-addition process.

The Otto (spark-ignition) cycle adds heat at constant volume; the Diesel (compression-ignition) cycle adds heat at constant pressure. Both reject heat at constant volume.

Give the thermal efficiency of the ideal Otto cycle in terms of compression ratio.

$\eta_{Otto} = 1 - \frac{1}{r^{\gamma-1}}$, where $r$ is the compression ratio and $\gamma$ the specific heat ratio.

Name the four components of an ideal vapour-compression refrigeration cycle and define the COP.

Evaporator, compressor, condenser, expansion valve. $COP_{ref} = \frac{Q_{cold}}{W_{in}} = \frac{\text{refrigeration effect}}{\text{compressor work}}$.

List the typical stages of the engineering design process.

1) Identify need/requirements, 2) define specification (PDS), 3) concept generation, 4) concept evaluation/selection, 5) detailed/embodiment design, 6) prototyping & testing, 7) manufacture & implementation, with iteration throughout.

What is a Product Design Specification (PDS) and what is the purpose of a FMEA?

A PDS is the controlling document listing all design requirements/constraints (performance, environment, cost, standards). A Failure Mode and Effects Analysis (FMEA) systematically identifies potential failure modes, their effects, and prioritises them by a risk priority number.

Define the factor of safety and write its basic form.

The factor of safety is the margin between a material's capacity and the applied/working condition: $FoS = \frac{\text{material strength}}{\text{working (applied) stress}}$ (e.g. $\frac{\sigma_y}{\sigma_{working}}$).

Name common machine elements used to transmit power and to join components.

Power transmission: gears, belts/pulleys, chains, shafts, couplings, bearings. Fasteners/joints: bolts and nuts, screws, rivets, keys, pins, welds, splines.

For a pair of meshing spur gears, write the gear (velocity) ratio in terms of teeth and speeds.

$\frac{\omega_1}{\omega_2} = \frac{N_2}{N_1} = \frac{d_2}{d_1}$, where $N$ is the number of teeth and $d$ the pitch diameter; the larger gear runs slower.

Distinguish CAD, CAE, and CAM in the design/manufacture workflow.

CAD (Computer-Aided Design): geometric modelling and drawings. CAE (Computer-Aided Engineering): analysis/simulation such as FEA/CFD. CAM (Computer-Aided Manufacturing): generating tool paths and machine instructions from the CAD model.

Classify the main categories of manufacturing processes.

Casting (e.g. sand, die), forming/deformation (forging, rolling, extrusion, sheet forming), machining/material removal (turning, milling, drilling, grinding), joining (welding, brazing, adhesives, fasteners), and additive manufacturing (3D printing).

Compare additive and subtractive manufacturing.

Additive builds parts layer by layer adding material (e.g. SLS, FDM), enabling complex geometry with little waste. Subtractive removes material from a blank (e.g. milling, turning), giving high accuracy/finish but more waste and geometric limits.

What is a closed-loop (feedback) control system, and what does the transfer function of a system represent?

A closed-loop system uses feedback to compare output with a reference (error) and adjust the input to reduce that error. The transfer function $G(s) = \frac{Y(s)}{X(s)}$ is the ratio of output to input in the Laplace domain, characterising system dynamics.

Write the standard PID controller equation and state the role of each term.

$u(t) = K_p e(t) + K_i \int e(t)\,dt + K_d \frac{de(t)}{dt}$. Proportional reduces error, integral eliminates steady-state offset, derivative improves damping/transient response.

For a single-degree-of-freedom undamped vibrating system, give the natural frequency.

$\omega_n = \sqrt{\frac{k}{m}}$ (rad/s), so $f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$ (Hz), where $k$ is stiffness and $m$ mass.

Define the damping ratio and the condition for critical damping.

$\zeta = \frac{c}{c_c}$ where $c_c = 2\sqrt{km} = 2m\omega_n$. $\zeta<1$ underdamped (oscillatory), $\zeta=1$ critically damped (fastest non-oscillatory return), $\zeta>1$ overdamped.

What is resonance, and how is the decibel level of sound defined?

Resonance occurs when the forcing frequency approaches the natural frequency, causing large amplitude response (limited only by damping). Sound level: $L = 10\log_{10}\left(\frac{I}{I_0}\right)$ dB, with reference intensity $I_0 = 10^{-12}\,\text{W m}^{-2}$.

What is the Finite Element Method (FEM) and what is mesh convergence?

FEM discretises a continuous domain into small elements with nodes, solving governing equations approximately over each element and assembling them. Mesh convergence is refining the mesh until the result no longer changes significantly, indicating a reliable solution.

In probability/statistics, write the mean and standard deviation of a sample, and state the empirical rule for a normal distribution.

Mean $\bar{x} = \frac{1}{n}\sum x_i$; standard deviation $s = \sqrt{\frac{1}{n-1}\sum (x_i-\bar{x})^{2}}$. For a normal distribution about 68%, 95%, and 99.7% of data lie within $\pm1\sigma$, $\pm2\sigma$, $\pm3\sigma$.

Define reliability $R(t)$ and its relationship with failure probability and the exponential model.

$R(t) = 1 - F(t)$, the probability of surviving to time $t$. For a constant failure rate $\lambda$ (exponential model), $R(t) = e^{-\lambda t}$ and $MTBF = \frac{1}{\lambda}$.

For components in series and in parallel, how do reliabilities combine?

Series (all must work): $R_{sys} = \prod_i R_i$. Parallel/redundant (at least one works): $R_{sys} = 1 - \prod_i (1 - R_i)$.

What does the bathtub curve describe in reliability engineering?

It describes how failure rate varies over a product's life: a decreasing infant-mortality (early-failure) region, a low constant useful-life region (random failures), and an increasing wear-out region.

What is a digital twin in modern mechanical engineering?

A digital twin is a dynamic virtual model of a physical asset or system, continuously updated with sensor/operational data, used to monitor, simulate, predict performance, and optimise maintenance in real time.

What is life cycle assessment (LCA) and name a key principle of sustainable/design-for-environment engineering.

LCA quantifies the environmental impacts of a product across its whole life (raw materials, manufacture, use, end-of-life). A key sustainable-design principle is the waste hierarchy / circular economy: reduce, reuse, recycle (and design for disassembly and material efficiency).