Comprehensive Biomedical and Mechanical Engineering Curriculum Reference Manual

Thermodynamics & Practical Foundations (BME 108 / BME 116)

• Fundamental Laws and Definitions

  • Thermodynamics: This is defined as the branch of physical science dealing with heat, work, and the transformation of energy.
  • System: Defined as a quantity of matter or a region in space chosen specifically for study.
  • Zeroth Law of Thermodynamics: States that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law serves as the empirical foundation for temperature measurement.
  • First Law of Thermodynamics (Law of Conservation of Energy): States that energy cannot be created or destroyed; it can only change form.
  • First Law Equation for a Closed System: For a closed system undergoing a cycle, the relation is given by:         $\Delta U = Q - W$
    • $\Delta U$ = change in internal energy in Joules ($J$).
    • $Q$ = heat added to the system in Joules ($J$).
    • $W$ = work done by the system in Joules ($J$).
  • Second Law of Thermodynamics:
    • Kelvin-Planck Statement: It is impossible for any device that operates on a thermodynamic cycle to receive heat from a single thermal reservoir and deliver a net amount of work.
    • Clausius Statement: It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.
  • Entropy ($S$): This is a measure of microscopic disorder within a system. For any real (irreversible) process, the total entropy of an isolated system always increases, expressed as:         $dS \ge \frac{dQ}{T}$

• Ideal Gas Laws & Equations of State

  • The state of an ideal gas is governed by:         $P \cdot V = m \cdot R \cdot T$         or         $P \cdot v = R \cdot T$
  • Variables:
    • $P$ = absolute pressure in Pascals ($Pa$).
    • $V$ = volume in cubic meters ($m^3$).
    • $v$ = specific volume ($V/m$).
    • $m$ = mass in kilograms ($kg$).
    • $R$ = specific gas constant in Joules per kilogram-Kelvin ($J/kg \cdot K$).
    • $T$ = absolute temperature in Kelvin ($K$).

• Thermodynamic Non-Flow Processes

  • Isochoric Process:
    • Governing Condition: Constant Volume ($V_1 = V_2$).
    • Work Done ($W$): $0$
    • Heat Transfer ($Q$): $m \cdot c_v \cdot (T_2 - T_1)$
  • Isobaric Process:
    • Governing Condition: Constant Pressure ($P_1 = P_2$).
    • Work Done ($W$): $P \cdot (V_2 - V_1)$
    • Heat Transfer ($Q$): $m \cdot c_p \cdot (T_2 - T_1)$
  • Isothermal Process:
    • Governing Condition: Constant Temperature ($T_1 = T_2$).
    • Work Done ($W$): $P_1 V_1 \cdot \ln(\frac{V_2}{V_1})$
    • Heat Transfer ($Q$): $Q = W$ (because $\Delta U = 0$).
  • Polytropic Process:
    • Governing Condition: $P \cdot V^n = \text{Constant}$.
    • Work Done ($W$): $\frac{P_1 V_1 - P_2 V_2}{n - 1}$
    • Heat Transfer ($Q$): $W + \Delta U$

• Practical Laboratory Experiments

  • Marcet Boiler Experiment: Measurement of the relationship between saturated steam pressure and saturation temperature used to verify the Clausius-Clapeyron equation.
  • Bomb Calorimeter: Used to measure the higher heating value ($HHV$) of solid and liquid fuels under constant volume conditions.

Engineering Mechanics & Practical (BME 114 / BME 118)

• Statics & Rigid Body Equilibrium

  • Statics involves the analysis of structures and rigid bodies in equilibrium under external forces, where total linear and angular acceleration are zero.
  • 2D Equilibrium Equations:
    • $\sum F_x = 0$
    • $\sum F_y = 0$
    • $\sum M_O = 0$

• Centroids & Moment of Inertia

  • Centroid ($\bar{x}, \bar{y}$): The geometric center of a body or area.
  • Area Moment of Inertia ($I$): This represents the resistance of a cross-section to bending.
  • Parallel Axis Theorem: Used to find the moment of inertia about any axis parallel to the centroidal axis:         $I_x = I_{cg} + A \cdot d^2$
    • $I_{cg}$ = moment of inertia about the centroidal axis.
    • $A$ = cross-sectional area.
    • $d$ = perpendicular distance between the two axes.

• Dynamics: Kinematics & Kinetics

  • Newton’s Second Law:
    • Linear Motion: $F = m \cdot a$
    • Rotational Motion: $\sum M = I \cdot \alpha$
  • Work-Energy Principle: States that the total work done by external forces equals the change in kinetic energy:         $W_{net} = \Delta K = \frac{1}{2} m (v_2^2 - v_1^2)$

Calculus I (BME 106)

• Differentiation Rules and Applications

  • Product Rule: $\frac{d}{dx} [u \cdot v] = u'v + uv'$
  • Quotient Rule: $\frac{d}{dx} [\frac{u}{v}] = \frac{u'v - uv'}{v^2}$
  • Chain Rule: $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$
  • Optimization: Critical points are identified where $f'(x) = 0$.
    • If $f''(x) > 0$, the point is a local minimum.
    • If $f''(x) < 0$, the point is a local maximum.

• Integration Techniques

  • Integration by Parts: Derived from the product rule:         $\int u \,dv = u \cdot v - \int v \,du$
  • Partial Fraction Decomposition: A method used to integrate complex rational functions by breaking them into simpler polynomial denominators.

Computer Aided Drawing (CAD) & Workshop Practice (BME 112 / BME 110)

• CAD and Projections

  • Orthographic Projection: A method used to represent 3D objects in 2D.
    • First Angle Projection: Commonly utilized in Europe and Africa.
    • Third Angle Projection: The standard utilized in the US.

• Workshop Operations

  • Lathe Machine Operations: Includes turning, facing, knurling, threading, and boring.
  • Milling Machine Operations: Includes face milling, end milling, slotting, and gear cutting.
  • Joining Processes: Includes Shielded Metal Arc Welding ($SMAW$), Tungsten Inert Gas ($TIG$), Metal Inert Gas ($MIG$), and Torch Brazing.

Fluid Mechanics I & Practical (BME 208 / BME 216)

• Fluid Properties & Hydrostatics

  • Fluid Density ($\rho$): Mass per unit volume measured in $kg/m^3$.
  • Dynamic Viscosity ($\mu$): Resistance to shear deformation measured in $Pa \cdot s$ or $N \cdot s/m^2$.
  • Hydrostatic Law: Defines pressure variation in a fluid at rest:         $P = P_0 + \rho \cdot g \cdot h$

• Fluid Dynamics & Flow Equations

  • Continuity Equation (Conservation of Mass):$A_1 \cdot v_1 = A_2 \cdot v_2 = Q$
    • $Q$ is the Volumetric Flow Rate in $m^3/s$.
  • Bernoulli’s Equation: Represents conservation of energy along a streamline for inviscid, incompressible, steady flow:         $\frac{P_1}{\rho g} + \frac{v_1^2}{2g} + z_1 = \frac{P_2}{\rho g} + \frac{v_2^2}{2g} + z_2$
    • $\frac{P}{\rho g}$ = Pressure head.
    • $\frac{v^2}{2g}$ = Velocity head.
    • $z$ = Elevation head.
  • Friction Head Loss (Darcy-Weisbach Equation):$h_f = f \cdot (\frac{L}{D}) \cdot (\frac{v^2}{2g})$
    • $f$ = Darcy friction factor.
    • $L$ = pipe length.
    • $D$ = inner diameter.

Electrical Machines & Practical (BME 212 / BME 218)

• DC Motors & Generators

  • Back EMF ($E_b$): The electromotive force induced in the armature during rotation:         $E_b = \frac{P \cdot \Phi \cdot N \cdot Z}{60 \cdot A}$
    • $P$ = poles, $\Phi$ = flux per pole, $N$ = speed in RPM, $Z$ = total conductors, $A$ = parallel paths.
  • Electromagnetic Torque ($T$):$T = \frac{P \cdot \Phi \cdot Z \cdot I_a}{2\pi \cdot A}$

• AC Transformers & Induction Motors

  • Transformer Voltage Transformation Ratio:$\frac{V_1}{V_2} = \frac{N_1}{N_2} = \frac{I_2}{I_1}$
  • Induction Motor Synchronous Speed ($N_s$):$N_s = \frac{120 \cdot f}{p}$
  • Slip ($s$):$s = \frac{N_s - N}{N_s}$
    • $f$ = supply frequency in Hz, $p$ = number of stator poles, $N$ = actual rotor speed.

Kinematics of Machines & Practical (BME 210 / BME 214)

• Planar Mechanism Analysis

  • Grübler's Criterion for Planar Mechanisms: Used to calculate Degrees of Freedom ($DOF$):         $DOF = 3(n - 1) - 2j_1 - j_2$
    • $n$ = total links.
    • $j_1$ = 1-DOF joints (revolute or prismatic).
    • $j_2$ = 2-DOF joints (higher pairs or cam contacts).

• Acceleration and Gears

  • Coriolis Acceleration Component ($a_c$): Occurs when a slider moves along a link that is rotating simultaneously:         $a_c = 2 \cdot \omega \cdot v$
    • $\omega$ = angular velocity of link in $rad/s$.
    • $v$ = linear sliding velocity in $m/s$.
  • Gear Train Speed Ratios: For simple and compound gear trains:         $\frac{N_1}{N_2} = \frac{T_2}{T_1}$
    • $T$ = number of teeth.

Probability & Statistics & Project Management (BME 204 / BME 206)

• Probability Distributions

  • Normal Distribution: A bell curve parameterized by the mean ($\mu$) and variance ($\sigma^2$).
  • Binomial Distribution: Models discrete success or failure outcomes over $n$ trials.

• Project Management Techniques

  • Critical Path Method (CPM): Deterministic network analysis used to identify the longest sequence of dependent activities (characterized by zero float).
  • PERT (Program Evaluation & Review Technique): Probabilistic scheduling using three time estimates:
    • Optimistic ($a$), Most Likely ($m$), and Pessimistic ($b$).
  • Expected Duration ($t_e$) Equation:$t_e = \frac{a + 4m + b}{6}$

Automatic Control / PLC Systems & Practical (BME 306 / BME 312)

• Classical Feedback Control Systems

  • Transfer Function $G(s)$: The ratio of the Laplace transform of output $Y(s)$ to input $X(s)$ with zero initial conditions:         $G(s) = \frac{Y(s)}{X(s)}$
  • PID Controller Equation:$u(t) = K_p \cdot e(t) + K_i \int e(t) \,dt + K_d \cdot \frac{de(t)}{dt}$
    • $K_p$ = Proportional gain.
    • $K_i$ = Integral gain.
    • $K_d$ = Derivative gain.
    • $e(t)$ = error signal.

• Programmable Logic Controllers (PLCs)

  • Hardware Components: Central Processing Unit ($CPU$), Input Modules (sensors, switches), Output Modules (actuators, relays, solenoids), and Power Supply.
  • Ladder Logic Constructs:
    • Normally Open ($NO$) Contact: --[ ]--
    • Normally Closed ($NC$) Contact: --[/]--
    • Output Coil: -- ( ) --
    • Timers and Counters: On-Delay Timers ($TON$) and Up/Down Counters ($CTU/CTD$).

Internal Combustion (I.C.) Engines & Practical (BME 310 / BME 314)

• Thermodynamic Engine Cycles

  • Air Standard Otto Cycle (Spark Ignition / Petrol): Thermal Efficiency ($\eta_{otto}$) is given by:         $\eta_{otto} = 1 - [\frac{1}{r^{\gamma - 1}}]$
    • $r$ = compression ratio ($V_1/V_2$).
    • $\gamma$ = specific heat ratio (approx. $1.4$ for air).
  • Air Standard Diesel Cycle (Compression Ignition): Efficiency ($\eta_{diesel}$):         $\eta_{diesel} = 1 - [\frac{1}{r^{\gamma - 1}}] \cdot [\frac{r_c^\gamma - 1}{\gamma(r_c - 1)}]$
    • $r_c$ = cut-off ratio ($V_3/V_2$).

• Engine Performance Calculations

  • Brake Power ($BP$):$BP = \frac{2 \cdot \pi \cdot N \cdot T}{60,000} \, (\text{kW})$
  • Mechanical Efficiency ($\eta_m$):$\eta_m = (\frac{\text{Brake Power}}{\text{Indicated Power}}) \times 100\%$

HVAC Load Analysis & System Design (BME 324)

• Psychrometrics & Cooling Load

  • Psychrometrics: The study of atmospheric air and moisture mixtures. Includes Dry-Bulb ($DBT$), Wet-Bulb ($WBT$), Relative Humidity ($RH\%$, and Specific Enthalpy ($h$).
  • Cooling Load Calculation: Heat gain through the building envelope is determined by:         $Q_{conduction} = U \cdot A \cdot \Delta T$
    • $U$ = overall heat transfer coefficient ($W/m^2 \cdot K$).
    • $A$ = surface area ($m^2$).
    • $\Delta T$ = temperature difference ($K$).

• Vapor Compression Refrigeration Cycle (VCRC)

  1. Stage 1 \u2192 2: Isentropic Compression in Compressor.
  2. Stage 2 \u2192 3: Isobaric Heat Rejection in Condenser.
  3. Stage 3 \u2192 4: Isenthalpic Expansion in Expansion Valve.
  4. Stage 4 \u2192 1: Isobaric Heat Absorption in Evaporator.

Mechatronics Design & Mechanical Maintenance (BME 320 / BME 322)

• System Components

  • Sensors: Strain gauges, LVDTs, Thermocouples, Optical Encoders.
  • Signal Conditioners: Op-Amps, Analog-to-Digital Converters ($ADCs$).
  • Actuators: DC Servos, Stepper motors, Solenoid valves.
  • Controllers: Microcontrollers, Digital Signal Processors ($DSPs$).

• Industrial Maintenance Strategies

  • Corrective / Breakdown Maintenance: Maintenance/repairs performed only after equipment failure.
  • Preventive Maintenance ($PM$): Scheduled routine servicing meant to prevent occurrence of failure.
  • Condition-Based Maintenance ($CBM$): Involves real-time monitoring including vibration spectrum analysis, oil spectrographic analysis, and infrared thermography.

Renewable Energy & Professional Ethics (BME 308 / BME 334)

• Renewable Energy Systems

  • Photovoltaic Systems: Utilizing photoelectric conversion through semiconductor P-N junctions; uses Maximum Power Point Tracking ($MPPT$) algorithms.
  • Wind Energy: Governed by Betz's Limit for maximum aerodynamic power extraction efficiency:         $C_{p,max} = \frac{16}{27} \approx 59.3\%$

• Law & Professional Ethics for Engineers

  • Professional Negligence: Defined as a breach of duty of care resulting in physical injury or financial damage.
  • Ghana Institution of Engineering (GhIE) Code of Conduct: Emphasizes a paramount duty to public safety, environmental sustainability, ethical bidding practices, and the avoidance of conflicts of interest.