Advanced Diploma in Mechanical Engineering

Explore engineering mechanics, focusing on statics and dynamics, and apply forces, equilibrium, and vector methods like the parallelogram and triangle laws to analyze rigid bodies.

use triangle and parallelogram methods to solve vector problems, apply cosine and sine laws to find the resultant and its angle, and resolve forces into the u and v axes.

Express forces with unit vectors i, j, k in Cartesian form, resolve x, y, z components, and apply direction cosines to find the resultant and equilibrium conditions.

Understand the dot product as a scalar, defined by a·b = ab cos theta, and its commutativity, distributive property, and rectangular form ax bx + ay by + az bz.

Explore how a force rotates a body about a point using moment m equals r cross f and the moment arm d, then apply Vernon's theorem to relate component moments.

Compute the moment of a force about axis ab using Mab = r f dot lambda, apply the right-hand rule, and obtain rectangular components.

Explore how a couple produces pure rotation with a moment and no resultant force, and compute its moment about any point using scalar and vector methods; recognize equivalent couples.

Move the force from B to A by introducing the transfer couple CT to preserve the moment of rotation, then reduce the force system to an equivalent force–couple at O.

Reduce coplanar force systems to a resultant and moment, yielding a single force or a couple; concurrent and parallel cases define the line of action and distance from O.

Draw free body diagrams to identify forces and reactions in coplanar structures, then apply equilibrium equations to solve for unknowns in bars, frames, and pulley systems.

Analyzes composite bodies by constructing free body diagrams, applying three independent equilibrium equations to determine internal forces, reactions, and statically determined beam behavior.

Analyze plane trusses using the method of joints and the method of sections to determine internal member forces, identifying tension or compression at joints.

Study how beams carry loads and determine their internal forces using free body diagrams and equilibrium. Identify normal force, shear force, and bending moment on cross section via centroidal axis.

Explore analysis of internal forces in coplanar loads, including normal force, shear force, and bending moment, deriving expressions for statically determinate beams using sign conventions and diagrams.

explores friction as a restricting force between contacting surfaces, detailing static and dynamic dry friction, coefficient of friction mu_s and mu_k, and the angle of repose with free-body problem solving.

Explore centroid as the center of area, independent of mass, located on symmetry axes to determine moment of inertia. Learn methods: geometrical concentration, method of moments, and integration for curves.

Compute centroids of areas using the method of moments and integration, obtaining x-bar and y-bar for plane shapes, including rectangles, triangles, circles, ellipses, parabolas, quarter circles, and semicircular regions.

Explore the moment of inertia and area moment of inertia, including the perpendicular axis theorem, parallel axis theorem, radius of gyration, and compute I for rectangular, triangle, and circle areas.

Explore the fundamentals of mechanics of materials, defining stress and strain, analyzing axial, torsional, and combined loads, and distinguishing tensile and compressive states.

Analyze bar behavior under tension and compression, examine stress–strain relationships, and apply Hooke's law to relate stress, strain, and the modulus of elasticity.

Explore Poisson effects and Poisson's ratio, linking axial and lateral strains under tension or compression, and define the factor of safety as failure load over working load.

Study non-uniform bars by summing segment elongations to get displacement, using delta = P L /(E A) for each segment with F_AB = P1 and F_BC = F1 + F2.

Extend non-uniform bar analysis to piecewise and continuously varying sections using the elongation integral ΔL = ∫_0^L dx/(E A); a linearly varying diameter example illustrates the method.

Explore statically indeterminate bars by comparing determinate and indeterminate cases, introduce releasing an axis and using compatibility equations to solve for unknown reactions and internal forces.

Examine how temperature changes cause expansion or contraction, producing thermal strains and stresses, using alpha, L, and d, and apply compatibility to solve for R.

Explore shear stress, defined as force parallel to a surface per unit area, compare average and maximum values, and discuss bolt bearing and double-shear connections.

Analyze how an inclined load on a prismatic bar induces normal and shear stresses on a plane, by decomposing the force into normal and parallel shear components.

Explain how shear stress causes shear strain via Hooke's law in shear and the shear modulus G, and outline bearing stress and the factor of safety for bolt connections.

Explore the mechanical behavior of a shaft under torque, focusing on shear stress, shear strain, the angle of twist, and uniform versus non-uniform torsion.

Study the mechanical behavior of a shaft by applying Hooke's law to normal and shear stresses, and relate shear stress to gamma via the modulus of elasticity.

Explore the shear stress in shafts versus bars, contrasting tensile stresses in bars with shear stresses in shafts, and review the similarities and differences through a comparative equations table.

Explore non-uniform shafts with changing cross sections or materials; determine total twist, internal torques, and maximum shear stress via torsion relations.

Analyze non-uniform shafts where torque and cross-section vary along x, derive the twist by integrating torque over the polar moment of inertia, and examine thin-tube and distributed-torque cases.

Study pure shear in a shaft element, derive the relation between shear stress and shear strain, and relate them through the shear modulus of elasticity g to deformation.

Solve torque problems on circular shafts by calculating polar moment of inertia, maximum shear stress, and shear strain using G, then compute inner and outer stresses and rotation under distributed torque.

Explore how to construct shear force and bending moment diagrams for statically determinate beams, using equilibrium, cross-sections, and sign conventions for shear and moment.

Explore how shear force and bending moment vary along a beam under distributed and concentrated loads, using small-beam equilibrium and noting jumps in shear and moments at load locations.

Explores how to construct shear force and bending moment diagrams for beams, applying rules for distributed and concentrated loads, and demonstrates with cantilever and simply supported examples.

Analyze shear force and bending moment diagrams for various beams using free body diagrams, equilibrium, and region-based equations to plot and interpret reactions, loads, and moments.

Study beam deflection and curvature in a simply supported beam under bending, including deflection U(x), radius of curvature ρ, curvature κ, and neutral axis with strain ε = −κ y.

Derive the flexure formula for beam bending, showing normal stress varies linearly with y, zero at the neutral axis (centroid), with top compression and bottom tension, via the moment-curvature relation.

analyze shear stresses in beams and derive the shear stress distribution over a rectangular cross section from shear force and bending moment, using the moment of area q.

Explore how plane-stress conditions transform normal and shear stresses across any angle theta using the x1, y1 axes and principal directions. Identify principal stresses, directions, and maximum shear stress.

Study dynamics as motion and its causes, compare kinematics and kinetics, and identify rectilinear, curvilinear, rotational, and general plane motion with displacement, velocity, and acceleration.

Apply the equations of motion to vertical motion under gravity using g = -9.8 m/s^2, calculating time to max height and the maximum height reached for a 15 m/s throw.

Analyze motion with varying acceleration using differential and integral equations of motion. Solve for velocity, displacement, and acceleration in straight-line motion given initial conditions and time-dependent acceleration.

Explore motion curves that link displacement, velocity, and acceleration with time, and use the area under velocity-time and acceleration-time graphs to compute displacement and velocity changes.

Explore curvilinear motion by detailing position, velocity, and acceleration in vector form, with velocity tangent to the path and rectangular components vx, vy, ax, ay.

Explore projectile motion in mechanical engineering dynamics, including trajectory, velocity of projection, angle of projection, time of flight, range, maximum height, and horizontal and vertical components forming a parabola.

Explore relative motion of particles with respect to moving reference frames and derive relative velocity and acceleration along straight and right-angled paths.

Address constrained motion with a constant cable length, derive v_a = -2 v_b and a_a = -2 a_b, and compute v_a = -7 m/s and a_a = 1.2 m/s^2.

Apply d'Alembert's principle to convert a dynamic problem into a static one by adding inertia force, then solve for P with friction coefficient 0.24 to get about 381 N.

Apply the work-energy approach to solve kinetic problems, derive work as force times distance, relate to kinetic energy change, and review impulse and momentum conservation with a worked example.

Explains springs as elastic bodies that distort under load, store energy, and cushion or control motion; introduces helical, conical, torsion, leaf, and disc springs and common spring materials.

Explore shear stress in helical springs, covering solid length, free length, spring index, pitch, and stiffness, and solve practical problems on torsion, axial loading, energy storage, and series-parallel configurations.

Understand cam and follower systems, including plate disc cams and cylindrical drums, and compare translating, pivoted, inline, and offset followers with roller, knife-edge, flat-faced, and spherical-faced contacts.

Explore the design and materials of bushings and roller bearings, including solid, split, and flange bushings, and learn about oil groove patterns and lubrication classes for journal bearings.

Explore rolling contact bearings, or antifriction bearings, using balls or rollers between hardened raceways to carry radial and thrust loads; learn ball and roller types, lubrication, and material properties.

Explore how power transmission links shafts with belts, rope, chain, and gears, comparing flexible and rigid connections and how pulley diameter, belt type, and slip affect speed and torque.

Learn how open belt drives keep shafts rotating in the same direction and cross belt drives reverse rotation; derive belt length formulas, tension relations, and power transmission.

Explore chain drive as a belt-slip solution with constant velocity ratio and lubrication. Learn pitch, pitch circle, chain length formula L, and chain types including block and roller.

Master gear drive fundamentals by examining gear types—spur, helical, bevel, hypoid, worm—and exploring involute and cycloidal teeth with pitch circle, addendum, module, and gear ratio.

Explore gear trends that transfer power between shafts, including simple, compound, reverted, planetary and sun and planet gear trains, and learn how to calculate output speeds in rpm.

Study how friction transmits torque by engaging and disengaging the driving and driven shafts through clutches, including single plate, multi-plate, conical, and centrifugal types.

Explore brake types such as block or shoe, band, and internal expanding shoe brakes, their lever-pivot operation, friction materials, and how leading and trailing shoes influence braking torque.

Explore fluid mechanics, including statics, kinematics, dynamics, hydrodynamics, hydraulics, gas dynamics, and aerodynamics, and apply these concepts to pumps, turbines, airplanes, ships, and more.

Explore fluid properties, including density, specific weight, pressure, and specific gravity, then examine viscosity, shear stress, Newton's law of viscosity, and dynamic versus kinematic viscosity.

Explore surface tension as a stretched elastic membrane from intermolecular attraction, its relation to surface energy, and the droplet pressure P = 4 sigma / d.

Explore capillarity, where liquid rises or falls in a capillary tube, governed by surface tension, density, gravity, contact angle, and tube diameter.

Understand how fluid pressure acts equally in all directions in a stationary fluid, as per Pascal's law, by analyzing a tiny fluid element in equilibrium.

Derive hydrostatic law by analyzing a small fluid element to show pressure increases with depth at the fluid's weight density, illustrating the hydrostatic paradox and p = ρ g h.

Explore hydrostatic forces on submerged surfaces in static fluids, calculating total pressure and center of pressure. Learn about area moments, centroid, and pressure distribution for horizontal and vertical planes.

Explore buoyancy and flotation by examining how a body immersed in a fluid experiences an upward buoyant force equal to the weight of displaced fluid, per Archimedes principle.

Explore meta centric height GM to evaluate floating body stability. Learn analytical and experimental methods to compute BM, BG, and center of buoyancy shifts during small tilts.

Explore atmospheric, absolute, gauge, and vacuum pressures, and learn how barometers and manometers measure pressure with piezometers and u-tube configurations, including practical example calculations.

Study single column manometers, vertical and inclined, and how reservoir area enables pressure measurement from a single reading; compare differential and compound manometers and gauge types.

Study liquids in relative equilibrium under horizontal acceleration, where the free surface inclines and pressure follows hydrostatic distribution, with tan alpha equal to a over g.

Study an open tank under constant vertical acceleration, yielding a linear pressure distribution and p = rho g h (1 ± a/g); pressure vanishes when a = g.

Analyze how an open tank's liquid surface tilts under acceleration along an inclined plane, deriving tan alpha equals a_x/(g ± a_y) from surface equilibrium.

Liquid in a rotating open cylinder forms a concave paraboloid; surface follows y = ω^2 x^2/(2g). For a 2 m diameter, 3 m depth tank, max speed is 59.82 rpm.

Analyze the geometry of fluid motion: displacement, velocity, and acceleration, without forces; express velocity as a function of space and time with components u, v, w and its magnitude.

Explore how streamlines, stream tubes, path lines, straight lines, and time lines describe fluid flow, including steady versus unsteady patterns and the differential relations dx/u = dy/v = dz/w.

Explore the continuity equation and discharge, defined as q = A v, and see how mass conservation yields m1 = m2 and a1 v1 = a2 v2 for incompressible flows.

Explore steady and unsteady flow, laminar and turbulent regimes, and see how Reynolds number links pipe diameter, velocity, density, and viscosity to transition.

Explore rotation and spinning of a liquid in flow, deriving angular velocities and vorticity, and compare forced vortex flow with irrotational free vortex flow, including natural vortices like hurricanes.

Describe how circulation around a closed curve equals the surface integral of vorticity via Stokes theorem, with CCW positive and implications for flow in impellers and wings.

Explore fluid dynamics by applying Newton's second law to a control volume, deriving energy heads—potential, kinetic, and pressure—and analyzing forces, Euler's, Reynolds, and Navier–Stokes equations.

Apply Newton's second law to a small fluid element along a streamline under steady, ideal, frictionless, zero-viscosity flow, balancing pressure forces and gravity to derive Euler's equation of motion.

Explain Bernoulli's equation for steady, incompressible, ideal flow along a streamline, with pressure, kinetic, and potential heads, and apply it to ducts and flow meters.

Explore the practical use of Bernoulli's equation in measuring flow with a venturi meter, including discharge calculation, head loss, and the role of differential manometers.

Explore Bernoulli's equation applications using pitot tubes to measure flow velocity via stagnation and static pressures. Calibrate with piezometers and manometers to determine velocity head, static head, and stagnation pressure.

Analyze how a free liquid jet exits a nozzle and travels in a parabolic trajectory under gravity. Compute maximum height, time of flight, and horizontal range from the given formulas.

This lecture analyzes a free liquid jet's parabolic trajectory under gravity, with horizontal velocity v cos alpha and vertical velocity v sin alpha, deriving height, time of flight, and range.

Apply the impulse momentum equation, based on Newton's second law, to steady fluid flow and compute forces on pipe bends, vanes, and jets using mass flux.

Explore flow through orifices and mouthpieces, including circular shapes and sharp-edge configurations, and apply Bernoulli’s equation to relate head, vena contracta velocity, and CD, CV, CC.

Analyze discharge through large rectangular and submerged orifices. Derive expressions from head differences H1 and H2, width b, and Cd, and apply Bernoulli for fully and partially submerged cases.

Determine time to empty a tank through an orifice by equating discharge to volume loss and integrating from h1 to h2 for constant-area and hemispherical tanks, using A and a.

Explore laminar (viscous) flow and how viscosity creates shear stresses, and learn how Reynolds number governs laminar, transitional, and turbulent regimes with thresholds <2000, 2000-4000, >4000.

Explain the Navier-Stokes equations for constant viscosity and density, deriving the balance of pressure, body, and viscous forces on a three-dimensional fluid element to analyze viscous flows.

Explore laminar flow in circular pipes through Hagen-Poiseuille theory. Derive shear stress distribution, parabolic velocity profile, and use pressure head loss and Darcy–Weisbach (Fanning) relations to solve an example.

Explore turbulent pipe flow, where Reynolds number exceeds 4000, creating irregular motion and mixing; learn to quantify head loss with the Darcy-weisbach equation, hydraulic radius, and friction factor.

Analyze internal flow through pipes, evaluating major and minor energy losses due to friction and fittings, and apply Darcy-Weisbach, Chezy, Manning, and Hazen-Williams formulas to compute head loss.

Explore how hydraulic turbines convert hydraulic energy into mechanical energy, detailing impulse turbines, nozzles and vanes, and the hydroelectric plant layout with dam, head, penstocks, and tailrace.

Study the Pelton turbine, a tangential flow impulse machine for high heads, detailing the penstock, spur-nozzle control, double-bucket runner with splitters, and jet deflection for maximum momentum change.

Explore velocity triangles in a Pelton turbine, including inlet and outlet jet velocities, bucket deflection, and the design notes for efficiency optimization and jet layout.

Compute the power at the nozzle and the hydraulic efficiency of a Pelton turbine from head, discharge, bucket speed, and jet velocity using the coefficient of velocity and deflection angles.

Explore how the Francis turbine, a mixed-flow reaction turbine, converts water pressure and velocity into shaft power, detailing penstock, scroll casing, stay and guide vanes, runner, and draft tube.

Explore the Francis turbine, an inward radial flow reaction turbine with radial discharge, analyzing velocity triangles at inlet and outlet, discharge, angular momentum, torque, work, and hydraulic efficiency.

Explore axial flow reaction turbines, notably propeller and Kaplan types, where water flows parallel to the shaft and energy transfers from pressure to kinetic energy, with fixed or variable-pitch blades.

Classify pumps into rotodynamic and positive displacement, detailing centrifugal, axial, and mixed flow rotodynamic types, plus reciprocating and rotary positive displacement pumps.

Explore the centrifugal pump, its impeller and casing types (volute, vortex, diffuser), and how centrifugal action converts kinetic energy into pressure.

Explore reciprocating pumps, positive displacement machines that use a crank and piston to draw in and push out liquid via suction and delivery strokes, with single-acting and double-acting configurations.

Explore rotary positive displacement pumps, including vane, lobe, gear, screw, and axial piston pumps, and learn how their rotors, vanes, lobes, gears, and swash plates create suction and discharge flow.

Explore thermodynamics as the science of energy transfer and its effect on substances, with macroscopic and microscopic perspectives, and define systems, boundaries, and the three types closed, open, isolated.

Define thermodynamic equilibrium across mechanical, chemical, and thermal types, explain diathermic walls, and illustrate quasi static (reversible) processes, plus the zeroth law and its role in temperature measurement.

Learn how work transfers energy in thermodynamics, with positive sign for work by the system and displacement work ∫ p dv. Distinguish point functions from path functions.

Explore temperature scales like Celsius and Kelvin and the thermodynamic temperature concept. Analyze internal energy U, enthalpy H = U + PV, Cp and Cv, and heat and work conventions.

The first law of thermodynamics links heat and work, showing that for a cycle the net heat supplied equals the net work done, since energy is conserved and constant.

Learn the first law of thermodynamics and isolated systems, where energy is constant with DQ = 0 and w = 0, and the perfect gas equation pv = nrt.

Define specific heats for solids, liquids, and gases; use dq = m c dT and distinguish cp and cv for constant pressure and constant volume, especially for a perfect gas.

This lecture presents Joule's law for a perfect gas, showing internal energy varies linearly with absolute temperature and equals m cv T.

Derive the relationship between cp and cv for a perfect gas, showing cp minus cv equals r and gamma equals cp over cv.

Define enthalpy as sum of internal energy and pressure-volume, H = U + P V = m h, and gamma = c_p / c_v > 1 for a perfect gas.

Apply the first law to closed systems, deriving heat and work for isochoric, isobaric, isothermal, adiabatic, and polytropic processes with pV^gamma and related relations.

Apply the first law to steady flow open systems, derive the steady flow energy equation, and use mass continuity with enthalpy, internal energy, and flow work.

Explore steady flow energy equation applications in turbines, pumps, compressors, boilers, condensers, evaporators, and nozzles, highlighting energy transformations and zero heat with sign conventions.

Explore the second law of thermodynamics, contrasting heat and work, and analyze heat engines, refrigerators, and Carnot cycles to understand entropy and irreversibility.

Explore power plant engineering across thermal, hydroelectric, nuclear, diesel, tidal, and geothermal systems; learn how coal and gas plants generate electricity with turbines, condensers, and generators, while exploring non-conventional sources.

Explore steam generators, including fire-tube and water-tube boilers, internal and external firing, and heat transfer from fuel to water, with Cochran, Lancashire, Cornish, and locomotive examples.

Explore boiler mountings that regulate safety and steam generation, including deadweight, spring-loaded, and lever safety valves, water level indicators, pressure gauges, feed and stop valves, and blow-down operations.

Explore boiler accessories such as economizers and heat exchangers reclaiming waste heat from flue gas to feedwater, plus air preheaters, superheaters, feed pumps, injectors, steam separators, and pressure reducing valves.

Discover how internal combustion engines power vehicles, comparing gasoline and diesel operation, and explore core components such as the cylinder block, piston, four-stroke cycle, valvetrain, and manifolds.

Examine automotive engine systems, including lubrication, cooling, fuel and air, emission control, exhaust, and ignition. Learn how oil flow, coolant, fuel delivery, and crankshaft sensor timing keep engines running efficiently.

Explore starting and charging systems that energize the engine. Understand electronic engine control, OBD II diagnostics, and how heating and air conditioning enhance comfort and efficiency.