BT-203 Basic Mechanical Engineering - Dec 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 8 Marks
   aDefine Hardness? Explain the Brinell Hardness test method in details?
   How to answer

   • Define hardness as resistance to indentation, abrasion, or scratching
   • Describe the Brinell Hardness test apparatus (indenter ball, applied load)
   • State the procedure for applying load and measuring indentation diameter
   • Give the formula for Brinell Hardness Number: $BHN = \frac{2P}{\pi D (D - \sqrt{D^2 - d^2})}$
   • Mention typical indenter diameters and test materials
2. 6 Marks
   bDefine the following mechanical properties: i) Strength ii) Ductility
   How to answer

   • Definition of strength: ability of a material to resist deformation or failure under external load
   • Types of strength (tensile, compressive, shear, yield, ultimate)
   • Definition of ductility: ability to undergo permanent tensile deformation before fracture (drawing into thin wires)
   • Measure of ductility: percentage elongation and reduction in area
3. 8 Marks
   aA mild steel specimen with an original diameter of $10\text{ mm}$ and a gauge length of $50\text{ mm}$ was found to have an ultimate load of $60\text{ kN}$ and breaking load of $40\text{ kN}$. The gauge length at rupture was $55\text{ mm}$ and diameter at rupture cross-section was $8\text{ mm}$. Determine: i) The ultimate stress ii) Breaking stress iii) True breaking stress iv) Percentage elongation
   How to answer

   • Calculate original area $A_0 = \frac{\pi}{4}(10)^2 = 78.54\text{ mm}^2$ and neck area $A_f = \frac{\pi}{4}(8)^2 = 50.27\text{ mm}^2$
   • Ultimate stress $= \frac{60 \times 10^3}{78.54} = 763.94\text{ N/mm}^2$ (MPa)
   • Breaking stress (nominal) $= \frac{40 \times 10^3}{78.54} = 509.30\text{ N/mm}^2$ (MPa)
   • True breaking stress $= \frac{40 \times 10^3}{50.27} = 795.77\text{ N/mm}^2$ (MPa)
   • Percentage elongation $= \frac{55 - 50}{50} \times 100 = 10\%$
4. 6 Marks
   bWith a neat sketch, explain the following lathe operations: i) Facing ii) Knurling
   How to answer

   • Explanation of facing: machining the end face of a workpiece flat and perpendicular to the axis of rotation
   • Sketch of facing operation showing tool motion perpendicular to the lathe axis
   • Explanation of knurling: process of producing a rough, patterned surface (diamond or straight) for better grip
   • Sketch of knurling operation showing revolving workpiece and knurling tool
5. 8 Marks
   aDiscuss the application vernier caliper and its method of measurement.
   How to answer

   • Applications of vernier caliper: measuring external diameter, internal diameter, length, and depth
   • Components: main scale, vernier scale, jaws, depth probe
   • Concept and formula of least count: $\text{LC} = 1\text{ MSD} - 1\text{ VSD}$
   • Method of measurement: Total Reading = Main Scale Reading + (Vernier Scale Reading $\times$ Least Count) $\pm$ Zero Error
6. 6 Marks
   bExplain the method of using Sine Bar with neat sketch.
   How to answer

   • Working principle based on trigonometry: $\sin \theta = \frac{h}{L}$
   • Setup components: sine bar of length $L$, rollers, slip gauges of height $h$, surface plate, dial indicator
   • Step-by-step measurement procedure for finding unknown angle/taper
   • Neat sketch showing sine bar inclined on slip gauges over a surface plate
7. 8 Marks
   aThe water is flowing through a pipe having diameters $30\text{ cm}$ and $20\text{ cm}$ at two sections 1 and 2, respectively. The rate of flow through the pipe is $80\text{ liters/sec}$. Section 1 is $8\text{ m}$ above the datum and section 2 is $5\text{ m}$ above the datum. If the pressure at section 1 is $4\text{ bar}$, find the intensity of pressure at section 2.
   How to answer

   • Convert units: $D_1=0.3\text{ m}$, $D_2=0.2\text{ m}$, $Q=0.08\text{ m}^3/\text{s}$, $P_1 = 4 \times 10^5\text{ N/m}^2$, $\rho = 1000\text{ kg/m}^3$
   • Calculate areas: $A_1 = \frac{\pi}{4}(0.3)^2 = 0.0707\text{ m}^2$, $A_2 = \frac{\pi}{4}(0.2)^2 = 0.0314\text{ m}^2$
   • Calculate velocities: $V_1 = \frac{Q}{A_1} = 1.132\text{ m/s}$, $V_2 = \frac{Q}{A_2} = 2.546\text{ m/s}$
   • Apply Bernoulli's equation: $\frac{P_1}{\rho g} + \frac{V_1^2}{2g} + Z_1 = \frac{P_2}{\rho g} + \frac{V_2^2}{2g} + Z_2$
   • Solve for $P_2$: $\frac{P_2}{\rho g} = \frac{4 \times 10^5}{1000 \times 9.81} + \frac{1.132^2}{2 \times 9.81} + 8 - \frac{2.546^2}{2 \times 9.81} - 5$
   • Compute $P_2 \approx 4.29\text{ bar}$ ($4.29 \times 10^5\text{ N/m}^2$)
8. 6 Marks
   bWhat is priming? Why is it required in a centrifugal pump?
   How to answer

   • Define priming: the process of filling the suction pipe, casing, and delivery valve up to delivery pipe with liquid before starting
   • Explain reason for necessity: density of air is very low compared to water, so head generated with air is negligible ($h = \frac{P}{\rho g}$)
   • Explain that the resulting pressure rise is insufficient to lift liquid from the sump
   • Consequence of not priming: pump will run dry, overheat, and fail to discharge water
9. 8 Marks
   aExplain the working and construction of single acting reciprocating pump with neat sketch?
   How to answer

   • Main components: cylinder, piston/plunger, piston rod, connecting rod, crank, suction valve, delivery valve
   • Suction stroke operation: piston moves away from cylinder head creating vacuum, opening suction valve and drawing liquid
   • Delivery stroke operation: piston moves toward cylinder head, pressurizing liquid, closing suction valve, opening delivery valve
   • Neat sketch showing cylinder, piston, crank-connecting rod mechanism, suction and delivery pipes with non-return valves
10. 6 Marks
    bDiscuss the concept of thermal equilibrium and state zeroth law of thermodynamics?
    How to answer

    • Define thermal equilibrium: condition where two bodies in contact reach the same temperature and no net heat flow occurs
    • State Zeroth Law: if two bodies A and B are each in thermal equilibrium with a third body C, then A and B are in thermal equilibrium with each other
    • Significance: provides the basis for temperature measurement and thermometer operation
    • Simple illustrative diagram showing bodies A, B, and C
11. 8 Marks
    aExplain the construction and working of Babcock and Wilcox boiler with a neat sketch.
    How to answer

    • Classification: water tube, horizontal, externally fired, natural circulation boiler
    • Main constructional parts: steam and water drum, inclined water tubes ($15^\circ$), uptake and downtake headers, mud box, furnace, baffles, superheater
    • Working: water circulates naturally due to density difference; hot flue gases pass over tubes directed by baffles; steam collects in drum
    • Neat schematic sketch labeling drum, tubes, headers, baffles, and path of flue gases
12. 6 Marks
    bState the Kelvin-Planck and the Clausius statements of the second law of thermodynamics. Explain the equivalence of Kelvin-Planck and Clausius statements.
    How to answer

    • State Kelvin-Planck statement: impossible to construct a device operating in a cycle that produces no effect other than heat extraction from a single reservoir and doing an equivalent amount of work
    • State Clausius statement: impossible to construct a device operating in a cycle that transfers heat from a lower-temperature reservoir to a higher-temperature reservoir without external work
    • Prove violation of Clausius statement leads to violation of Kelvin-Planck statement (combining refrigerator violating Clausius with heat engine)
    • Prove violation of Kelvin-Planck statement leads to violation of Clausius statement (combining heat engine violating Kelvin-Planck with refrigerator)
    • Block diagrams illustrating both equivalence cases
13. 8 Marks
    aExplain the structure and working of four-stroke petrol engine with a neat sketch.
    How to answer

    • Major components: cylinder, piston, spark plug, inlet valve, exhaust valve, connecting rod, crankshaft
    • Four strokes explained: 1) Suction (intake of air-fuel mixture), 2) Compression (isentropic compression of charge), 3) Power/Expansion (ignition by spark and power delivery), 4) Exhaust (burnt gases expelled)
    • Valve timing / positions of valves and piston motion during each stroke
    • Neat sketches showing the piston, valves, and spark plug for each of the four strokes
14. 6 Marks
    bWrite short notes on surging, choking and stalling.
    How to answer

    • Surging: unsteady, pulsating flow in compressor due to flow reversal at low mass flow rates and high pressure ratios; leads to severe vibration
    • Choking: condition of maximum possible mass flow rate through the compressor when Mach number reaches 1 at the throat/passage
    • Stalling: aerodynamic flow separation from blade surfaces due to excessive angle of attack or low mass flow rate, leading to loss of pressure rise
    • Characteristic performance curve showing regions of surging, stall, and choke
15. 14 Marks
    Write Short note on any two: a) Hooks law and modulus of elasticity b) Micrometer c) Newton's law of viscosity d) Natural and artificial draught
    How to answer

    • Hooke's Law & Modulus: Stress $\propto$ Strain within elastic limit ($\sigma = E\epsilon$), types of moduli ($E$, $G$, $K$)
    • Micrometer: screw-nut principle, pitch, least count calculation, barrel and thimble scales
    • Newton's Law of Viscosity: shear stress directly proportional to rate of shear strain ($\tau = \mu \frac{du}{dy}$), definition of dynamic viscosity
    • Draught: definition (pressure difference to supply air/remove flue gases); natural draught by chimney; artificial draught (forced, induced, balanced) by fans