(a) An SI engine working on the Otto cycle has cylinder bore of 210 mm and stroke length of 240 mm. The clearance volume is 1550 cc. The pressure and temperature at the beginning of compression are 1 bar and 17 °C respectively. The maximum pressure o

Question

(a) An SI engine working on the Otto cycle has cylinder bore of 210 mm and stroke length of 240 mm. The clearance volume is 1550 cc. The pressure and temperature at the beginning of compression are 1 bar and 17 °C respectively. The maximum pressure of the cycle is 50 bar. Determine the pressure and temperature at the salient points in the cycle, the air-standard efficiency, the work done and the mean effective pressure. Show the cycle on P-v and T-s diagrams. Evaluate the fuel consumption in kg/kWh, if the calorific value of the fuel is 40 MJ/kg.

Take Cp and Cv of air as 1·005 kJ/kg-K and 0·718 kJ/kg-K respectively.

(b) Air flowing at the rate of 100 m³/min at 40 °C DBT and 50% RH is mixed with another stream of air flowing at the rate of 20 m³/min at 26 °C DBT and 50% RH. The mixture flows over a cooling coil whose ADP temperature is 10 °C and bypass factor is 0·2. Find the DBT and RH of air leaving the coil. If this air is supplied to an air-conditioned room, where DBT of 26 °C and RH of 50% are maintained, then calculate the (i) room sensible heat factor and (ii) coil cooling capacity in tons of refrigeration.

Draw a schematic diagram of the system and show all the processes on a skeleton psychrometric chart.

Psychrometric chart is given.

(c) A process industry employs a medium pressure boiler to produce steam. The mass flow rate of fuel consumed is 0·847 kg/s and c.v. of the fuel is 44 MJ/kg. For efficient combustion, 16 kg of air per kg of fuel is required, for which a draught of 30 mm of the water column is required at the base of the chimney. The flue gases leave the boiler at 350 °C. The average temperature of gases in the stack may be taken as 300 °C. The atmosphere is at 20 °C.

Assuming the velocity of gases at the stack exit to be negligible, determine the height of the stack and the diameter at its base.

Also, calculate the mass flow rate of the gases.

Take Patmosphere = 101·3 kPa, Rair = Rgases = 0·287 kJ/kg-K, g = 9·81 m/s²,

ρwater = 1000 kg/m³.

UPSC Answer Check · Accepted Answer

Calculate systematically across all three sub-parts: spend ~40% time on (a) Otto cycle (highest computational load with multiple salient points, efficiency, work, MEP and fuel consumption), ~35% on (b) psychrometric mixing and cooling coil analysis (requires chart reading and bypass factor application), and ~25% on (c) chimney draught and stack design (natural draught formula with temperature-dependent density). Present each part with clear headings, state assumptions, show all formulae with substitutions, and conclude with labelled diagrams as demanded.
- Part (a): Compression ratio r = (V_s + V_c)/V_c = 6.32; T2 = 562 K, p2 = 12.6 bar; T3 = 2233 K after heat addition; T4 = 1125 K, p4 = 3.97 bar; η_otto = 51.1%; W_net = 287 kJ/kg; MEP = 4.52 bar; fuel consumption = 0.202 kg/kWh
- Part (b): Mixing line on psychrometric chart yields mixture at ~37°C DBT, 50% RH; after cooling coil with BPF=0.2, outlet DBT = 15.4°C, RH ~95%; room SHF = 0.82; coil cooling capacity = 8.6 TR
- Part (c): Chimney height H = 42.3 m using draught equation Δp = gH(ρ_a - ρ_g); base diameter D = 1.85 m from continuity with mass flow; mass flow rate of flue gases = 14.4 kg/s
- P-v and T-s diagrams for Otto cycle with all four states labelled and heat/work arrows indicated; skeleton psychrometric chart showing mixing, cooling coil process, and room condition line
- Correct application of isentropic relations pV^γ = constant and T2/T1 = (V1/V2)^(γ-1) for Otto cycle; use of psychrometric relations ω = 0.622p_v/(p-p_v) and bypass factor definition
- Unit consistency throughout: pressures in bar or kPa, temperatures in K for calculations, specific volumes in m³/kg, mass flow rates in kg/s or kg/min as appropriate

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	2	Correctly applies isentropic process relations for Otto cycle (a), uses psychrometric chart principles and bypass factor correctly for coil analysis (b), and applies natural draught equation with proper temperature-dependent gas densities for chimney (c); identifies γ = Cp/Cv = 1.4 for air.	Uses correct basic formulae but makes minor errors in applying isentropic exponent or confuses BPF with contact factor; draught equation correct but uses atmospheric density instead of average stack temperature for gas density.	Treats Otto cycle as Diesel cycle or uses wrong compression ratio formula; confuses DBT with WBT in psychrometrics; applies Bernoulli instead of hydrostatic draught equation for chimney.
Numerical accuracy	20%	2	All salient point values within 2% of expected: T2≈562K, T3≈2233K, T4≈1125K, η≈51%, MEP≈4.5 bar; mixture condition and coil outlet within chart precision; chimney height ≈42m, diameter ≈1.8m; fuel consumption 0.20-0.21 kg/kWh.	Correct methodology but arithmetic slips leading to 5-10% deviation in key values; correct final answers for some parts but errors in intermediate states affecting subsequent calculations.	Order-of-magnitude errors (e.g., T3 in hundreds instead of thousands K); wrong compression ratio leading to completely wrong efficiency; chimney height off by factor of 2 or more.
Diagram quality	20%	2	Clear P-v and T-s diagrams for Otto cycle with all four states labelled, isentropic curves shown, heat addition and rejection indicated; neat psychrometric skeleton showing mixing point M, cooling coil process line to ADP and outlet, room condition R; schematic of AC system with components labelled.	Diagrams present but missing labels for some states or incorrect curve shapes (e.g., straight lines instead of curves for isentropes); psychrometric chart shows processes but mixing point approximate.	No diagrams despite explicit demand; or diagrams drawn without any labels; or completely wrong diagrams (e.g., Diesel cycle instead of Otto cycle).
Step-by-step derivation	20%	2	Shows all formulae with symbols first, then numerical substitution: swept volume calculation, compression ratio, isentropic relations with γ=1.4; psychrometric property calculations with steam table interpolation; draught equation derived from hydrostatic pressure balance with density as p/RT.	Shows key steps but skips some intermediate derivations (e.g., jumps from T2 to T3 without showing heat addition calculation); some formulae quoted without derivation.	Final answers only with no working; or working so disorganized that logic cannot be followed; missing critical steps like unit conversions or temperature conversions.
Practical interpretation	20%	2	Comments on practical significance: for (a) compares η_otto≈51% with real SI engine efficiency (~25-30%) due to losses; for (b) notes high humidity at coil outlet and need for reheat; for (c) discusses stack thermal efficiency and pollution dispersion implications for Indian industrial boilers.	Brief mention of practical relevance for one part but not others; or generic statements without specific connection to calculated values.	No interpretation; treats entire problem as abstract mathematics with no engineering context; fails to note that calculated fuel consumption is idealized vs actual.

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