Q1 50M Compulsory solve Thermodynamics, gas dynamics, heat transfer, heat exchangers
(a) A 50 kg block of iron at 500 K is placed into open atmosphere which is at a temperature of 285 K. The iron block eventually reaches thermal equilibrium with the atmosphere. Assuming an average specific heat of 0·45 kJ/kg-K for iron, determine the (i) entropy change for the iron block and the atmosphere, and (ii) irreversibility. (10 marks)
(b) Show that for normal shock in a perfect gas, M*ₓ M*ᵧ = 1. (10 marks)
(c) In the axial flow compressor, for 50% reaction, the blading design is sometimes called symmetrical blading. Explain, with proper equations and justification, why it is called so. (10 marks)
(d) An industrial furnace (blackbody) is emitting radiation at 2700 °C. Calculate the following: (i) Spectral emissive power at λ = 1·2 μm, (ii) Wavelength at which the emissive power is maximum, (iii) Maximum spectral emissive power, (iv) Total emissive power. Use Planck's distribution law equation given below: $$E_{b\lambda} = \frac{C_1}{\lambda^5 \left[\exp(C_2/\lambda T)-1\right]}$$ where $C_1 = 3.742 \times 10^8$ W-μm⁴/m², $C_2 = 1.438 \times 10^4$ μm-K. Take $\sigma = 5.67 \times 10^{-8}$ W/m²-K⁴. (10 marks)
(e) (i) Write down the basic assumptions for LMTD method in case of heat exchanger analysis. (5 marks)
(ii) Write down in which case LMTD method and in which case NTU method will be applicable in basic heat exchanger analysis. (5 marks)
Answer approach & key points
Solve each sub-part systematically with clear section headings. For (a), apply entropy balance for irreversible heat transfer to surroundings; for (b), derive the characteristic Mach number relation using normal shock relations; for (c), prove symmetrical velocity triangles using reaction definition; for (d), apply Planck's law and Wien's displacement law with proper unit conversions; for (e), state LMTD assumptions and compare method applicability. Allocate time proportionally: ~15% each to (a), (b), (c), (d) and ~20% to (e) combined.
- (a) Entropy change of iron: ΔS_iron = mc ln(T2/T1) = 50×0.45×ln(285/500) = -12.52 kJ/K; heat transfer Q = mcΔT = 4837.5 kJ; ΔS_atm = Q/T_atm = +16.97 kJ/K; S_gen = +4.45 kJ/K; Irreversibility I = T0×S_gen = 285×4.45 = 1268.25 kJ
- (b) Characteristic Mach number M* = V/a* where a* is critical speed of sound; using M*² = [(γ+1)M²]/[2+(γ-1)M²]; apply across normal shock using M_y² = [2+(γ-1)M_x²]/[2γM_x²-(γ-1)]; algebraic manipulation yields M*_x × M*_y = 1
- (c) 50% reaction R = (Δh_rotor)/(Δh_stage) = 0.5 implies equal enthalpy rise in rotor and stator; from velocity triangles, R = 0.5 gives V1 = V3 and V2 = V4 (mirror symmetry); blade shapes are mirror images → symmetrical blading
- (d) T = 2973 K; (i) E_bλ at 1.2 μm using Planck's law = 2.42×10¹⁴ W/m²·μm; (ii) λ_max = 2898/2973 = 0.974 μm (Wien's law); (iii) E_bλ,max using Planck's law at λ_max = 4.10×10¹⁴ W/m²·μm; (iv) E_b = σT⁴ = 3.72×10⁶ W/m²
- (e)(i) LMTD assumptions: steady-state, constant overall heat transfer coefficient U, constant specific heats, no phase change, negligible heat loss to surroundings, counter-flow or parallel-flow configuration
- (e)(ii) LMTD method: suitable when inlet/outlet temperatures are known, design problem; NTU method: suitable when effectiveness is required, rating problem, or when outlet temperatures are unknown
Q2 50M solve Thermodynamics, gas turbine cycles, nozzle flow
(a) A 15 m high cylinder with a cross-sectional area of 0.6 m² contains 3 m³ of liquid water at 25 °C on the top of a thin insulated piston of mass 20 kg. Below the piston, argon gas is at 15 °C with a volume of 3 m³, as shown in the figure. Heat is supplied to argon such that the piston rises and pushes the water out over the top edge. Find the (i) work done (kJ) to remove the whole water from the top of the piston and (ii) heat transferred (kJ) to argon during the process. (iii) Plot the process on P-v diagram for argon. Assume atmospheric pressure (P₀) as 101 kPa, Cᵥ and R for argon as 0·312 kJ/kg-K and 0·2081 kJ/kg-K respectively. The specific volume of water at 25 °C is 0·001003 m³/kg. Neglect piston thickness. (20 marks)
(b) Air at 100 kPa and 290 K enters a gas turbine cycle with two stages of compression and two stages of expansion. This system uses ideal regenerator, reheater and intercooler. The pressure ratio across each stage is 4. 300 kJ/kg of heat is added in combustion chamber and reheater each. The regenerator increases the air temperature by 20 °C. Draw T-s plot and determine the (i) total heat rejected (kJ/kg), (ii) net work output (kJ/kg) and (iii) thermal efficiency of the system. Assume isentropic operation for all compressors and turbines. Take Cₚ of air = 1·005 kJ/kg-K and γ = 1·4. (20 marks)
(c) A convergent-divergent nozzle has a throat area of 250 mm² and an exit area of 500 mm². Air enters the nozzle with a stagnation temperature of 350 K and stagnation pressure of 1 MPa. Determine the maximum flow rate of air through the nozzle and the static pressure, static temperature, Mach number and velocity at the exit from the nozzle. Given γ = 1·4, R = 0·287 kJ/kg-K. Use Gas Table to solve the problem. (10 marks)
Answer approach & key points
Solve all three parts systematically, allocating approximately 40% time to part (a) as it carries the highest marks (20), and 30% each to parts (b) and (c). For (a), establish equilibrium states of argon gas with varying water head; for (b), construct the complete T-s diagram for the modified Brayton cycle with regeneration, reheating and intercooling; for (c), use isentropic flow tables to determine choked conditions and exit properties. Present derivations clearly with state points labelled on all diagrams.
- Part (a): Initial argon pressure = P₀ + (m_piston·g)/A + (ρ_water·g·h_water)/A = 101 + 0.327 + 49.05 ≈ 150.4 kPa; mass of argon calculated using ideal gas law
- Part (a): Work done = ∫P_ext dV = area under P-V curve = P_avg·ΔV + mgh term for water lifting; final answer ~90-95 kJ
- Part (a): Heat transfer using First Law Q = ΔU + W = m·Cv·(T₂-T₁) + W; temperature rise from ideal gas law with variable pressure
- Part (b): T-s diagram shows 6 state points with two isentropic compressions (intercooled), two isentropic expansions (reheated), regenerator heat exchange, and heat addition/rejection
- Part (b): With pressure ratio 4 per stage, overall ratio = 16; regenerator effectiveness implied by 20°C temperature rise; net work and efficiency calculated from enthalpy changes
- Part (c): Check if nozzle choked: A_exit/A* = 2.0 > 1, so subsonic or supersonic solution possible; from gas tables at γ=1.4, A/A*=2.0 gives Mach ~0.3 (subsonic) or ~2.2 (supersonic)
- Part (c): Maximum flow occurs when throat is choked (M=1 at throat); use choked flow equation with stagnation conditions; mass flow rate ~0.45-0.50 kg/s
- Part (c): For supersonic exit solution: static pressure ~0.1 MPa, temperature ~175 K, velocity ~450 m/s; subsonic alternative also acceptable if justified
Q3 50M calculate Heat transfer and thermodynamics
(a) Heat is generated in a stainless steel plate (thermal conductivity = 22 W/m-K) of thickness 1 cm, at a uniform rate of 600 MW/m³. The left side of the plate is maintained at 200 °C and the right side is maintained at 100 °C. What will be the (i) temperature distribution across the plate, (ii) location and value of maximum temperature and (iii) heat flux from both sides of the plate and its direction? Assume one-dimensional, steady-state heat conduction. (20 marks)
(b) A combination of a heat engine driving a heat pump (see the figure) takes waste energy at 50 °C as a source, Q̇W1, to the heat engine rejecting heat at 30 °C. The remainder, Q̇W2, goes into the heat pump that delivers Q̇H at 150 °C. If the total waste energy is 5 MW, find the rate of energy delivered at the higher temperature. Assume heat engine and heat pump as reversible : (20 marks)
(c) A centrifugal compressor delivers 1·25 kg/s of air while running at 6000 r.p.m. The diameters at the inlet and outlet are 0·5 m and 1 m respectively. The power input factor is 1·04, while the slip factor is unity. The power consumed by the compressor is 50 kW. State the type of impeller used, whether forward, radial or backward curved. Draw velocity triangles. Assume no prewhirl at the inlet. (10 marks)
Answer approach & key points
Calculate solutions for all three sub-parts systematically: spend ~40% time on part (a) given its 20 marks, ~35% on part (b) for 20 marks, and ~25% on part (c) for 10 marks. For (a), derive the temperature distribution from the heat conduction equation with internal generation; for (b), apply Carnot efficiency and COP relationships for the reversible heat engine-pump combination; for (c), use Euler's pump equation with slip factor and power input factor to determine impeller type. Present each part with clear headings, governing equations, substitutions, and final answers with units.
- Part (a): Governing equation d²T/dx² + q̇/k = 0 integrated to T(x) = -q̇x²/2k + C₁x + C₂; boundary conditions T(0)=200°C, T(L)=100°C applied to find C₁, C₂
- Part (a): Temperature distribution T(x) = -13.636x² - 954.55x + 200 (x in m, T in °C); maximum temperature location x = -0.035 m (outside plate, so max at left boundary) or recalculated correctly if interior
- Part (a): Heat fluxes q''_L = -k(dT/dx)|_{x=0} and q''_R = -k(dT/dx)|_{x=L} with directions stated (leftward at left face, rightward at right face)
- Part (b): Carnot efficiency η = 1 - T_L/T_H = 1 - 303/323 for engine; COP_HP = T_H/(T_H - T_L) = 423/(423-303) for heat pump; energy balance Q̇_W1 + Q̇_W2 = 5 MW
- Part (b): Work output from engine Ẇ = ηQ̇_W1 drives heat pump; simultaneous solution yields Q̇_H delivered at 150°C
- Part (c): Euler work W = σψu₂²/g where σ=1, ψ=1.04; compare with actual power to find u₂; then tanβ₂ = V_f2/(u₂ - V_w2) to determine blade angle and impeller type
- Part (c): Velocity triangles drawn with inlet radial flow (α₁=90°, V_w1=0) and outlet with calculated blade angle β₂
Q4 50M derive Fluid mechanics and thermodynamics
(a) Considering an ideal, isentropic gas flow through a nozzle, show that choking will occur at Mach number (M) = 1. (20 marks)
(b) Water at 30 °C enters a 1·5 cm diameter horizontal tube with a velocity of 1 m/s. The tube wall is maintained at a constant temperature of 90 °C. Calculate the length of the tube if the exit water temperature is 65 °C. One may assume that the flow is turbulent, fully developed and the internal surface of the tube is smooth.
The properties of water are given:
Thermal conductivity (k) = 0·656 W/m-K
Density (ρ) = 984·4 kg/m³
Kinematic viscosity (ν) = 0·497×10⁻⁶ m²/s
Specific heat (Cp) = 4178 J/kg-K
Prandtl number (Pr) = 3·12
Friction factor (F) = 0·079 (Reynolds number)⁻⁰·²⁵
Reynolds number ≡ ReD
Average Nusselt number (NuD) = [(F/2)(ReD - 1000)Pr] / [1 + 12·7(F/2)¹/²(Pr²/³ - 1)]
Also, calculate the water temperature at the middle of the tube and pressure drop across the tube. (20 marks)
(c) An evacuated 150 L tank is connected to a line flowing air (constant specific heat) at room temperature 25 °C and 8 MPa pressure. The valve is opened, allowing air to flow into the tank until the pressure inside is 6 MPa. At this point, the valve is closed. The filling process occurs rapidly and is essentially adiabatic. The tank is then placed in storage, where it eventually returns to room temperature. What is the final pressure inside the tank? (10 marks)
Answer approach & key points
Derive the choking condition in part (a) by starting from isentropic relations and showing that mass flow rate maximizes at M=1. For part (b), calculate Reynolds number first, then apply the given Nusselt number correlation to find heat transfer coefficient, use the LMTD or energy balance to find tube length, then compute midpoint temperature and pressure drop. For part (c), apply unsteady filling analysis with adiabatic assumption first, then isochoric cooling to find final pressure. Allocate approximately 40% time to (a), 40% to (b), and 20% to (c) based on marks distribution.
- Part (a): Derivation showing d(m_dot)/dM = 0 leads to M=1; area-Mach relation A/A* = (1/M)[(2/(γ+1))(1+(γ-1)M²/2)]^((γ+1)/(2(γ-1)))
- Part (a): Physical explanation that sonic throat is the minimum area where upstream information cannot propagate
- Part (b): Re_D = VD/ν = 1×0.015/(0.497×10⁻⁶) ≈ 30181 (turbulent, valid for correlation)
- Part (b): Application of Gnielinski correlation (given) to find h, then energy balance Q = m_dot×Cp×(T_out-T_in) = h×A_s×LMTD to solve for length L
- Part (b): Midpoint temperature found from exponential temperature profile or iterative energy balance; pressure drop from ΔP = f(L/D)(ρV²/2)
- Part (c): Adiabatic filling gives T_tank = γT_line for ideal gas with constant specific heats; final pressure after cooling p_f = p_tank×(T_room/T_tank)
- Part (c): Final pressure calculation yielding approximately 4.5 MPa (or exact value based on γ=1.4)
Q5 50M Compulsory calculate Thermodynamics and IC Engines
(a) Show in the form of a table, how the increase in the following variables affects (increase or decrease) the ignition delay period of a compression ignition (CI) engine: (i) Self-ignition temperature, (ii) Cetane number, (iii) Compression ratio, (iv) Intake pressure, (v) Intake temperature, (vi) Air-fuel ratio, (vii) Exhaust gas recirculation. (10 marks)
(b) What are the desirable characteristics of an ideal working fluid for vapour power cycle? (10 marks)
(c) What is reheat factor of a steam turbine? Derive an expression to show that the reheat factor is always greater than unity. (10 marks)
(d) Compare vapour compression and vapour absorption refrigeration systems. (10 marks)
(e) Without using psychrometric chart, calculate (i) relative humidity, (ii) humidity ratio, (iii) dew point temperature and (iv) enthalpy of moist air, when DBT is 35 °C and WBT is 23 °C. The barometer reads 755 mm of Hg. Use modified Apjohn equation (take values of pressure in bar): p_v = p'_v - (1.8p(t-t'))/2700 where, p_v = partial pressure of water vapour (w.v.) corresponding to DPT, p'_v = partial pressure of w.v. corresponding to WBT, t = DBT, t' = WBT, p = barometric pressure. Use the properties of water vapour given below: t (°C) | Vapour pressure (bar) ---|--- 10 | 0·012272, 12 | 0·014017, 14 | 0·015977, 16 | 0·018173, 18 | 0·020630, 20 | 0·023373, 22 | 0·026431, 24 | 0·029832, 32 | 0·047552, 34 | 0·053201, 36 | 0·059423. (10 marks)
Answer approach & key points
Begin with part (a) presenting a clear table with seven variables and their effects on ignition delay, citing physical reasoning for each. For (b), enumerate 6-8 desirable characteristics of working fluids with brief justification. Part (c) requires defining reheat factor, then deriving the inequality RF > 1 using T-s diagram and isentropic efficiency concepts. Part (d) should present a structured comparison across 5-6 parameters (energy source, COP, components, applications). Part (e) demands systematic calculation: apply modified Apjohn equation, interpolate vapor pressures, then compute all four psychrometric properties with proper units. Allocate time proportionally: (e) ~25%, (a)-(d) ~18.75% each.
- Table in (a): Self-ignition temp ↑ → delay ↑; Cetane number ↑ → delay ↓; Compression ratio ↑ → delay ↓; Intake pressure ↑ → delay ↓; Intake temp ↑ → delay ↓; Air-fuel ratio ↑ → delay ↑; EGR ↑ → delay ↑
- Part (b): Ideal working fluid characteristics—high critical temp, low triple point, high latent heat, chemically stable, non-toxic, low cost, easy availability (water/steam, ammonia, refrigerants cited)
- Part (c): Reheat factor definition as ratio of cumulative enthalpy drop to single isentropic enthalpy drop; derivation showing RF = Σ(Δh_actual)/Δh_single > 1 due to reheat effect and increasing isentropic efficiency at lower pressures
- Part (d): Comparison table covering—energy input (work vs heat), COP range, moving parts, noise, maintenance, suitability for waste heat/remote areas (vapour absorption preferred for solar/EGR applications in Indian context)
- Part (e): Correct application of modified Apjohn equation with p = 1.0066 bar; interpolation for p'_v at 23°C (between 22°C and 24°C); calculation of p_v, then RH, ω, DPT by interpolation, and h = c_p*t + ω*h_g
Q6 50M calculate IC Engine Testing and Steam Turbines
(a) The power output of a six-cylinder, four-stroke CI engine is absorbed by a hydraulic dynamometer for which the law is P = WN/20000, where P is the power in kW, W is the brake load in newton and N is the engine speed in r.p.m. The following observations are made during a test on the engine: Bore = 100 mm; Stroke = 110 mm; Brake load = 540 N; Engine speed = 2500 r.p.m.; C/H ratio of the fuel (by mass) = 83/17; Ambient pressure = 1·0 bar; Ambient temperature = 27 °C; Time taken for 100 cc of fuel consumption = 18 s; Fuel density = 780 kg/m³; Calorific value of the fuel = 45 MJ/kg; Mass flow rate of atmospheric air consumed by the engine = 5·301126 kg/min. Calculate the bmep, bsfc, brake thermal efficiency, volumetric efficiency and the percentage of excess air. Given, R_air = 0·287 kJ/kg-K. (20 marks)
(b) (i) Draw typical velocity triangles of a stage of a reaction turbine, clearly showing the various velocities. (ii) Derive an expression to show that the optimum value of ρ, the blade-to-steam speed ratio for a Parsons reaction turbine is given by ρ = cos α, where α is the inlet angle of the fixed blades. (iii) Also, show that the maximum efficiency of the Parsons reaction turbine is given by η_maximum = (2 cos² α)/(1 + cos² α). (iv) Draw the velocity triangles of the Parsons reaction turbine operating at ρ_optimum. (20 marks)
(c) Explain briefly the various methods of air-conditioning duct design. (10 marks)
Answer approach & key points
Calculate all engine performance parameters in part (a) using systematic thermodynamic formulas, ensuring unit consistency throughout. For part (b), derive the optimum blade speed ratio and maximum efficiency expressions using velocity triangle analysis, with clear diagrams at ρ_optimum. For part (c), enumerate duct design methods with brief explanations. Allocate approximately 40% time to (a), 40% to (b), and 20% to (c) based on marks distribution.
- Part (a): Brake power P = WN/20000 = 67.5 kW; bmep = (60×P×1000)/(L×A×n×N/2) = 7.82 bar; bsfc = ṁ_f/P = 0.208 kg/kWh; brake thermal efficiency = P/(ṁ_f×CV) = 38.46%; volumetric efficiency = (ṁ_a×R×T_a)/(P_a×V_s×N/2×n) = 85.2%; stoichiometric air-fuel ratio from C/H=83/17 gives excess air ≈ 25%
- Part (b)(i): Velocity triangles showing inlet/outlet absolute velocities (V₁, V₂), relative velocities (V_{r1}, V_{r2}), blade velocities (u), and angles (α, β, φ, ψ) for 50% reaction stage
- Part (b)(ii): Derivation using symmetrical triangles (V_{r1}=V₂, V₁=V_{r2}), power output expression, and dP/du = 0 leading to ρ_opt = u/V₁ = cos α
- Part (b)(iii): Substitution of ρ_opt into efficiency expression η = 2ρ(cos α - ρ)/(1 - 2ρ cos α + ρ²) yielding η_max = 2cos²α/(1+cos²α)
- Part (b)(iv): Velocity triangles at ρ_opt showing α = β₂ and φ = ψ with V_{r2} perpendicular to blade or specific geometric relationships
- Part (c): Equal friction method, velocity reduction method, static regain method, and T-method (total pressure method) with brief principles of each
Q7 50M calculate Thermodynamics - Nozzles, Refrigeration, Lubricants
(a) A convergent-divergent nozzle receives steam at 5 bar, 250 °C and expands it isentropically into a space at 1 bar. Neglecting the inlet velocity, calculate the exit area required for a mass flow of 0·5 kg/s for the following cases:
(i) When the flow is in equilibrium
(ii) When the flow is supersaturated with pv^1.3 = constant
Given, at 5 bar, 250 °C
v = 0·4744 m³/kg, s = 7·2709 kJ/kg-K, h = 2960·7 kJ/kg
and at 1 bar
v_f = 0·001044 m³/kg, v_g = 1·6729 m³/kg
h_f = 419·04 kJ/kg, h_g = 2676·1 kJ/kg
s_f = 1·3069 kJ/kg-K, s_g = 7·3549 kJ/kg-K
(b) A 1 TR refrigeration plant works on R134a simple saturated vapour compression refrigeration cycle. The evaporator and condenser temperatures are –10 °C and 44 °C respectively. Determine the (i) mass flow rate of the refrigerant, (ii) compressor power, (iii) volumetric cooling capacity and (iv) COP. Also, calculate the (v) increase in the specific compressor work due to superheat horn and (vi) throttling loss, in comparison to reversed Carnot cycle operating between the same temperature limits. Consider the entry to compressor as saturated vapour and saturated liquid refrigerant is leaving the condenser in the reversed Carnot cycle. The properties of R134a are given in the table:
Take specific heat of vapour refrigerant as 1·26 kJ/kg-K.
(c) Explain how the following characteristics of the lubricating oils affect the operation of an internal combustion (IC) engine:
(i) Viscosity
(ii) Viscosity index
(iii) Pour point
(iv) Flash point and fire point
Answer approach & key points
Calculate numerical solutions for all sub-parts with systematic working. For (a), apply isentropic flow relations for both equilibrium and supersaturated steam, determining exit area using continuity equation. For (b), use given R134a properties to compute cycle parameters and compare with reversed Carnot cycle. For (c), explain lubricant properties with clear IC engine operational implications. Allocate approximately 40% time to part (a) due to dual cases, 35% to part (b) for six numerical outputs, and 25% to part (c) for conceptual explanations.
- Part (a)(i): Determine exit enthalpy at 1 bar using s_1 = s_2 = 7.2709 kJ/kg-K, find quality x_2, then velocity from h_0 = h_2 + V_2^2/2000, and exit area A_2 = m_dot*v_2/V_2
- Part (a)(ii): Apply pv^1.3 = constant for supersaturated flow, calculate T_2 from isentropic relation, find v_2, h_2 using c_p for superheated steam, then velocity and area
- Part (b): Use 1 TR = 3.517 kW, extract h_f, h_g at -10°C and 44°C from tables, compute refrigerant effect, mass flow rate, compressor work using h_2 = h_g at 44°C + c_p(T_2' - T_2), COP = RE/W
- Part (b)(v)-(vi): Calculate Carnot COP and work, then find superheat horn loss (area under superheat on T-s diagram) and throttling loss (h_4 - h_4' on enthalpy basis)
- Part (c): Viscosity affects film strength and pumping losses; VI ensures performance across temperature; pour point determines cold-start capability; flash/fire points indicate safety against crankcase ignition
- Steam tables interpolation skills demonstrated where needed; all units consistent (kJ/kg, m/s, m², kg/s, kW, kJ/m³)
- Comparison between actual VCRS and reversed Carnot cycle clearly quantified with percentage or absolute differences
Q8 50M calculate IC Engines, Psychrometrics, Boiler and Chimney
(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.
Answer approach & key points
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