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ENGR5003 / Week 4
ENGR217 2023 Q A1Past paperOld spec ENGR2172:225 marks30 min

ENGR217 Summer 2023 Q A1[VALID] official answers

Answer ALL parts (a) - (d).

A small hatchback car has a 4-cylinder, 1 litre petrol engine, which outputs 52 kW of power at 4000 rpm and can be modelled as an Otto cycle. You may assume Rg=0.287 kJ/kg/KR_g = 0.287\ \mathrm{kJ/kg/K} and γ=1.4\gamma = 1.4, where γ\gamma is the adiabatic index.

Formulas you may need
  • Adiabatic process: pVγ=constantpV^\gamma = \text{constant}, TVγ−1=constantTV^{\gamma-1} = \text{constant} (on the formula sheet)
  • Gay-Lussac (isochoric): p2T2=p3T3\dfrac{p_2}{T_2} = \dfrac{p_3}{T_3} (on the formula sheet)
  • Isochoric heat: ΔQ=mcvΔT\Delta Q = mc_v\Delta T, cv=Rgγ−1c_v = \dfrac{R_g}{\gamma-1} (on the formula sheet)
  • Otto efficiency ηth=1−1rγ−1\eta_{th} = 1 - \dfrac{1}{r^{\gamma-1}}; ηth=1−QoutQin\eta_{th} = 1 - \dfrac{Q_{out}}{Q_{in}}; Wnet=Qin−QoutW_{net} = Q_{in} - Q_{out} (on the formula sheet)
  • Work ratio: rw=WnetWoutr_w = \dfrac{W_{net}}{W_{out}} (given in the question; Brayton form on the sheet)
  • Brake power: Pb=P ηv ηmP_b = P\,\eta_v\,\eta_m (learn this)
  • P=Fv=mvdvdtP = Fv = mv\dfrac{dv}{dt} (given in the question)
  1. (a)
    At the intake, the temperature and pressure are p1=101 kPap_1 = 101\ \mathrm{kPa} and T1=22∘CT_1 = 22^\circ\mathrm{C}. The compression ratio is 3.2 and the maximum temperature of the cycle is 900∘C900^\circ\mathrm{C}. Determine the temperature and pressure at all stages of the cycle.
    [5]
  2. (b)
    Determine the specific heat addition and heat rejection of the cycle, as well as the thermal efficiency and work ratio, which is given as: rw=WnetWoutr_w = \dfrac{W_{net}}{W_{out}}
    [7]
  3. (c)
    Given that the volumetric and mechanical efficiencies for the engine are 70% and 78% respectively, determine the brake power output at the road wheels of the car. Given that the car weighs 1000 kg, determine the time it would take the car to accelerate from stationary to 100 kph, assuming a constant power output from the engine, given that power can be expressed as: P=Fv=mvdvdtP = Fv = mv\dfrac{dv}{dt}
    [7]
  4. (d)
    On a particularly cold winter morning, the ambient air temperature is −5∘C-5^\circ\mathrm{C}. Discuss how this might affect the isentropic, volumetric and mechanical efficiencies of the engine, when the engine starts up cold and once the car and engine are up to full operating temperature.
    [6]2:1