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ENGR5003 / Week 4
ENGR217 2022 Q A1Past paperOld spec ENGR2172:225 marks30 min

ENGR217 Summer 2022 Q A1[VALID] official answers

Answer ALL parts (a) - (d).

A 700 kg sports car is powered with a 1.6 litre, 4-stroke, 6-cylinder engine. At 5,000 rpm, the engine produces 100 kW of power. The engine has an overall efficiency of 46% and the breathing and mechanical efficiencies are 90% and 82% respectively. We will model this as an Otto cycle operating on an ideal gas and you may assume that 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
  • Otto cycle efficiency: ηth=1−T1T2=1−1rγ−1\eta_{th} = 1 - \dfrac{T_1}{T_2} = 1 - \dfrac{1}{r^{\gamma-1}} (on the formula sheet)
  • Overall efficiency: ηo=ηth ηb ηm\eta_o = \eta_{th}\,\eta_b\,\eta_m (learn this)
  • Power: P=Wnet N ηb ηmP = W_{net}\,N\,\eta_b\,\eta_m with N=rpm120N = \dfrac{\mathrm{rpm}}{120} for a 4-stroke (learn this)
  • Brake work: Wb=ηmWnetW_b = \eta_m W_{net} (learn this)
  • Ideal gas pV=mRgTpV = mR_gT, cv=Rgγ−1c_v = \dfrac{R_g}{\gamma-1}, TVγ−1=constantTV^{\gamma-1} = \text{constant} (on the formula sheet)
  • ηth=WnetQin=1−QoutQin\eta_{th} = \dfrac{W_{net}}{Q_{in}} = 1 - \dfrac{Q_{out}}{Q_{in}}; isochoric ΔQ=mcvΔT\Delta Q = mc_v\Delta T (on the formula sheet)
  • Adiabatic work ΔW=−ΔU=mcvΔT\Delta W = -\Delta U = mc_v\Delta T (on the formula sheet)
  • Fuel economy: distance per litre == speed ×\times time to burn 1 litre (learn this)
  1. (a)
    Determine the compression ratio, brake work and net work output per cylinder, per cycle.
    [10]
  2. (b)
    At the intake, the air pressure and temperature are p1=101 kPap_1 = 101\ \mathrm{kPa} and T1=288 KT_1 = 288\ \mathrm{K}. Determine the temperature at each stage in the process, the work done during compression and expansion and the heat rejection per cylinder per cycle.
    [8]
  3. (c)
    Suggest two ways in which the thermal efficiency of the engine could be improved and briefly explain how each method works.
    [2]Third
  4. (d)
    The air-fuel mix consists of 1.6% petrol by mass and petrol has a density of 0.8 kg/litre. Assuming the car travels at 70 mph (112 km/hour) in 6th gear at 5000 rpm, determine the fuel economy of the engine in km/litre.
    [5]2:1