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ENGR5003 / Week 2
ENGR266 2019 Q A2Past paperOld spec ENGR2662:215 marks18 min

ENGR266 Summer 2019 Q A2[PARTIAL] Left out: Part (b) (10 marks: area-velocity relation $\frac{du}{dx} = -\frac{u}{A}\left(\frac{1}{1 - M^2}\right)\frac{dA}{dx}$ and subsonic/supersonic flow in converging and diverging nozzles) is left out: compressible nozzle flow and the area-velocity relation have been dropped from the current syllabus and formula sheet (OBSOLETE in the audit).

Answer ALL parts (a) - (c).

Formulas you may need
  • Heat exchanger energy balance (adiabatic exchanger, each stream): Q˙=m˙cpΔT\dot Q = \dot m c_p \Delta T, heat lost by the hot stream = heat gained by the cold stream (dQ=mcpdTdQ = mc_p dT on the formula sheet; the exchanger balance: learn this)
  • Adiabatic process of an ideal gas: pVγ=pV^\gamma = const, γ=cp/cv\gamma = c_p/c_v (on the formula sheet)
  • Adiabatic / polytropic work: W=p2V2−p1V1n−1W = \dfrac{p_2V_2 - p_1V_1}{n - 1} (as printed: positive for compression, i.e. work done on the gas) (on the formula sheet)
  • First law for an adiabatic process: ΔU=−Wby=ncvΔT\Delta U = -W_{by} = n c_v\Delta T (on the formula sheet)
  • Ideal gas: pV=nRTpV = nRT (on the formula sheet)
  1. (a)
    Oil is cooled from an initial temperature of 96∘C96^\circ\mathrm{C} to 30∘C30^\circ\mathrm{C} by water in an adiabatic concentric heat exchanger. The flow rates for the oil and water are 0.7 kg s−10.7\ \mathrm{kg\,s^{-1}} and 0.4 kg s−10.4\ \mathrm{kg\,s^{-1}} respectively. If water enters the heat exchanger with a temperature of 20∘C20^\circ\mathrm{C}, what is the temperature of the water when it leaves the heat exchanger? Assume the following: heat capacities are constant as a function of temperature, Cp(Oil)=2131 J kg−1 K−1C_p(\mathrm{Oil}) = 2131\ \mathrm{J\,kg^{-1}\,K^{-1}} and Cp(Water)=4178 J kg−1 K−1C_p(\mathrm{Water}) = 4178\ \mathrm{J\,kg^{-1}\,K^{-1}}.
    [6]
  2. (c(i))
    An air breathing jet engine cycle consists of the following steps:
    1. Adiabatic compression
    2. Isobaric expansion
    3. Adiabatic expansion
    4. Isobaric compression
    Draw this engine cycle on a pressure-volume diagram and indicate the direction of the cycle and where heat enters and leaves the system.
    [5]
  3. (c(ii))
    Calculate the work done during the adiabatic compression stage of the cycle if an ideal gas with volume of 0.0102 m3 mol−10.0102\ \mathrm{m^3\,mol^{-1}} experiences an increase in pressure from 0.35 MPa to 2 MPa. For the ideal gas assume that Cp=5/2RC_p = 5/2R and Cv=3/2RC_v = 3/2R.
    [4]