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Unformatted text preview: ASE 362KI Assignment 5 Thursday, February 14I 2007 We are not quite ready to move on to questions on oblique shocks so here are some problems on
topics we have covered — all are from old midsemester exams. 1) 2) 3) in many engineering flow problems there is a transfer of heat from the flowing gas to its
surroundings (or viceverse). An example would be a heat exchanger. The velocity of the gas
is affected by the heat interaction. We find in practice that when the gas velocity is “small”, the
flow is accelerated by heat addition, but when the flow velocity is ‘large’ heat addition
decelerates the gas. The transition point between the flow acceleration and flow deceleration occurs when 6q/dv is zero (oq is the heat added, v is the velocity). At this transition point (when 6q/dv=0) we find that v=,/yRT = 3 (Le. M=1). Assuming 1D, steady flow, prove this
result. [Hintz start with the energy equation in differential form and assume a perfect gas.] An aircraft flies supersonically at 10km altitude on a “standard” day. (Static pressure and
temperature at that altitude are 26.5kPa and 223.3K respectively). The true air speed of the
aircraft is 659 m/s. A pitot tube attached to the aircraft is used to sense stagnation pressure
which is then converted to flight Mach number by an onboard computer. However the
computer programmer has made an error ‘he (not a UT graduate) has assumed that the gas
deceleration to zero velocity at the probe face occurs isentropically rather than via a normal
shock. What is the difference between the true airspeed and the airspeed calculated by the computer program? The slab shown is moving at 270 m/s into still ambient air whose static temperature and
pressure are 293K and 105 Nm'2 respectively. The slab is at zero angle of attack so face
ABCD is normal to the oncoming flow. Assuming that the drag only comes from pressure
forces calculate the drag (you can take the pressure on face EFGH as being the undisturbed
ambient value). If you had assumed that the flow had been incompressible how much in error
would your drag estimate have been? Now assume that the slab velocity increases to 540 m/s.
By what factor does the drag increase over its value when the slab is moving at 270 m/s? 4) 2 kg/s of airflow through a convergent duct. You are told that P1=150kPa, T1=35OK, P2=101.3kPa, T2=320K and that A1=0.1m2. Calculation of the entropy change between
stations 1 and 2 reveals that the flow is nonisentropic. Calculate the axial force on the duct. a z [(I~\j(2k}> (223'3>3h2
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 Spring '07
 DOLLING,D

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