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# Exercise1:!Flow!Models,!Mach!Number!and!Mach!Wave! · 2015. 2. 23. ·...

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Aerodynamic II Exercise 1: Mach Number and Mach Wave 1 Exercise 1: Flow Models, Mach Number and Mach Wave 1. An aircraft is capable of flying at a maximum Mach no. of 0.91 at sealevel. Find the maximum velocity at which this aircraft can fly at sealevel if the air temperature is (a.) 5 °C (b.) 45 °C. 2. An aircraft is driven by propellers with a diameter of 4 m. At what engine speed will the tips of the propellers reach sonic velocity if the air temperature is 15 °C? 3. In evaluating the performance of an aircraft, a “standard atmosphere” is usually introduced. The conditions in the “standard atmosphere” are meant to represent average conditions in the atmosphere. In the U.S. Standard Atmosphere, the temperature in the inner portion of the atmosphere is defined by the following equations: For altitudes, H, of from O m. (sealevel) to 11 019 m.: T = 288.16 – 0.0065H Above an altitude, H, of 11 019 m.: T = 216.66 The altitude, H, is measured in meters and the temperature, T in K. Plot a graph showing how the speed of sound varies with altitude in this atmosphere for altitudes from sealevel to 12 000 m. 4. An observer on the ground finds that an airplane flying horizontally at an altitude of 5000m. has traveled 12 km from the overhead position before the sound of the airplane is first heard. Estimate the speed at which the airplane is flying.
Transcript
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Aerodynamic  II  -‐  Exercise  1:  Mach  Number  and  Mach  Wave

1

Exercise  1:  Flow  Models,  Mach  Number  and  Mach  Wave

1. An  aircraft  is  capable  of  flying  at  a  maximum  Mach  no.  of  0.91  at  sea-‐level.  Find  the  maximum  velocity  at  which  this  aircraft  can  fly  at  sea-‐level  if  the  air  temperature  is  (a.)  5  °C  (b.)  45  °C.

2. An  aircraft  is  driven  by  propellers  with  a  diameter  of  4  m.  At  what  engine  speed   will   the   tips   of   the   propellers   reach   sonic   velocity   if   the   air  temperature  is  15  °C?

3. In  evaluating  the  performance  of  an  aircraft,  a   “standard  atmosphere”   is  usually   introduced.   The   conditions   in   the   “standard   atmosphere”   are  meant   to   represent   average   conditions   in   the   atmosphere.   In   the   U.S.  Standard   Atmosphere,   the   temperature   in   the   inner   portion   of   the  atmosphere  is  defined  by  the  following  equations:  For  altitudes,  H,  of  from  O  m.  (sea-‐level)  to  11  019  m.:

T  =  288.16  –  0.0065H

Above  an  altitude,  H,  of  11  019  m.:

T  =  216.66

The  altitude,  H,  is  measured  in  meters  and  the  temperature,  T  in  K.  Plot  a  graph  showing  how  the  speed  of  sound  varies  with  altitude  in  this  atmosphere  for  altitudes  from  sea-‐level  to  12  000  m.

4. An  observer  on  the  ground  finds  that  an  airplane  flying  horizontally  at  an  altitude  of  5000m.  has  traveled  12  km  from  the  overhead  position  before  the  sound  of   the  airplane   is   first  heard.  Estimate   the  speed  at  which  the  airplane  is  flying.

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Aerodynamic  II  -‐  Exercise  1:  Mach  Number  and  Mach  Wave

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5. Typical  cruising  speeds  and  altitudes  for  three  commercial  aircraft  are:

Find  the  Mach  number  of  these  three  aircraft  when  flying  at  these  cruise  conditions.   Use   the   properties   of   the   standard   atmosphere   discussed   in  the  previous  problem.

6. Air  at  a  temperature  of  -‐10°C  flows  through  a  supersonic  wind  tunnel.  The  flow  reveals  weak  waves  originating  at   imperfections  on   the  wallsThese  weak  waves  are  at  an  angle  of  40°  to  the  flow.  Find  the  Mach  number  and  velocity  in  the  wind  tunnel.

Dash  8:    Cruising  speed:  500  km/h    at  an  altitude  of  4570  m.

Boeing  747:    Cruising  speed:  978  km/h  at  an  altitude  of  9150  m.

Concorde:    Cruising  speed:  2340  km/h    at  an  altitude  of  16  600  m.

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Aerodynamic  II  -‐  Exercise  1:  Mach  Number  and  Mach  Wave

3

7. A  pitot-‐static  tube  is  placed  in  a  subsonic  airflow.  The  static  pressure  and  temperature  in  the  flow  are  96  kPa  and  27°C  respectively.  The  difference  between  the  pitot  and  static  pressures  is  measured  using  a  liquid-‐in-‐glass  manometer   and   found   to   be   241   mm   Hg   (mm   of   mercury).   The  measurement   is   performed   at   Chulalongkorn   University.   Find   the   air  velocity:

a. Assuming  incompressible  flow  and  b. Assuming  compressible  flow.

(Hint.    1.The  value  of  approximated  local  gravity  in  Thailand  is  9.78  m  s-‐2.  2.The  density  of  the  liquid  in  the  manometer,  which  is  mercury,  is          13  580  kg  m-‐3.)

8. A  weak   pressure  wave   (sound  wave)   across  which   the   pressure   rise   is  0.05  kPa  is  traveling  down  a  pipe  into  air  at  a  temperature  of  30°C  and  a  pressure  of  105  kPa.  Estimate  the  velocity  of  the  air  behind  the  wave.

Appendix    Isentropic  Flow  Table  for  γ  =  1.4

Mach  Number  (M)   p0/p  0.64   1.317  29  0.66   1.339  59

241  mm  Hg

Mercury

p  =  96  kPa  T  =  27  °C

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