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Question: in the infinitesimal neighborhood of a point in an inviscid...

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In the infinitesimal neighborhood of a point in an inviscid flow, the small change in pressure  d p corresponding to a change in velocity  d u is given by  d p equals negative rho   u   d u .

  1. Using this relation, derive a differential relation for the fractional density  d rho divided by rho as a function of the fractional change in velocity  d u divided by u with the compressibility  tau as a coefficient.
  2. The velocity in a point in isentropic flow of air is 10m/s (a low speed flow) and the density and pressure are 1.23 kg/m3 and 1.01x105 N/m2. The fractional change in velocity is 0.01. Calculate the fractional change in density.
  3. Repeat part (b) except for a local velocity of 1000m/s (a high speed flow). Compare this result with that of part (b) and comment on the differences.
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