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A thermocouple, mounted flush in an insulated flat surface in a supersonic laminar flow of air measures the

  • A.static temperature.
  • B.temperature greater than static but less than total temperature.
  • C.total temperature.
  • D.temperature greater than total temperature.

Answer: B

It measures a temperature greater than static but less than total temperature.

An insulated surface reaches the adiabatic wall (recovery) temperature, where the frictional heating in the boundary layer balances the heat conducted away. It is written with a recovery factor r:

\[ T_{aw} = T + r\frac{V^{2}}{2c_{p}} \]

For a laminar boundary layer in air, \(r \approx \sqrt{Pr} \approx 0.85\). Since r is less than 1, the wall recovers most but not all of the kinetic energy, so \(T \lt T_{aw} \lt T_{0}\).

The static temperature would be read only with no recovery at all (r = 0), the total temperature only with full recovery (r = 1), and a temperature above total would need r greater than 1, which laminar flow of air does not give.

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