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Air enters a diffuser at \( 200 \ \mathrm{m/s} \) and leaves at \( 80 \ \mathrm{m/s} \). With \( c_p = 1005 \ \mathrm{J/(kg\,K)} \), the ideal static temperature rise is approximately

  • A.33.4 K
  • B.5.6 K
  • C.16.7 K
  • D.11.9 K

Answer: C

Correct answer: 16.7 K

The kinetic energy given up appears as static temperature: \[ \Delta T = \frac{V_1^2 - V_2^2}{2c_p} = \frac{200^2 - 80^2}{2 \times 1005} = \frac{33{,}600}{2010} = 16.7\ \mathrm{K}. \] Note it is the difference of the squares, not the square of the difference - the latter would give 7.2 K.

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