Question

Air at 320 K is flowing in a duct at a velocity of (a) 1, (b) 10, (c) 100, and (d) 1000 m/s. Determine the temperature that a stationary probe inserted into the duct will read for each case.

Solution

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Step 1

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A stationary probe inserted into the duct is a device for measuring temperature. In the task, we are given the starting temperature of the air that flows into the duct, and we are given 4 different velocities of the air. We need to determine what will be the new amount of the temperature of the air after it enters the duct. Like in the previous examples we will assume the following:

  1. Both the diffuser and the compressor are isentropic.
  2. Air is an ideal gas with constant specific heat at room temperature.

For the temperature of 320K we can approximately obtain the number from Table A-2, the constant-pressure specific heat cpc_p and the specific heat ratio k of air at room temperature are:

cp=1.05 kJkgKk=1.4\begin{aligned} &c_p = 1.05\ \mathrm{\frac {kJ}{kgK} }\\\\ &k = 1.4\\ \end{aligned}

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