Solve Problem 6.8 using the method of least squares.

Problem 6.8

A vortex tube is a device that splits a flow of air into two streams, one hot and one cold, without any moving parts. If you are not familiar with vortex tubes, read about them online. They are sometimes used in industrial applications for spot cooling. The cooling performance data for a particular vortex tube are shown in Table P6.8. This table shows the temperature difference between the incoming air flow and the cold air leaving the tube as a function of the inlet pressure of the air into the tube and the mass flow rate of the cold air stream, represented as a percent of the incoming flow. Use the exact fitting technique to develop an empirical equation that can be used to predict the temperature difference between the inlet air and the cold exit air over the range of the data provided. Estimate the accuracy of the empirical equation by developing a deviation plot that shows all of the available data.

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TABLE P6.8 Temperature Drop (R) of the Cold Air in a Vortex Tube Cold Fraction (%) Inlet Pressure (psig) 40 60 80 100 120 30 85.0 100.0 110.0 118.0 124.0 40 80.0 93.0 102.0 110.0 116.0 50 73.0 84.0 92.0 99.0 104.0 60 62.5 73.0 80.0 86.0 90.5 70 51.5 59.5 65.5 70.0 74.0