Air flows steadily through a long pipe with a speed of

Chapter 4, Problem 4.56

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Air flows steadily through a long pipe with a speed of u = 50 + 0.5x, where x is the distance along the pipe in feet, and u is in ft/s. Due to heat transfer into the pipe, the air temperature, T, within the pipe is \(\mathrm{T=300+10x ~^\circ F}\). Determine the rate of change of the temperature of air particles as they flow past the section at x = 5 ft.

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