An approximate solution is derived for the pressure ratio in high-speed subsonic flow through constant-cross-section circular tubes with friction and heating. The results are compared with those obtained from an accurate numerical calculation. The gas used is air. A wide range of variables such as temperature ratio, exit Mach number (up to 0.90), tube length-to-diameter ratio, and shape of the power distribution function is examined. The derived expression is found to be quite accurate in all cases.

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