The scale heights of stratification and the widths of steady solar coronal loops exhibit properties unexplained by standard theory: observed scale heights are often much greater than static theory predicts, while the nearly-constant widths of loop emission signatures defy theoretical expectations for large flux tubes in stratified media. In this work we relate the cross-sectional profile of a coronal flux tube to its density scale height in steady-state plasma flow regimes. Steady flows may

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... ten or lengthen the scale height according to how the tube cross-sectional area varies with arclength. In a near-potential corona the flux tubes are expected to be sufficiently expansive in many active regions for scale heights to be increased by steady flows. On the other hand, cases where scale lengths are actually increased to observed sizes form a small part of the solution space, close to regimes where density profiles reverse. Therefore, although steady flows are the only steady process known to be capable of extending scale heights significantly, they are not expected to be not responsible for the majority of extended active region scale heights.