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...Mit department of mechanical engineering advanced fluid mechanics problem this is from problems by a h shapiro and sonin consider the frictionless steady ow compressible uid in an innitesimal stream tube demonstrate continuity momentum theorems that d da dv v dp gdz b determine integrated forms these equations for incompressible c derive appropriate unsteady cross sectional area which depends on both space time copyright inviscid flows solution p cs cv ds dz gdv here we arbitrary control volume sitting along streamline length may write integral mass conservation equation as u nda to evaluate must decompose it into three integrals sub surfaces located at upstream portion result adv ad where have neglected higher order terms there no across so combining eq obtain dividing e fs f pa s z n calculate left hand side ux g when neglect now sum forces acting direction since friction less streamwise come only pressure gravity hence gravitational force...