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9. Demonstrate the ability to apply continuity and energy concepts in an analysis of control volumes. 3 FLOW DIMENSIONALITY AND AVERAGE VELOCITY As we observe ﬂuid moving around, the various properties can be expressed as functions of location and time. 2) or Since it is necessary to specify three spatial coordinates and time, this is called threedimensional unsteady ﬂow. 4) The assumption of one-dimensional ﬂow is a simpliﬁcation normally applied to ﬂow systems and the single coordinate is usually taken in the direction of ﬂow.

8 Identiﬁcation of work quantities. 38) 38 CONTROL VOLUME ANALYSIS—PART I This is called ﬂow work or displacement work. 39) This represents work done by the system (positive) to force ﬂuid out of the control volume and represents work done on the system (negative) to force ﬂuid into the control volume. Thus the total work δWs δW = + dt dt mpv ˙ We may now rewrite our energy equation in a more useful form which is applicable to one-dimensional ﬂow. 40) cv If we consider steady ﬂow, the term involving the partial derivative with respect to time is zero.

82 psia and −240°F, respectively. What is the average velocity at this section? 30). 30) and then differentiating the result. This is called logarithmic differentiation. Try it. This differential form of the continuity equation is useful in interpreting the changes that must occur as ﬂuid ﬂows through a duct, channel, or streamtube. It indicates that if mass is to be conserved, the changes in density, velocity, and crosssectional area must compensate for one another. For example, if the area is constant (dA = 0), any increase in velocity must be accompanied by a corresponding decrease in density.