Fundamentals of Gas Dynamics by Robert D. Zucker, Oscar Biblarz

By Robert D. Zucker, Oscar Biblarz

Offers all invaluable equations, tables, and charts in addition to self tests.* incorporated chapters hide response propulsion platforms and actual fuel effects.* Written and arranged in a way that makes it obtainable for self studying.

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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.

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