Flow Analysis Using Control Volume Finite Control Volume

Flow Analysis Using Control Volume (Finite Control Volume Analysis ) CE 311 Chapter 5 1

• Many practical problems in fluid mechanics require analysis of the behavior of the contents of a finite region in space (a control volume). for example, to determine the amount of time to allow for complete filling of a large storage tank. to estimate of how much power it would take to move water from one location to another at a higher elevation and several miles away may be sought. 2

• The bases of this analysis method are some fundamental principle of physics, namely, Conservation of mass Newton’s second law of motion , and the first and second laws of thermodynamics. • The finite control volume formulas are easy to interpret physically and are not difficult to use. 3

Conservation of Mass-The continuity Equation • Derivation of the continuity Equation t = t-δt t=t t = t+δt 4

time rate of change of net rate of flow of mass of the = the mass of the contents + through the control coincident system of the coincident c. v. surface 5

For varying velocity across a control surface: 6

Fixed, non-deforming Control Volume 7

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Moving, Non-deforming Control Volume • Example of moving, non-deforming control volume ---Control volumes containing a gas turbine engine on an aircraft in flight, and gasoline tank of an automobile passing. 12

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Deforming Control Volume • A deforming Control volume ~Changing volume size & control surface movement. 14

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