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# Class Note for BSysE 595 at WSU 10

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COURSE
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TYPE
Class Notes
PAGES
4
WORDS
KARMA
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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Washington State University taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15
Conservation of Fluid Mass 1 Physics of Fluid Flow Conservation Statement Fluid mass conservation Mass In ow Rate Mass Out ow rate Change in Mass Storage with Time This statement is generally valid regardless of the size of the domain of interest Yet when using the statement together with Darcy s law macroscopic a threshold exists for the domain srze Representative Elementary Volume REV the smallest volume for point P which includes sufficient number of pores to permit meaningful statistical averaging and below which no single value exists that can represent the porosity at P 2 Mathematical Representation Given a REV with volume AxAyAz mass in ow rate through face ABCD is pw qx AyA z mass out ow rate through face EFGH is 8pwqxAx AA 6x yz pwqx The net in ow rate is thus 6pwqx ax AxAyAz Similarly net in ow rate through face ABFE is 6pwqy AxAyAz 6y and net in ow rate though face BCGF is 6pqu AxAyAz az The total net in ow rate through all faces is then apwqx apwqy 6pqu AxA Az ax 6y az y 45 in units of M T l t The change in mass storage is a pwn AxAyAz 46 at Collecting Eq 45 and 46 and dividing both sides by AxAyAz yields 6pw196pwqp6pwqg 226pwn ax 6y dz at 47 Assume pw does not vary spatially Eq 47 becomes 1 6pwn pw at aqx aqy aqz 6x 6y dz 4s With the lefthand side expressing the net in ow rate per unit porous medium REV and right hand side the time rate of change of uid awn volume per unit REV ie a t

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