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# Class Note for BSysE 595 at WSU 29

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

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This 5 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 15 views.

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Date Created: 02/06/15
Unsaturated Flow Governing Equations 1 Richards Eq A Apply mass conservation principle to REV Mass In ow Rate Mass Out ow rate Change in Mass Storage with Time For a REV with volume AxAyAz mass in ow rate through face ABCD is pwqx AyAz Mass out ow rate through face EFGH is 6pwqxAx 6x pwqx AyAz The net in ow rate is thus 6pwqx 6x AxAyAz Similarly net in ow rate thru face ABFE is 6pwqp AxAyAz 6y and net in ow rate thru face BCGF is 6pwq AxAyAz az The total net in ow rate through all faces is then 6pwqgapwqp 6pwqg ax 6y az AxAyAz The change in mass storage is 6pw0 AxAyAz 6t where 6 is the volumetric water content L3 L 3 Equating net in ow rate and time rate of change in mass storage and dividing both sides by AxAyAz leads to 6pwqx 6pwqy 6pqu Z 6pw0 6x a y dz 6 t 1 In fact 1 can be obtained directly from 6pw 6 V39pwq d1vpwq at If pw varies neither spatially nor ternporally 1 becomes 2 69 8t aqx dqy aqz 2 6x 8y dz B Apply Darcy s law to Eq 2 6 Kah 6 Kah 6 Kah 6x 6x 6y 6y az az 60 3 at h z11 Bernoulli eq 39 zai zai0 a 1 H 8x 6x 3 6y 6y az 62 Substituting the above equations into Eq 3 leads to a K 6 1 a K 8 1 a K a I BK 6x 6x 6 y 6 y az az az Q at 4 Eq 4 is the 3d Richards equation the basic theoretical framework for unsaturated flow in a homogeneous isotropic porous medium Eq 4 is not applicable to macropore ows Eq 4 Darcy s law for unsaturated ow does not address hysteresis effects Both K and I are a function of 6 making Richards equation nonlinear and hard to solve 2 Simplified Cases If V2 gravity gradient negligible 4 becomes 6K61l1 a K6111 6Kaq1 66 8x 8x 6y 6y dz 82 at If lateral ow elements negligible 4 becomes a K61 8K 60 az dz 87 at

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