flow3 - 53:030 Class Notes C.C Swan University of Iowa...

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Period #9: Multi-dimensional Fluid Flow in Soils A. Objective: To this point in time, we have considered one-dimensional flow in soils, where all fluid is flowing in the same direction . In most cases, however, fluid in different regions will be flowing in different directions. We call this multi-dimensional flow . Our objective here is to learn how to solve multi-dimensional flow problems such as the one shown below. To develop these capabilities, we will use two considerations: 1) conservation of fluid mass in the soil (or continuity ); 2) multi-dimensional forms of Darcy’s Law. 1 Multi-dimensional flow situation. 53:030 Class Notes; C.C. Swan, University of Iowa
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B. Conservation of Fluid Mass (or Continuity ) Consider the case of fluid flowing through a region of soil in space as shown below: Mass of water M w in R: M w = R n ρ w dR, where: ρ w is the mass density of water (constant) n is the porosity of the soil (constant) Net rate of fluid mass outflow from R: rate of mass outflow = S l .
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