Mathematical Modeling in the Environment
Mathematical Modeling in the Environment MATH 1050
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This 12 page Class Notes was uploaded by Mary Veum on Thursday September 17, 2015. The Class Notes belongs to MATH 1050 at University of Connecticut taught by Dmitriy Leykekhman in Fall. Since its upload, it has received 6 views. For similar materials see /class/205810/math-1050-university-of-connecticut in Mathematics (M) at University of Connecticut.
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Date Created: 09/17/15
MATH 1050QC Mathematical Modeling in the Environment Lecture 13 OneDimensional Diffusion Dmitriy Leykekhman Spring 2009 Diffusion in Thin Long Tube LONG THIN TUBE ramIon huei lt 3 i 6 figure 312 from C Hadlock39s book 1D Model Equation Our goal is to understand the onedimensional diffusion equation M 2 5 4m V 4th where gt C concentration units of masslength M mass of material instantaneously injected t time D diffusion constant units of lengthQtime X distance from center at which concentration is calculated Class Problem Consider the onedimensional diffusion in a long tube Assume that a solid is being released into a liquid that fills the tube and that solid is diffusing Let I 0 corresponds to the center of the tube If a mass of 10 grams is released at the center of this tube and the diffusion constant D 005 cm2sec calculate the concentration C at all of these locations and at each of the following time values t1 2t107 7t1007 t 1000 sec Graph these results in the form of curves showing concentration as a function of location a different curve for each time value MATH 1050QC Mathematical Modeling in the Environment Lecture 6 Interstitial Velocity Equation Dmitriy Leykekhman Spring 2009 General Issues We are trying to answer two general questions 1 the quantity of water flowing through the aquifer 2 the speed or velocity of the flow General Issues We are trying to answer two general questions 1 the quantity of water flowing through the aquifer 2 the speed or velocity of the flow Darcy39s Law give us the answer to the first question and we turn to the second question Flow through open Channel with unit cross sectional area AIDMOMMNIHB1WM END VIEW CMNER VIEW figure 217 from C Hadlock39s book Flow through open Channel with half cross sectional area blocked E wxmmmmmm END VIEW comm VIEW fi ure 218 from C Hadlock39s book quotV g m Flow through Channel filled with porous material with porosity 77 05 EmmaMot uwMammm WWIt nunnah Ind figure 219 from C Hadlock39s book Interstitial Velocity Definition Interstitial Velocity is the speed at which the molecules of water are progressing in the direction of movement Let 1 represent interstitial velocity
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