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Cell[CellGroupData[{
Cell["MATH 342 Advanced Math for Applications", "Title"],

Cell["\<\
Assignment 2
Due Wednesday, April 2, 2008\
\>", "Subtitle"],

Cell["Name: ", "Subtitle"],

Cell[CellGroupData[{

Cell["Problem Statement", "Section"],

Cell["Suppose that the velocity of a fluid is", "Text"],

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              y} + \[ExponentialE]\^\(\(-1\)/20 \((x\^2 + y\^2)\)\)\ {x, 0, 
              z}\  + \ a\ \ {x, y, 
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  ", ",
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",
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  " axis.  If ",
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  " > 0, the velocity vectors in the third term all point away from the \
origin.   This makes the third term a fluid source; that is, it puts fluid \
into the system at the origin.  If ",
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    FontSlant->"Italic"],
  " < 0, the third term is a fluid sink,  drawing fluid out the system at the \
origin.  The magnitude of the coefficient, ",
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    FontSlant->"Italic"],
  ", determines the strength of the source or sink."
}], "Text"],

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  "Let ",
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  " be the region consisting of the interior of a cylinder with a hemisphere \
on the top.  The cylinder is ",
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      \(TraditionalForm\`x\^2 + y\^2 = 9, \ \(-6\) \[LessEqual] 
        z \[LessEqual] 0, \)]],
  " and the hemisphere is ",
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  ".  Your assignment is to use ",
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  " to find a value of ",
  StyleBox["a",
    FontSlant->"Italic"],
  " so that the the net mass flow of fluid across the boundaries of the \
region, ",
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  ", is zero.  Note that the boundary of ",
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    FontSlant->"Italic"],
  " includes the end of the cylinder.  Assume that the fluid density is \
constant."
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