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{SECT 0 {PARA 256 "" 0 "" {TEXT 256 12 "Air Pressure" }}{PARA 256 "" 
0 "" {TEXT -1 18 "(Cylinder or Cone)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 257 "" 0 "" {TEXT 257 12 "by Greg Crow" }}{PARA 258 "" 0 "" 
{TEXT 258 22 "(please report errors)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 147 "In exa
mple 3 of section 8.1 of the text, the authors give a function that ap
proximates the density at a height h above the surface of the earth as
 " }{XPPEDIT 18 0 "P = f(h) " "/%\"PG-%\"fG6#%\"hG" }{TEXT -1 3 " = " 
}{XPPEDIT 18 0 "1.28*exp(-0.000124*h)" "*&$\"$G\"!\"#\"\"\"-%$expG6#,$
*&$\"$C\"!\"'F&%\"hGF&!\"\"F&" }{XPPEDIT 18 0 "kg" "I#kgG6\"" }{TEXT 
-1 1 "/" }{XPPEDIT 18 0 "m^3" "*$%\"mG\"\"$" }{TEXT -1 3 ".  " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 12 "Example \+
1:  " }}{PARA 0 "" 0 "" {TEXT -1 129 "Compute the mass of the cylinder
 of air above a circle of diameter 1 meter to an altitude of 25km abov
e the surface of the earth " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
259 "" 0 "" {TEXT -1 11 "Solution 1:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Int(Pi*1.28*exp(-0.000124*
h),h=0..25000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&%#PiG
\"\"\"-%$expG6#,$%\"hG$!$C\"!\"'F)$\"$G\"!\"#/F.;\"\"!\"&+]#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "int(Pi*1.28*exp(-0.000124*h)
,h=0..25000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+[F%o4$!\"&" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT 260 10 "Example 2:" }}{PARA 0 "" 0 "" {TEXT -1 129 "Co
mpute the mass of the cylinder of air above a circle of diameter 1 met
er to an altitude of 25km above the surface of the earth " }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 11 "Solution 2:" }}
{PARA 0 "" 0 "" {TEXT -1 166 "The density function can be adjusted so \+
that the height is measured in meters from the center of the earth by \+
changing h to (h-6378000).  In this case the new f(h) = " }{XPPEDIT 
18 0 "1.28*exp(-0.000124*(h-6378000)) " "*&$\"$G\"!\"#\"\"\"-%$expG6#,
$*&$\"$C\"!\"'F&,&%\"hGF&\"(+!yj!\"\"F&F2F&" }{TEXT -1 161 ".  Note th
at the mean radius of the earth is approximately 6378km so the upper l
imit of integration is 6378000+25000=6403000 meters from the center of
 the earth." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 59 "Int(Pi*1.28*exp(-0.000124*(h-6378000)),h=6378000..6
403000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&%#PiG\"\"\"-%
$expG6#,&%\"hG$!$C\"!\"'$\"*+?(3zF1F)F)$\"$G\"!\"#/F.;\"(+!yj\"(+IS'" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(Pi*1.28*exp(-0.000124
*(h-6378000)),h=6378000..6403000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"+[F%o4$!\"&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" 
{TEXT -1 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 12 "Convert the " 
}{XPPEDIT 18 0 "31000kg/(Pi m^2)" "*(\"&+5$\"\"\"%#kgGF$*&%#PiGF$*$%\"
mG\"\"#F$!\"\"" }{TEXT -1 29 " into pounds per square inch." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 11 "Solution 3:" }
}{PARA 0 "" 0 "" {TEXT -1 24 "There are approximately " }{XPPEDIT 18 
0 "2.2lb/kg" "*($\"#A!\"\"\"\"\"%#lbGF&%#kgG!\"\"" }{TEXT -1 3 " , " }
{XPPEDIT 18 0 "100cm/m" "*(\"$+\"\"\"\"%#cmGF$%\"mG!\"\"" }{TEXT -1 6 
" and  " }{XPPEDIT 18 0 "2.54cm/In" "*($\"$a#!\"#\"\"\"%#cmGF&%#InG!\"
\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "evalf(\"/Pi*
(2.2/1)*(2.54/100)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+rU8*R\"!
\")" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "T
his is approximately the 14.7 lb/sq in. that we would expect." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT 262 10 "Example 4:" }}{PARA 0 "" 0 "" {TEXT -1 54 "Com
pute the volume of a cone of radius r and height h." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 9 "Solution:" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g:=x-
>(r/h)*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG:6#%\"xG6\"6$%)oper
atorG%&arrowGF(*(%\"rG\"\"\"%\"hG!\"\"9$F.F(F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "Int(Pi*(g(x)^2),x=0..h);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$IntG6$**%#PiG\"\"\"%\"rG\"\"#%\"hG!\"#%\"xGF*/F-;\"
\"!F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "int(Pi*(g(x)^2),x=
0..h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%\"hG\"\"\"%#PiGF&%\"rG
\"\"##F&\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 126 "Question 1:  Find the mass of the air in a cone from sea
 level to 25km.  Use the function f(x) given in above (from the text).
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "Ques
tion 2: Find the air pressure at sea level using the cone as model wit
h the function f(x) given in the text." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 133 "Question 3: Use fsolve to find a sui
table replacement for the -0.000124 in the book's function that will g
ive a result of 14.7 p.s.i." }}{PARA 0 "" 0 "" {TEXT -1 21 "(use the c
one model)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 78 "Question 4:  What is the effect in the cone model of integratin
g to the stars?" }}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }