.MCAD 304020000 1 76 103 0
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.200000 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* |P *empty*
.CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
.CMD COLORTAB_ENTRY 128 128 0
.CMD COLORTAB_ENTRY 0 0 128
.CMD COLORTAB_ENTRY 128 0 128
.CMD COLORTAB_ENTRY 0 128 128
.CMD COLORTAB_ENTRY 128 128 128
.CMD COLORTAB_ENTRY 192 192 192
.CMD COLORTAB_ENTRY 255 0 0
.CMD COLORTAB_ENTRY 0 255 0
.CMD COLORTAB_ENTRY 255 255 0
.CMD COLORTAB_ENTRY 0 0 255
.CMD COLORTAB_ENTRY 255 0 255
.CMD COLORTAB_ENTRY 0 255 255
.CMD COLORTAB_ENTRY 255 255 255
.TXT 5 14 8 0 0 0
Cg a45.125000,45.125000,39
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Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4\f0\fs20 \fi420 Paragraph;}{\s5
\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 \li2160 Indent;}{\s7\f1\fs48
\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 Subtitle;}}\plain\fs28\b 
\pard\plain\s1\f0\fs28\b Letting Mathcad Handle Unit Conversions}
.TXT 5 -13 4 0 0 0
Cg a72.000000,72.000000,528
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 For historical 
reasons, we are often faced with performing calculations involving 
quantities from both the SI system and the English engineering units.  
Conversion of units is a major headache and also the major source of 
errors in most student's work.  This Mathcad module shows how to 
perform these unit conversions automatically with little extra effort 
by the student. \par \par To illustrate, we will take a few 
calculations from our first Hwk assignment.  In particular, we will 
look at the solution to Prob. 4.3-8 in Geankoplis. }
.TXT 16 0 10 0 0 0
Cg a72.250000,72.250000,61
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
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\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 The heat 
transfer coefficient {\i h}{\i\dn i} is given as 500 btu/h.ft{\up 2}.{
\up o}F}
.EQN 5 0 11 0 0 0
{0:hi}NAME:500
.TXT 0 34 12 0 0 0
Cg a38.250000,38.250000,70
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 If we define hi 
to be 500, Mathcad take the number to be diminsionless}
.TXT 6 -34 19 0 0 0
Cg a71.250000,71.250000,676
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 To get Mathcad 
to make the unit conversions, we must assign the units to all 
constants instead of leaving them dimensionless.  This can be done by 
multiplying (or dividing) the constant "500" by built-in constants 
representing the units.  This is done in the example below: after 
typing "500", I typed the "multiply" symbol (*) and then typed "BTU".  {
\ul You must use the }{\i\ul exact}{\ul  name Mathcad uses for each 
unit (including upper or lower case)}.  If you don't remember the name 
of the unit, click on the "measuring cup" in the toolbar (if the 
'toolbar' is not visible, go to the View menu and click on 'toolbar').  
A dialog box will appear which allows you to select the proper unit.}
.TXT 15 28 80 0 0 0
Cg a43.875000,43.875000,231
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 After entering 
"BTU", I typed "/hr*ft^2 *R" (the blank denotes a space made by 
hitting the space bar).  Again, if I didn't know Mathcad's name for a 
unit, I can insert it at the current cursor location using the 
measuring cup tool.}
.EQN 3 -27 32 0 0 0
{0:hi}NAME:500*({0:BTU}NAME)/({0:hr}NAME*({0:ft}NAME)^(2)*{0:R}NAME)
.TXT 7 -1 27 0 0 0
Cg a70.500000,70.500000,135
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 Once you have 
defined a variable like "hi", you can either use it in any 
calculations or display its value in any desired set of units.}
.TXT 7 28 76 0 0 0
Cg a44.750000,44.750000,278
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 If you just type 
"=" after the constant, Mathcad displays the value in its default set 
of units (usually MKS unless you have declared a different default).  
Notice that the value displayed at left (as well as the units) are 
different from what we entered in the statement above.}
.EQN 1 -28 28 0 0 0
{0:hi}NAME={0}?_n_u_l_l_
.TXT 11 0 34 0 0 0
Cg a72.250000,72.250000,311
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 If you click on 
the equation above, you will notice a placeholder appears at the end 
of the list of units.  This placeholder is denoted by a solid square 
(about 1mm x 1mm in size).  Moving the cursor to select this 
placeholder, you can enter any desired units in which the value of 
constant are to be displayed.}
.TXT 9 27 59 0 0 0
Cg a44.375000,44.375000,259
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 For example, if 
we enter "kW/m^2 *K" in this placeholder, we obtain the result at 
left.  Notice that the value of hi has changed to reflect the 
different units used.  Mathcad has automatically applied the 
conversion 1 kW = 1000 joules/sec = 1000 kg*m/sec^3.  }
.EQN 3 -27 52 0 0 0
{0:hi}NAME={0}?({0:kW}NAME)/(({0:m}NAME)^(2)*{0:K}NAME)
.TXT 9 27 60 0 0 0
Cg a43.625000,43.625000,237
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 If we 
incorrectly enter the units as "BTU/ft^2 *R" (we have omitted the hr), 
Mathcad uses them, but appends the default unit of time "s^-1" to 
indicate that additional units are required.  Of course, we do not 
recover our original value.}
.EQN 4 -27 53 0 0 0
{0:hi}NAME={0}?({0:BTU}NAME)/(({0:ft}NAME)^(2){53}{0:R}NAME)
.TXT 8 27 61 0 0 0
Cg a43.250000,43.250000,128
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 If instead, we 
enter "BTU/hr*ft^2 *R" (including the "hr") in the units placeholder, 
we do recover the original value and units.}
.EQN 1 -27 57 0 0 0
{0:hi}NAME={0}?({0:BTU}NAME)/({0:hr}NAME*({0:ft}NAME)^(2)*{0:R}NAME)
.TXT 6 0 65 0 0 0
Cg a72.250000,72.250000,108
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 Now we will 
enter the rest of the variables appearing in this problem in the most 
convenient units (for us).}
.EQN 8 0 66 0 0 0
{0:ho}NAME:1500*({0:BTU}NAME)/({0:hr}NAME*({0:ft}NAME)^(2)*{0:R}NAME)
.EQN 0 20 68 0 0 0
{0:k}NAME:45.1*({0:W}NAME)/({0:m}NAME*{0:K}NAME)
.EQN 0 15 69 0 0 0
{0:Di}NAME:2.067*{0:in}NAME
.EQN 0 13 70 0 0 0
{0:Do}NAME:2.375*{0:in}NAME
.EQN 7 -48 75 0 0 0
{0:xW}NAME:({0:Do}NAME-{0:Di}NAME)/(2)
.EQN 0 20 82 0 0 0
{0:xW}NAME={0}?{0:in}NAME
.TXT 0 15 84 0 0 0
Cg a37.250000,37.250000,93
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 Here we 
calculate the wall thickness.  I specified "in" as the unit to display 
the answer in.}
.TXT 7 0 86 0 0 0
Cg a37.250000,37.250000,99
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 Here we 
calculate the log-mean diameter.  Again I specified "in" as the unit 
to display the result.}
.EQN 1 -34 87 0 0 0
{0:Dlm}NAME:({0:Do}NAME-{0:Di}NAME)/({0:ln}NAME(({0:Do}NAME)/({0:Di}NAME)))
.EQN 0 19 83 0 0 0
{0:Dlm}NAME={0}?{0:in}NAME
.TXT 7 11 103 0 0 0
Cg a40.000000,40.000000,278
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 Here we are 
calculating the overall coefficient using the formula at the top of 
page 9 of the class notes.  Notice that we have mixed different sets 
of units when specifying values for the variables appearing in this 
equation.  The units are correctly converted automatically.  }
.EQN 2 -30 88 0 0 0
{0:Uo}NAME:(1)/((1)/({0:ho}NAME)+({0:xW}NAME)/({0:k}NAME)*({0:Do}NAME)/({0:Dlm}NAME)+(1)/({0:hi}NAME)*({0:Do}NAME)/({0:Di}NAME))
.TXT 14 34 93 0 0 0
Cg a37.250000,37.250000,63
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 This is the 
display of the result using Mathcad's default units}
.EQN 1 -34 91 0 0 0
{0:Uo}NAME={0}?_n_u_l_l_
.EQN 9 0 94 0 0 0
{0:Uo}NAME={0}?({0:BTU}NAME)/({0:hr}NAME*({0:ft}NAME)^(2)*{0:R}NAME)
.TXT 0 34 102 0 0 0
Cg a37.250000,37.250000,139
{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0
\fcharset0\fnil Arial;}}{\stylesheet{\cf1\f0\fs20 Normal;}{\s1\f0\fs28
\b Heading 1;}{\s2\f0\fs24\b\i Heading 2;}{\s3\f0\fs24 Heading 3;}{\s4
\f0\fs20 \fi420 Paragraph;}{\s5\f0\fs20 \li285\fi-285 List;}{\s6\f0\fs20 
\li2160 Indent;}{\s7\f1\fs48\b \qc Title;}{\s8\f1\fs36 \qc \sbasedon0 
Subtitle;}}\plain\cf1\fs20 \pard\plain\s0\cf1\f0\fs20 What remains is 
the display of the answer in two different sets of units.  The last 
value should match with the answer in the solution key.}
.EQN 7 -34 95 0 0 0
{0:Uo}NAME={0}?({0:W}NAME)/(({0:m}NAME)^(2)*{0:K}NAME)