Arjen Markus (17 june 2004) Here is a first almost trivial example of how Tcl could be used to facilitate certain physical computations ... I hope I can make this grow into a more serious package ;)

AM (18 june 2004) One thing that might be very useful in such a package: a short explanation of the various procedures and constants, especially if you are using it interactively. BTW, the unit converter is a much better way to achieve the unit conversions I haphazardly implemented here.

AM (25 june 2004) An improved version (note the laziness with regard to unit conversion) of the original script. What I added:

- One extra relation, the velocity of sound in gases
- The superposition principle for linear phenomena such as the diffusion of a substance

# physics.tcl -- # Provide access to physical constants, relations and # formulas # # Simple example: # Conversion of temperature to absolute temperature # In many formulas you need to specify the absolute temperature # rather than the temperature most people are used to (degrees # centigrade or the infamous degrees Fahrenheit). # Mistakes are easily made ... so include the unit in the value. # # Note: # In this implementation I have been less than consistent # in the use of unit conversions. I mainly wanted to get # something working ;) # # physics -- # Namespace for the physical computations # namespace eval ::physics { # # Add common constants etc. # variable gas_constant 8.3143 ;# J/mol.K namespace export abs_temperature wien_wavelength \ velocity_sound_gas diffusivePoint1d \ superpose } # Conversions -- # Set of conversion procedures # proc ::physics::Conv_K_K {t} {return $t} proc ::physics::Conv_oC_K {t} {expr {$t+273.15}} proc ::physics::Conv_oF_K {t} {Conv_oC_K [Conv_oF_oC $t]} proc ::physics::Conv_oF_oC {t} {expr {5.0*$t/9.0+32.0}} # abs_temperature -- # Return the absolute temperature # # Arguments: # temp (Relative) temperature # # Result: # The temperature in kelvin (no capital, there was only one # lord Kelvin, AFAIK :) # proc ::physics::abs_temperature {temp} { if { [llength $temp] == 2 } { set temp [Conv_[lindex $temp 1]_K [lindex $temp 0]] } list $temp K } # wien_wavelength -- # Return the wave length at which a perfect black body emits most # energy, given the temperature # # Arguments: # temp (Relative) temperature # # Result: # The wave length in micrometers (um) # proc ::physics::wien_wavelength {temp} { list [expr {2898.0/[lindex [abs_temperature $temp] 0]}] um } # velocity_sound_gas -- # Return the (approximate) velocity of sound in gas, # given the kind of gas and the temperature # # Arguments: # cpcv Ratio of cp and cv or "mono", "di", "poly" for # the type of molecules the gas consists of # molarw Molar weight (g/mol) # temp Temperature (K) # Result: # The sound velocity in m/s # proc ::physics::velocity_sound_gas {cpcv molarw temp} { variable gas_constant set abstemp [lindex [abs_temperature $temp] 0] set molarw [expr {$molarw/1000.0}] switch -- $cpcv { "mono" { set cpcv 1.66 } "di" { set cpcv 1.4 } "poly" { set cpcv 1.3 } } set csound [expr {sqrt($cpcv*$gas_constant*$abstemp/$molarw)}] list $csound "m/s" } # diffusivePoint1d -- # Create a function that describes the concentration from a # point source under diffusion in one dimension # # Arguments: # name Name of the function to create # diff Diffusion coefficient (m/s2) # mass Mass that was released # pos Position of the release point # Result: # Name of the function # proc ::physics::diffusivePoint1d {name diff mass pos} { proc ::physics::$name {x t} \ [string map [list %diff $diff %mass $mass %pos $pos] { expr {%mass/sqrt(4.0*3.1415926*%diff*$t)*exp(-($x-%pos)*($x-%pos)/4.0/$t/%diff)} }] return ::physics::$name } # superpose -- # Create a function that computes the sum of the individual # functions - the superposition principle # # Arguments: # name Name of the function to create # args List of one or more functions to superpose # Result: # Name of the function # proc ::physics::superpose {name args} { set body "expr {" set arglist [info args [lindex $args 0]] set values "\$[join $arglist " $"]" foreach fnc $args { append body "+\[$fnc $values\]" } append body "}" proc ::physics::$name $arglist $body return ::physics::$name } # main -- # A simple demonstration # namespace import ::physics::* puts "20 degrees centigrade = [abs_temperature {20 oC}]" puts "50 degrees Fahrenheit = [abs_temperature {50 oF}]" puts "At 20 degrees centigrade a black body emits most energy with a wave length of [wien_wavelength {20 oC}]" puts "Velocity of sound in air at 20 oC: \ [velocity_sound_gas di 28.9 {20 oC}]" # # Use a fairly large diffusion coefficient: # otherwise the concentration will be nearly zero # and we risk underflow # (I ought to use larger times ;) # set pointsrc [diffusivePoint1d point1 1.0 1.0e3 0.0] set pointsrc2 [diffusivePoint1d point2 1.0 1.0e3 4.0] foreach t {0.1 0.3 1.0 3.0 10.0} { puts "t=$t: concentration = [$pointsrc 1.0 $t]" } foreach x {0.1 0.3 1.0 2.0 3.0} { puts "x=$x: concentration = [$pointsrc $x 1.0]" } puts "Two sources:" set all [superpose twopoints $pointsrc $pointsrc2] foreach x {0.1 0.3 1.0 2.0 3.0 3.9 4.0 4.1 5.0 6.0} { puts "x=$x: concentration = [$all $x 1.0] (= sum of [$pointsrc $x 1.0] and [$pointsrc2 $x 1.0])" }

How does this relate to Unit converter and Unit math ?

AM Closely - though my intentions are different than "merely" converting from one unit to another. I want to make the unit an integral part of the quantity's value. This way I can use such quantities in all kinds of simple computations (that is, computations that do not require the solution of partial differential equations and the like).

Something like: I want to know the density of sea water at a given temperature and salinity - so use one of the constitutional equations that people have developed.

VPT - have you seen Frink http://futureboy.homeip.net/frinkdocs/ ? I'm sorry I gave the wrong link. You should find this one more relevant.

AM I know Frink, but that does not relate to the subject of this page (unless I horribly screwed up the code above, which I did not check with Frink, I admit ...).

AM Ah, another kind of Frink :). No, I did not know that one. Printed the information ...