kill(all)$

maxima:differential volume element cylindrical coordinates for pde construct ,version 1.0
peter.vlasschaert@gmail.com,01/09/2021

ref :
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new: 19/08/2021:maxima       : principle balance ,conservation, momentum 'version 1.0'
download  (Maxima,code)       :maximaprincipalbalancesmassmomentumversion12021
download  (Maxima,png)         :maximaprincipalbalancesmassmomentumversion12021outp
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see :chemical reaction engineering 'website:appendix'.
maxima:differential volume element spherical coordinates for pde construct ,version 1.0

 differential volume cylindrical coordinates
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given : :dv =r*dθ*dr*dz

rem : figure 1:(Δθ =dθ,Δr=dr,Δz=dz}

dvb:r*dθ*dr*dz;

la2:dvb=dv;

reverse for la2

laa2:rhs(la2)=lhs(la2);

→  needed for build : pde equations in cylindrical coordinates

l1:["surface", "direction","incremental"];
l2:[r*dθ*dz,r,dvb];
l2a:[l2[1],l2[2],dvb/l2[1]];
l3:[dr*dz,θ,dvb];
l3a:[l3[1],l3[2],dvb/l3[1]];
l4:[r*dr*dθ,φ,dvb];
l4a:[l4[1],l4[2],dvb/l4[1]];

table_form([l1,l2a,l3a,l4a])$

→ check for table, 'cylindrical coordinates'

la1:append(l1,["check"]);

l2aa:[l2a[1],l2a[2],l2a[3],l2a[1]*l2a[3]];
l3aa:[l3a[1],l3a[2],l3a[3],l3a[1]*l3a[3]];
l4aa:[l4a[1],l4a[2],l4a[3],l4a[1]*l4a[3]];
l5aa:["","",l2aa[3]*l3aa[3]*l4aa[3],""];

ll:[la1,l2aa,l3aa,l4aa,l5aa];

table_form([la1,l2aa,l3aa,l4aa,l5aa])$

rem : r*dθ = [length]

ll:subst([la2],ll);

result :check  'cylindrical coordinates'
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table_form(ll)$

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