\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i1) | kill(all); |
\[\]\[\tag{%o0} \ensuremath{\mathrm{done}}\]
| (%i2) | nu:1.004·10··−6;del:0.02·10··−3; |
\[\]\[\tag{%o1} 1.004 {{10}^{-6}}\]
\[\]\[\tag{%o2} 2.0 {{10}^{-5}}\]
| (%i5) | K1:0.679;K2:0.378;K3:0.679; |
\[\]\[\tag{%o3} 0.679\]
\[\]\[\tag{%o4} 0.378\]
\[\]\[\tag{%o5} 0.679\]
| (%i8) | D1:0.25;D2:0.2;D3:0.25; |
\[\]\[\tag{%o6} 0.25\]
\[\]\[\tag{%o7} 0.2\]
\[\]\[\tag{%o8} 0.25\]
| (%i11) | L1:400;L2:200;L3:500; |
\[\]\[\tag{%o9} 400\]
\[\]\[\tag{%o10} 200\]
\[\]\[\tag{%o11} 500\]
| (%i12) | Q:100; |
\[\]\[\tag{%o12} 100\]
| (%i13) | eq:Q1+Q2+Q3=Q; |
\[\]\[\tag{%o13} \ensuremath{\mathrm{Q3}}\mathop{+}\ensuremath{\mathrm{Q2}}\mathop{+}\ensuremath{\mathrm{Q1}}\mathop{=}100\]
| (%i14) | eq1:Q1−Q2·(K1/K2)·sqrt(L2/L1)=0; |
\[\]\[\tag{%o14} \ensuremath{\mathrm{Q1}}\mathop{-}\frac{1.7962962962962965 \ensuremath{\mathrm{Q2}}}{\sqrt{2}}\mathop{=}0\]
| (%i15) | eq2:Q1−Q3·(K1/K3)·sqrt(L3/L1)=0; |
\[\]\[\tag{%o15} \ensuremath{\mathrm{Q1}}\mathop{-}0.5 \sqrt{5} \ensuremath{\mathrm{Q3}}\mathop{=}0\]
| (%i16) | solve([eq,eq1,eq2],[Q1,Q2,Q3]); |
\[\]\[rat: replaced -1.7962962962962965 by -97/54 = -1.7962962962962963 \]\[rat: replaced -0.5 by -1/2 = -0.5\]
\[\]\[\tag{%o16} \]
| (%i17) | q1:−((sqrt(2)·(788549472·5^(7/2)−145409499000)−2903165768·5^(5/2)−92918579500)/3999761039),numer; |
\[\]\[\tag{%o17} 37.28948214754591\]
| (%i18) | q2:(−(877972608·5^(7/2))+sqrt(2)·(1616195376·5^(5/2)+51727869000)+161899236000)/3999761039,numer; |
\[\]\[\tag{%o18} 29.357791081383073\]
| (%i19) | q3:(sqrt(2)·(2326551984·5^(5/2)−197137368000)+1486697272·5^(5/2)+145158288400)/3999761039,numer; |
\[\]\[\tag{%o19} 33.35272677107102\]
| (%i20) | q1+q2+q3; |
\[\]\[\tag{%o20} 100.0\]
| (%i21) | V1:(q1/((%pi·D1··2)/4))·10··−3,numer; |
\[\]\[\tag{%o21} 0.7596550923672213\]
| (%i22) | V2:(q2/((%pi·D2··2)/4))·10··−3,numer; |
\[\]\[\tag{%o22} 0.934487513772255\]
| (%i23) | V3:(q3/((%pi·D3··2)/4))·10··−3,numer; |
\[\]\[\tag{%o23} 0.6794561703947958\]
| (%i26) | Re1:(V1·D1)/nu;Re2:(V2·D2)/nu;Re3:(V3·D3)/nu; |
\[\]\[\tag{%o24} 189157.1445137503\]
\[\]\[\tag{%o25} 186152.89118969225\]
\[\]\[\tag{%o26} 169187.29342499893\]
| (%i29) | Re1·del/D1;Re2·del/D2;Re3·del/D3; |
\[\]\[\tag{%o27} 15.132571561100026\]
\[\]\[\tag{%o28} 18.615289118969226\]
\[\]\[\tag{%o29} 13.534983473999915\]
KRAMER
| (%i30) | (K1/K2)·sqrt(L2/L1),numer; |
\[\]\[\tag{%o30} 1.270173292131391\]
| (%i31) | (K1/K3)·sqrt(L3/L1),numer; |
\[\]\[\tag{%o31} 1.118033988749895\]
| (%i32) | M:matrix([1,1,1],[1,−1.27,0],[1,0,−1.12]); |
\[\]\[\tag{%o32} \begin{pmatrix}1 & 1 & 1\\ 1 & \mathop{-}1.27 & 0\\ 1 & 0 & \mathop{-}1.12\end{pmatrix}\]
| (%i33) | DET:determinant(M); |
\[\]\[\tag{%o33} 3.8124000000000002\]
| (%i34) | M1:matrix([100,1,1],[0,−1.27,0],[0,0,−1.12]); |
\[\]\[\tag{%o34} \begin{pmatrix}100 & 1 & 1\\ 0 & \mathop{-}1.27 & 0\\ 0 & 0 & \mathop{-}1.12\end{pmatrix}\]
| (%i35) | M2:matrix([1,100,1],[1,0,0],[1,0,−1.12]); |
\[\]\[\tag{%o35} \begin{pmatrix}1 & 100 & 1\\ 1 & 0 & 0\\ 1 & 0 & \mathop{-}1.12\end{pmatrix}\]
| (%i36) | DET2:determinant(M2)/DET; |
\[\]\[\tag{%o36} 29.377819746091703\]
| (%i37) | M3:matrix([1,1,100],[1,−1.27,0],[1,0,0]); |
\[\]\[\tag{%o37} \begin{pmatrix}1 & 1 & 100\\ 1 & \mathop{-}1.27 & 0\\ 1 & 0 & 0\end{pmatrix}\]
| (%i38) | DET3:determinant(M3)/DET; |
\[\]\[\tag{%o38} 33.31234917637184\]
| (%i39) | TEST:DET1+DET2+DET3; |
\[\]\[\tag{%o39} \ensuremath{\mathrm{DET1}}\mathop{+}62.69016892246354\]
| (%i40) |
MTR: matrix( [1,1,1], [1,−1.27,0], [1,0,−1.12] ); |
\[\]\[\tag{%o40} \begin{pmatrix}1 & 1 & 1\\ 1 & \mathop{-}1.27 & 0\\ 1 & 0 & \mathop{-}1.12\end{pmatrix}\]
| (%i41) | determinant(%); |
\[\]\[\tag{%o41} 3.8124000000000002\]
Gaussa
| (%i43) | N1:[1,1,1,100];n1:[1,1,1,100]; |
\[\]\[\tag{%o42} \left[ 1\mathop{,}1\mathop{,}1\mathop{,}100\right] \]
\[\]\[\tag{%o43} \left[ 1\mathop{,}1\mathop{,}1\mathop{,}100\right] \]
| (%i45) | N2:[1,−1.27,0,0];n2:[1,−1.27,0,0]; |
\[\]\[\tag{%o44} \left[ 1\mathop{,}\mathop{-}1.27\mathop{,}0\mathop{,}0\right] \]
\[\]\[\tag{%o45} \left[ 1\mathop{,}\mathop{-}1.27\mathop{,}0\mathop{,}0\right] \]
| (%i47) | N3:[1,0,−1.12,0];n3:[1,0,−1.12,0]; |
\[\]\[\tag{%o46} \left[ 1\mathop{,}0\mathop{,}\mathop{-}1.12\mathop{,}0\right] \]
\[\]\[\tag{%o47} \left[ 1\mathop{,}0\mathop{,}\mathop{-}1.12\mathop{,}0\right] \]
| (%i48) | for i:1 thru 4 step 1 do (a:N2[i]−N1[i],N2[i]:a)$ |
| (%i49) | N2; |
\[\]\[\tag{%o49} \left[ 0\mathop{,}\mathop{-}2.27\mathop{,}\mathop{-}1\mathop{,}\mathop{-}100\right] \]
| (%i50) | for i:1 thru 4 step 1 do (a:N3[i]−N1[i],N3[i]:a)$ |
| (%i51) | N3; |
\[\]\[\tag{%o51} \left[ 0\mathop{,}\mathop{-}1\mathop{,}\mathop{-}2.12\mathop{,}\mathop{-}100\right] \]
| (%i52) | for i:1 thru 4 step 1 do (a:N3[i]+(N2[i]/N2[2]),N3[i]:a)$ |
| (%i53) | N3; |
\[\]\[\tag{%o53} \left[ -0.0\mathop{,}0.0\mathop{,}\mathop{-}1.6794713656387668\mathop{,}\mathop{-}55.947136563876654\right] \]
| (%i54) | matrix([N1],[N2],[N3]); |
\[\]\[\tag{%o54} \begin{pmatrix}\left[ 1\mathop{,}1\mathop{,}1\mathop{,}100\right] \\ \left[ 0\mathop{,}\mathop{-}2.27\mathop{,}\mathop{-}1\mathop{,}\mathop{-}100\right] \\ \left[ -0.0\mathop{,}0.0\mathop{,}\mathop{-}1.6794713656387668\mathop{,}\mathop{-}55.947136563876654\right] \end{pmatrix}\]
| (%i55) | Q3:N3[4]/N3[3]; |
\[\]\[\tag{%o55} 33.31234917637184\]
| (%i56) | Q2:(N2[4]−N2[3]·Q3)/N2[2]; |
\[\]\[\tag{%o56} 29.3778197460917\]
| (%i57) | Q1:(N1[4]−N1[3]·Q3−N1[2]·Q2)/N1[1]; |
\[\]\[\tag{%o57} 37.30983107753646\]
| (%i58) | Q1+Q2+Q3; |
\[\]\[\tag{%o58} 100.0\]
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