\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i1) | kill ( all ) ; |
\[\operatorname{ }\ensuremath{\mathrm{done}}\]
| (%i6) | ro : 1000 ; g : 9 . 81 ; H1 : 3 ; p_a : 101325 ; B : 2 ; H2 : 1 . 5 ; |
\[\operatorname{ }1000\]
\[\operatorname{ }9.81\]
\[\operatorname{ }3\]
\[\operatorname{ }101325\]
\[\operatorname{ }2\]
\[\operatorname{ }1.5\]
| (%i7) | h_c1 : H1 / 2 , numer ; |
\[\operatorname{ }1.5\]
| (%i8) | p_c1 : ro · g · h_c1 ; |
\[\operatorname{ }14715.0\]
| (%i9) | w1 : H1 · B ; |
\[\operatorname{ }6\]
| (%i10) | P_x1 : p_c1 · w1 ; |
\[\operatorname{ }88290.0\]
| (%i11) | I_01 : ( B · ( H1 · · 3 ) ) / ( 12 ) , numer ; |
\[\operatorname{ }4.5\]
| (%i12) | h_d1 : h_c1 + ( I_01 / ( h_c1 · w1 ) ) ; |
\[\operatorname{ }2.0\]
| (%i13) | h_c2 : H2 / 2 , numer ; |
\[\operatorname{ }0.75\]
| (%i14) | p_c2 : ro · g · h_c2 ; |
\[\operatorname{ }7357.5\]
| (%i15) | w2 : H2 · B ; |
\[\operatorname{ }3.0\]
| (%i16) | P_x2 : p_c2 · w2 ; |
\[\operatorname{ }22072.5\]
| (%i17) | I_02 : ( B · ( H2 · · 3 ) ) / ( 12 ) , numer ; |
\[\operatorname{ }0.5625\]
| (%i18) | h_d2 : h_c2 + ( I_02 / ( h_c2 · w2 ) ) ; |
\[\operatorname{ }1.0\]
| (%i19) | h_d1_1 : H1 − h_d1 ; |
\[\operatorname{ }1.0\]
| (%i20) | h_d2_1 : H2 − h_d2 ; |
\[\operatorname{ }0.5\]
| (%i21) | P : P_x1 − P_x2 ; |
\[\operatorname{ }66217.5\]
| (%i22) | mP : h_d1_1 · P_x1 − h_d2_1 · P_x2 ; |
\[\operatorname{ }77253.75\]
| (%i23) | h_D : mP / P ; |
\[\operatorname{ }1.1666666666666667\]
K123 two plates
| (%i24) | P1 : integrate ( ro · g · ( H1 − h ) · B , h , 0 , H1 ) ; |
\[\operatorname{ }88290.0\]
| (%i25) | ' integrate ( ro · g · ( H1 − h ) · B , h , 0 , H1 ) ; |
\[\operatorname{ }19620.0 \int_{0}^{3}{\left. 3\operatorname{-}hdh\right.}\]
| (%i26) | mP1 : integrate ( ro · g · ( H1 − h ) · B · h , h , 0 , H1 ) ; |
\[\operatorname{ }88290.0\]
| (%i30) | ' integrate ( ro · g · ( H1 − h ) · B · h , h , 0 , H1 ) ; |
\[\operatorname{ }19620.0 \int_{0}^{3}{\left. \left( 3\operatorname{-}h\right) hdh\right.}\]
| (%i27) | P2 : integrate ( ro · g · ( H2 − h ) · B , h , 0 , H2 ) ; |
\[\]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 3.0 by 3/1 = 3.0 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.125 by 9/8 = 1.125\]
\[\operatorname{ }22072.5\]
| (%i28) | mP2 : integrate ( ro · g · ( H2 − h ) · B · h , h , 0 , H2 ) ; |
\[\]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 0.5625 by 9/16 = 0.5625\]
\[\operatorname{ }11036.25\]
| (%i29) | h_D_k123 : ( mP1 − mP2 ) / ( P1 − P2 ) ; |
\[\operatorname{ }1.1666666666666667\]
| (%i38) | ' h_D_k123 = ( ' mP1 − ' mP2 ) / ( ' P1 − ' P2 ) ; |
\[\operatorname{ }\ensuremath{\mathrm{h\_ D\_ k123}}\operatorname{=}\frac{\ensuremath{\mathrm{mP1}}\operatorname{-}\ensuremath{\mathrm{mP2}}}{\ensuremath{\mathrm{P1}}\operatorname{-}\ensuremath{\mathrm{P2}}}\]
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