\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i10) | kill ( all ) ; |
\[\operatorname{ }\ensuremath{\mathrm{done}}\]
| (%i4) | ro : 1000 ; g : 9 . 81 ; H : 3 ; B : 1 ; |
\[\operatorname{ }1000\]
\[\operatorname{ }9.81\]
\[\operatorname{ }3\]
\[\operatorname{ }1\]
| (%i5) | P : integrate ( ro · g · ( H − h ) · B , h , 0 , H ) ; |
\[\operatorname{ }44145.0\]
| (%i6) | mP : integrate ( ro · g · ( ( H − h ) · · 2 ) · B , h , 0 , H ) ; |
\[\operatorname{ }88290.0\]
| (%i7) | h_D : mP / P ; |
\[\operatorname{ }2.0\]
| (%i8) | mP_down : integrate ( ( ro · g · ( H − h ) · B ) · h , h , 0 , H ) ; |
\[\operatorname{ }44145.0\]
| (%i9) | h_D_down : mP_down / P ; |
\[\operatorname{ }1.0\]
| (%i10) | h1 : 1 ; |
\[\operatorname{ }1\]
| (%i11) | P_h1 : integrate ( ro · g · ( H − h + h1 ) · B , h , 0 , H ) ; |
\[\operatorname{ }73575.0\]
| (%i12) | mP_h1 : integrate ( ro · g · ( ( H − h + h1 ) · · 2 ) · B , h , 0 , H ) ; |
\[\operatorname{ }206010.0\]
| (%i13) | h_D_h1 : mP_h1 / P_h1 ; |
\[\operatorname{ }2.8\]
| (%i14) | mP_h1_down : integrate ( ro · g · ( ( H − h + h1 ) · h ) · B , h , 0 , H ) ; |
\[\operatorname{ }88290.0\]
| (%i15) | h_D_h1_down : mP_h1_down / P_h1 ; |
\[\operatorname{ }1.2\]
| (%i16) | h_D_h1 + h_D_h1_down ; |
\[\operatorname{ }4.0\]
| --> | /* Rectangle with h1 (up) + p_m */ |
| (%i73) | p_m : 10000 ; |
\[\operatorname{ }10000\]
| (%i74) | P_h1_pm : integrate ( ro · g · ( H − h + h1 + p_m / ( ro · g ) ) · B , h , 0 , H ) ; |
\[\]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 12.038735983690112 by 11810/981 = 12.038735983690112 \]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 16.077471967380223 by 15772/981 = 16.077471967380223\]
\[\operatorname{ }157720.0\]
| (%i75) | mP_h1_pm_up : integrate ( ro · g · ( H − h + h1 + p_m / ( ro · g ) ) · ( H − h ) · B , h , 0 , H ) ; |
\[\]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056\]
\[\operatorname{ }367760.0\]
| (%i76) | h_D_h1_pm_up : mP_h1_pm_up / P_h1_pm ; |
\[\operatorname{ }2.3317271113365456\]
| --> | /* Rectangle with h1 (down) + p_m */ |
| (%i66) | P_h1_pm : integrate ( ro · g · ( H − h + h1 + p_m / ( ro · g ) ) · B , h , 0 , H ) ; |
\[\]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 12.038735983690112 by 11810/981 = 12.038735983690112 \]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 16.077471967380223 by 15772/981 = 16.077471967380223\]
\[\operatorname{ }157720.0\]
| (%i67) | mP_h1_pm_down : integrate ( ro · g · ( H − h + h1 + p_m / ( ro · g ) ) · h · B , h , 0 , H ) ; |
\[\]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056 \]\[rat: replaced 6.019367991845056 by 5905/981 = 6.019367991845056\]
\[\operatorname{ }263120.0\]
| (%i68) | h_D_h1_pm_down : mP_h1_pm_down / P_h1_pm ; |
\[\operatorname{ }1.6682728886634541\]
| (%i77) |
/* test all H = 4 OK! */
h_D_h1_pm_up + h_D_h1_pm_down ; |
\[\operatorname{ }4.0\]
| (%i17) | H : 4 ; |
\[\operatorname{ }4\]
| (%i18) | fB ( h ) : = ( B / H ) · ( H − h ) ; |
\[\operatorname{ }\operatorname{fB}(h)\operatorname{:=}\frac{B}{H} \left( H\operatorname{-}h\right) \]
| (%i20) | fB ( 0 ) ; fB ( H ) ; |
\[\operatorname{ }1\]
\[\operatorname{ }0\]
| (%i21) | P_tri : integrate ( ro · g · ( H − h ) · fB ( h ) , h , 0 , H ) ; |
\[\operatorname{ }52320.0\]
| (%i22) | mP_tri : integrate ( ro · g · ( ( H − h ) · · 2 ) · fB ( h ) , h , 0 , H ) ; |
\[\operatorname{ }156960.0\]
| (%i23) | h_D_tri : mP_tri / P_tri ; |
\[\operatorname{ }3.0\]
| (%i24) | P_trap : integrate ( ro · g · ( H − h ) · fB ( h ) , h , 0 , H / 2 ) ; |
\[\operatorname{ }45780.0\]
| (%i25) | mP_trap : integrate ( ro · g · ( ( H − h ) · · 2 ) · fB ( h ) , h , 0 , H / 2 ) ; |
\[\operatorname{ }147150.0\]
| (%i26) | h_D_trap : mP_trap / P_trap ; |
\[\operatorname{ }3.2142857142857144\]
| (%i27) | mP_trap_down : integrate ( ro · g · ( ( H − h ) · h ) · fB ( h ) , h , 0 , H / 2 ) ; |
\[\operatorname{ }35970.0\]
| (%i28) | h_D_trap_down : mP_trap_down / P_trap ; |
\[\operatorname{ }0.7857142857142857\]
| (%i29) | R : 1 ; |
\[\operatorname{ }1\]
| (%i30) | fB_circle ( h ) : = 2 · sqrt ( R · · 2 − h · · 2 ) ; |
\[\operatorname{ }\operatorname{fB\_ circle}(h)\operatorname{:=}2 \sqrt{{{R}^{2}}\operatorname{-}{{h}^{2}}}\]
| (%i32) | fB_circle ( 0 ) ; fB_circle ( R ) ; |
\[\operatorname{ }2\]
\[\operatorname{ }0\]
| (%i33) | P_cir_up : integrate ( ro · g · ( R − h ) · fB_circle ( h ) , h , 0 , R ) ; |
\[\operatorname{ }19620.0 \left( \frac{\ensuremath{\pi} }{4}\operatorname{-}\frac{1}{3}\right) \]
| (%i34) | P_cir_up , numer ; |
\[\operatorname{ }8869.511965857935\]
| (%i35) | mP_cir_up : integrate ( ro · g · ( ( R − h ) · · 2 ) · fB_circle ( h ) , h , 0 , R ) ; |
\[\operatorname{ }19620.0 \left( \frac{5 \ensuremath{\pi} }{16}\operatorname{-}\frac{2}{3}\right) \]
| (%i36) | h_D_cir_up : mP_cir_up / P_cir_up , numer ; |
\[\operatorname{ }0.6969819738807302\]
| (%i41) | h_c : ( 1 − 0 . 4244 ) · R ; p : ro · g · h_c ; w : ( %pi · ( R · · 2 ) ) / 2 ; P : p · w , numer ; I : 0 . 1098 · R · · 4 ; |
\[\operatorname{ }0.5756\]
\[\operatorname{ }5646.636\]
\[\operatorname{ }\frac{\ensuremath{\pi} }{2}\]
\[\operatorname{ }8869.715087547827\]
\[\operatorname{ }0.1098\]
| (%i42) | h_D : h_c + I / ( h_c · w ) , numer ; |
\[\operatorname{ }0.6970399774252266\]
| (%i44) | fB_circle_d ( h ) : = 2 · sqrt ( R · · 2 − ( R − h ) · · 2 ) ; |
\[\operatorname{ }\operatorname{fB\_ circle\_ d}(h)\operatorname{:=}2 \sqrt{{{R}^{2}}\operatorname{-}{{\left( R\operatorname{-}h\right) }^{2}}}\]
| (%i46) | fB_circle_d ( 0 ) ; fB_circle_d ( R ) ; |
\[\operatorname{ }0\]
\[\operatorname{ }2\]
| (%i48) | P_cir_d : integrate ( ro · g · ( R − h ) · fB_circle_d ( h ) , h , 0 , R ) ; |
\[\operatorname{ }6540.0\]
| (%i49) | mP_cir_d : integrate ( ro · g · ( ( R − h ) · h ) · fB_circle_d ( h ) , h , 0 , R ) ; |
\[\operatorname{ }19620.0 \left( \frac{1}{3}\operatorname{-}\frac{\ensuremath{\pi} }{16}\right) \]
| (%i50) | h_D_cir_d : mP_cir_d / P_cir_d , numer ; |
\[\operatorname{ }0.41095137745191374\]
| (%i55) | h_c : ( 0 . 4244 ) · R ; p : ro · g · h_c ; w : ( %pi · ( R · · 2 ) ) / 2 ; P : p · w , numer ; I : 0 . 1098 · R · · 4 ; |
\[\operatorname{ }0.4244\]
\[\operatorname{ }4163.364\]
\[\operatorname{ }\frac{\ensuremath{\pi} }{2}\]
\[\operatorname{ }6539.796878310107\]
\[\operatorname{ }0.1098\]
| (%i60) | h_D : h_c + I / ( h_c · w ) , numer ; |
\[\operatorname{ }0.5891051154711603\]
| (%i61) |
/* test from down coordinates */
R − h_D ; |
\[\operatorname{ }0.4108948845288397\]
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