\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
Задача. Визначити силу тиску на плоску прямокутну поверхню шириною B=3 м та висотою H=7 м. На вільній поверхні рідини атмосферний тиск .
| (%i47) | kill ( all ) ; |
\[\operatorname{ }\ensuremath{\mathrm{done}}\]
| (%i5) | ro : 1000 ; g : 9 . 81 ; H : 7 ; B : 3 ; p_m : 10000 ; |
\[\operatorname{ }1000\]
\[\operatorname{ }9.81\]
\[\operatorname{ }7\]
\[\operatorname{ }3\]
\[\operatorname{ }10000\]
| (%i10) | del1 : H / 15 , numer ; del2 : H / 10 , numer ; del3 : H / 7 , numer ; del4 : H / 5 , numer ; del5 : H / 3 , numer ; |
\[\operatorname{ }0.4666666666666667\]
\[\operatorname{ }0.7\]
\[\operatorname{ }1\]
\[\operatorname{ }1.4\]
\[\operatorname{ }2.3333333333333335\]
| (%i11) | dh : H / 5 , numer ; |
\[\operatorname{ }1.4\]
| (%i13) | ' integrate ( ( ro · g · ( H − h ) ) · B , h , 0 , H ) ; integrate ( ( ro · g · ( H − h ) ) · B , h ) ; |
\[\operatorname{ }29430.0 \int_{0}^{7}{\left. 7\operatorname{-}hdh\right.}\]
\[\operatorname{ }29430.0 \left( 7 h\operatorname{-}\frac{{{h}^{2}}}{2}\right) \]
| (%i14) | pi ( h ) : = 9810 . 0 · ( H − h ) ; |
\[\operatorname{ }\operatorname{pi}(h)\operatorname{:=}9810.0 \left( H\operatorname{-}h\right) \]
| (%i15) | P : integrate ( ro · g · ( H − h ) · B , h , 0 , H ) ; |
\[\operatorname{ }721035.0\]
| (%i16) |
if
P
<
10
then
scale
:
3
elseif
P
<
100
then
scale
:
20
elseif P < 1000 then scale : 200 elseif P < 10000 then scale : 2000 elseif P < 100000 then scale : 20000 elseif P < 1000000 then scale : 200000 elseif P < 10000000 then scale : 2000000 ; |
\[\operatorname{ }200000\]
| (%i18) | pi ( 0 ) ; pi ( 0 ) / scale ; |
\[\operatorname{ }68670.0\]
\[\operatorname{ }0.34335\]
| (%i19) | ' integrate ( ro · g · ( ( H − h ) · · 2 ) · B , h , 0 , H ) ; |
\[\operatorname{ }29430.0 \int_{0}^{7}{\left. {{\left( 7\operatorname{-}h\right) }^{2}}dh\right.}\]
| (%i20) | mP : integrate ( ro · g · ( ( H − h ) · · 2 ) · B , h , 0 , H ) ; |
\[\operatorname{ }3364830.0\]
| (%i22) | h_D : mP / P ; h_D_ : H − h_D ; |
\[\operatorname{ }4.666666666666667\]
\[\operatorname{ }2.333333333333333\]
| (%i24) | x_draw : 3 · B ; y_draw : H + 2 ; |
\[\operatorname{ }9\]
\[\operatorname{ }9\]
| (%i26) | n : h_D_ ; mod ( n , 1 ) ; |
\[\operatorname{ }2.333333333333333\]
\[\operatorname{ }0.33333333333333304\]
| --> | /* make float to string */ ; |
| (%i27) | if floor ( n · 100 ) / 100 > 0 then n : floor ( n · 100 ) / 100 elseif floor ( n · 1000 ) / 1000 > 0 then n : floor ( n · 1000 ) / 1000 ; |
\[\operatorname{ }\frac{233}{100}\]
| (%i28) | n : n , numer ; |
\[\operatorname{ }2.33\]
| (%i29) | hh : sconcat ( n ) ; |
\[\operatorname{ }"2.33"\]
| (%i30) | hh ; |
\[\operatorname{ }"2.33"\]
| (%i31) | pp : sconcat ( P ) ; |
\[\operatorname{ }"721035.0"\]
| (%i32) | pp ; |
\[\operatorname{ }"721035.0"\]
| --> | /* p_:printf(false, "~d", n);stringp(pp);p_;n; */ ; |
| --> | /* https://sourceforge.net/p/maxima/mailman/maxima-discuss/thread/34939E59-E2C1-484B-A0CF-C6D70CB9E835@peterpall.de/ */ ; |
| (%i33) | scale_p : pi ( 0 ) ; |
\[\operatorname{ }68670.0\]
| (%i34) |
draw2d
(
xrange
=
[
−
5
,
x_draw
]
,
yrange = [ 0 , y_draw ] , font = "Arial" , font_size = 16 , title = "Rectangle" , xlabel = "Presure, Pa" , ylabel = "h,m" , grid = true , proportional_axes = xy , line_type = solid , color = black , fill_color = "#cccccc" , line_width = 1 , rectangle ( [ 0 , 0 ] , [ B , H ] ) , line_width = 2 , color = blue , water : polygon ( [ [ − 3 , H ] , [ − 1 , H ] ] ) , water : polygon ( [ [ 0 , H ] , [ B , H ] ] ) , color = black , line_width = 1 , head_both = true , head_length = 0 . 2 , head_angle = 10 , vector ( [ 0 , H + del1 ] , [ B , 0 ] ) , label ( [ "B" , B / 2 , H + del3 ] ) , points_joined = true , points ( [ [ 0 , H ] , [ 0 , H + del2 ] ] ) , points ( [ [ B , H ] , [ B , H + del2 ] ] ) , points ( [ [ B , 0 ] , [ B + del4 , 0 ] ] ) , points ( [ [ B , H ] , [ B + del4 , H ] ] ) , vector ( [ B + del4 , 0 ] , [ 0 , H ] ) , points_joined = false , label_orientation = ' vertical , label ( [ "H" , B + del2 , H / 2 ] ) , /* p_a */ color = black , label_orientation = ' horizontal , head_both = false , line_type = solid , head_length = 0 . 2 , head_angle = 10 , color = black , vector ( [ − 2 . 5 , ( H + del3 ) ] , [ 0 , − del3 ] ) , label ( [ "p_a" , − 2 . 5 − 0 . 5 + del3 , H + del3 ] ) , /* Epura */ line_width = 1 , color = blue , line_type = solid , fill_color = lightblue , poly : polygon ( [ [ − 1 , 0 ] , [ − 1 , H ] , [ − pi ( 0 ) / scale_p − 1 , 0 ] , [ 0 − 1 , 0 ] ] ) , head_length = 0 . 3 , head_angle = 10 , color = blue , line_width = 2 , head_both = false , vector ( [ − pi ( dh · 0 ) / scale_p − 1 , H − 5 · dh ] , [ pi ( dh · 0 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 1 ) / scale_p − 1 , H − 4 · dh ] , [ pi ( dh · 1 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 2 ) / scale_p − 1 , H − 3 · dh ] , [ pi ( dh · 2 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 3 ) / scale_p − 1 , H − 2 · dh ] , [ pi ( dh · 3 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 4 ) / scale_p − 1 , H − 1 · dh ] , [ pi ( dh · 4 ) / scale_p , 0 ] ) , transparent = true , line_width = 1 , color = black , points_joined = true , point_size = 0 . 1 , points ( [ [ − 2 , 0 ] , [ − 1 , 0 ] , [ − 1 , H + del2 ] ] ) , line_width = 2 , color = blue , water : points ( [ [ − 2 , H ] , [ − 1 , H ] ] ) , color = red , label ( [ "Px" , − 1 − del4 , h_D_ + del2 ] ) , label ( [ hh , − 1 + del2 , h_D_ + del1 ] ) , line_type = solid , head_length = 0 . 3 , head_angle = 15 , line_width = 2 , point_type = filled_circle , point_size = 1 , vector ( [ − 1 − P / ( scale · 2 ) , h_D_ ] , [ P / ( scale · 2 ) , 0 ] ) , points ( [ [ − 1 , h_D_ ] ] ) , points ( [ [ B / 2 , h_D_ ] ] ) , label_orientation = ' horizontal , label ( [ "D" , B / 2 + del1 , h_D_ ] ) , /* h_D */ color = black , line_width = 1 , head_both = true , head_length = 0 . 2 , head_angle = 10 , vector ( [ − 1 + del2 , 0 ] , [ 0 , h_D_ ] ) , points_joined = false , label_orientation = ' vertical , label ( [ "h_D_" , − del2 , h_D_ / 2 ] ) , points_joined = true , point_size = 0 . 1 , points ( [ [ − 1 , h_D_ ] , [ − 1 + del3 , h_D_ ] ] ) , /* copy right */ color = "#0e406e" , label_orientation = ' vertical , label ( [ "www.k123.org.ua " , 3 · B − 1 , H / 2 ] ) , label ( [ "Kopanytsia Y (c) 2025" , 3 · B − 0 . 5 , H / 2 ] ) , /* Results */ color = "#0e406e" , /* rectangle([0,y_draw-del4],[x_draw,y_draw]), */ label_orientation = ' horizontal , label ( [ hh , x_draw / 2 , y_draw − del3 ] ) , label ( [ "h_D [m]" , x_draw / 2 , y_draw − del1 / 2 ] ) , label ( [ pp , x_draw − del4 , y_draw − del3 ] ) , label ( [ "P [N]" , x_draw − del4 , y_draw − del1 / 2 ] ) /* key = "Force", xtics_secondary = true, ytics_secondary = true, xaxis_secondary = true, yaxis_secondary = true, xlabel_secondary="P[N]", ylabel_secondary="p[Pa]", yrange_secondary=[-49050.0,2/5*49050.0], xrange_secondary=[-P,P] */ ) $ |
| (%i36) | P ; P / scale ; |
\[\operatorname{ }721035.0\]
\[\operatorname{ }3.605175\]
| (%i37) | H − 2 · dh ; H ; dh ; |
\[\operatorname{ }4.2\]
\[\operatorname{ }7\]
\[\operatorname{ }1.4\]
| (%i38) | ' integrate ( ro · g · ( ( H − h ) · h ) · B , h , 0 , H ) ; |
\[\operatorname{ }29430.0 \int_{0}^{7}{\left. \left( 7\operatorname{-}h\right) hdh\right.}\]
| (%i39) | mP_down : integrate ( ro · g · ( ( H − h ) · h ) · B , h , 0 , H ) ; |
\[\operatorname{ }1682415.0\]
| (%i40) | h_D_down : mP_down / P ; |
\[\operatorname{ }2.3333333333333335\]
Numerical method K123 (Rectangle)
| (%i44) | P_sum : 0 ; n : 5 ; dh : H / n ; P_sum2 : 0 ; |
\[\operatorname{ }0\]
\[\operatorname{ }5\]
\[\operatorname{ }\frac{7}{5}\]
\[\operatorname{ }0\]
| (%i45) | fP ( i ) : = ro · g · ( H − i · dh ) · ( B · dh ) ; |
\[\operatorname{ }\operatorname{fP}(i)\operatorname{:=}\ensuremath{\mathrm{ro}} g\, \left( H\operatorname{-}i\, \ensuremath{\mathrm{dh}}\right) \, \left( B\, \ensuremath{\mathrm{dh}}\right) \]
| (%i46) | tex ( fP ( i ) : = ro · g · ( H − i · dh ) · ( B · dh ) ) ; |
\[\]\[\backslash begin\{verbatim\} \]\[fP(i):=ro\ensuremath{\cdot}g\ensuremath{\cdot}(H-i\ensuremath{\cdot}dh)\ensuremath{\cdot}(B\ensuremath{\cdot}dh); \]\[\backslash end\{verbatim\}\]
\[\operatorname{ }false\]
| (%i47) | fP2 ( i ) : = ro · g · ( H − ( i · dh + dh / 2 ) ) · ( B · dh ) ; |
\[\operatorname{ }\operatorname{fP2}(i)\operatorname{:=}\ensuremath{\mathrm{ro}} g\, \left( H\operatorname{-}\left( i\, \ensuremath{\mathrm{dh}}\operatorname{+}\frac{\ensuremath{\mathrm{dh}}}{2}\right) \right) \, \left( B\, \ensuremath{\mathrm{dh}}\right) \]
| (%i48) | for i : 0 thru n − 1 step 1 do ( Pi : fP ( i ) , P_sum : P_sum + Pi ) $ |
| (%i49) | for i : 0 thru n − 1 step 1 do ( Pi : fP2 ( i ) , P_sum2 : P_sum2 + Pi , Pv [ i ] : Pi ) $ |
| (%i52) | P_sum ; P_sum2 ; P ; |
\[\operatorname{ }865242.0\]
\[\operatorname{ }721035.0\]
\[\operatorname{ }721035.0\]
| (%i54) | ( P − P_sum ) / ( P / 100 ) ; ( P − P_sum2 ) / ( P / 100 ) ; |
\[\operatorname{ }\operatorname{-}20.0\]
\[\operatorname{ }0.0\]
| (%i55) | Pv [ 4 ] ; |
\[\operatorname{ }28841.4\]
| (%i56) | scale_p2 : scale_p / 2 ; |
\[\operatorname{ }34335.0\]
| (%i57) |
draw2d
(
xrange
=
[
−
5
,
x_draw
]
,
yrange = [ 0 , y_draw ] , font = "Arial" , font_size = 16 , title = "Rectangle" , xlabel = "Presure, Pa" , ylabel = "h,m" , grid = true , proportional_axes = xy , line_type = solid , color = black , fill_color = "#cccccc" , line_width = 1 , rectangle ( [ 0 , 0 ] , [ B , H ] ) , line_width = 2 , color = blue , water : polygon ( [ [ − 3 , H ] , [ − 1 , H ] ] ) , water : polygon ( [ [ 0 , H ] , [ B , H ] ] ) , color = black , line_width = 1 , head_both = true , head_length = 0 . 2 , head_angle = 10 , vector ( [ 0 , H + del1 ] , [ B , 0 ] ) , label ( [ "B" , B / 2 , H + del3 ] ) , points_joined = true , points ( [ [ 0 , H ] , [ 0 , H + del2 ] ] ) , points ( [ [ B , H ] , [ B , H + del2 ] ] ) , points ( [ [ B , 0 ] , [ B + del4 , 0 ] ] ) , points ( [ [ B , H ] , [ B + del4 , H ] ] ) , vector ( [ B + del4 , 0 ] , [ 0 , H ] ) , points_joined = false , label_orientation = ' vertical , label ( [ "H" , B + del2 , H / 2 ] ) , /* p_a */ color = black , label_orientation = ' horizontal , head_both = false , line_type = solid , head_length = 0 . 2 , head_angle = 10 , color = black , vector ( [ − 2 . 5 , ( H + del3 ) ] , [ 0 , − del3 ] ) , label ( [ "p_a" , − 2 . 5 − 0 . 5 + del3 , H + del3 ] ) , /* Epura */ line_width = 1 , color = blue , line_type = solid , fill_color = lightblue , /* poly:polygon([[−1,0],[−1,H],[−pi(0)/scale_p2−1,0],[0−1,0]]), */ head_length = 0 . 3 , head_angle = 10 , color = blue , line_width = 1 , head_both = false , rectangle ( [ − 1 , dh · 0 ] , [ − pi ( dh · 0 + dh / 2 ) / scale_p2 − 1 , dh ] ) , vector ( [ − pi ( dh · 0 + dh / 2 ) / scale_p2 − 1 , H − 5 · dh + dh / 2 ] , [ pi ( dh · 0 + dh / 2 ) / scale_p2 , 0 ] ) , label ( [ "p_i" , − pi ( dh · 0 + dh / 2 − del5 ) / scale_p2 , H − 5 · dh + dh / 2 + del1 ] ) , rectangle ( [ − 1 , dh · 1 ] , [ − pi ( dh · 1 + dh / 2 ) / scale_p2 − 1 , dh · 2 ] ) , vector ( [ − pi ( dh · 1 + dh / 2 ) / scale_p2 − 1 , H − 4 · dh + dh / 2 ] , [ pi ( dh · 1 + dh / 2 ) / scale_p2 , 0 ] ) , label ( [ "p_i" , − pi ( dh · 1 + dh / 2 − del5 ) / scale_p2 , H − 4 · dh + dh / 2 + del1 ] ) , rectangle ( [ − 1 , dh · 2 ] , [ − pi ( dh · 2 + dh / 2 ) / scale_p2 − 1 , dh · 3 ] ) , vector ( [ − pi ( dh · 2 + dh / 2 ) / scale_p2 − 1 , H − 3 · dh + dh / 2 ] , [ pi ( dh · 2 + dh / 2 ) / scale_p2 , 0 ] ) , label ( [ "p_i" , − pi ( dh · 2 + dh / 2 − del5 ) / scale_p2 , H − 3 · dh + dh / 2 + del1 ] ) , rectangle ( [ − 1 , dh · 3 ] , [ − pi ( dh · 3 + dh / 2 ) / scale_p2 − 1 , dh · 4 ] ) , vector ( [ − pi ( dh · 3 + dh / 2 ) / scale_p2 − 1 , H − 2 · dh + dh / 2 ] , [ pi ( dh · 3 + dh / 2 ) / scale_p2 , 0 ] ) , label ( [ "p_i" , − pi ( dh · 3 + dh / 2 − del5 ) / scale_p2 , H − 2 · dh + dh / 2 + del1 ] ) , rectangle ( [ − 1 , dh · 4 ] , [ − pi ( dh · 4 + dh / 2 ) / scale_p2 − 1 , dh · 5 ] ) , vector ( [ − pi ( dh · 4 + dh / 2 ) / scale_p2 − 1 , H − 1 · dh + dh / 2 ] , [ pi ( dh · 4 + dh / 2 ) / scale_p2 , 0 ] ) , label ( [ "p_i" , − pi ( dh · 4 − del5 ) / scale_p2 , H − 1 · dh + dh / 2 + del1 ] ) , color = black , line_type = dashes , transparent = true , /* fill_color = lightblue, */ poly : polygon ( [ [ − 1 , 0 ] , [ − 1 , H ] , [ − pi ( 0 ) / scale_p2 − 1 , 0 ] , [ 0 − 1 , 0 ] ] ) , transparent = true , line_width = 1 , color = black , points_joined = true , point_size = 0 . 1 , points ( [ [ − 2 , 0 ] , [ − 1 , 0 ] , [ − 1 , H + del2 ] ] ) , line_width = 2 , color = blue , water : points ( [ [ − 2 , H ] , [ − 1 , H ] ] ) , color = red , label ( [ "Px" , − 1 − del4 , h_D_ + del2 ] ) , label ( [ hh , − 1 + del2 , h_D_ + del1 ] ) , line_type = solid , head_length = 0 . 3 , head_angle = 15 , line_width = 2 , point_type = filled_circle , point_size = 1 , vector ( [ − 1 − P / ( scale · 2 ) , h_D_ ] , [ P / ( scale · 2 ) , 0 ] ) , points ( [ [ − 1 , h_D_ ] ] ) , points ( [ [ B / 2 , h_D_ ] ] ) , label_orientation = ' horizontal , label ( [ "D" , B / 2 + del1 , h_D_ ] ) , /* h_D */ color = black , line_width = 1 , head_both = true , head_length = 0 . 2 , head_angle = 10 , vector ( [ − 1 + del2 , 0 ] , [ 0 , h_D_ ] ) , /* dh */ vector ( [ − 1 − del1 − pi ( dh · 0 + dh / 2 − del4 ) / scale_p2 , 0 ] , [ 0 , dh ] ) , points_joined = true , point_size = 0 . 1 , points ( [ [ − 1 − del1 − pi ( dh · 0 + dh / 2 − del5 ) / scale_p2 , dh ] , [ − 1 − del1 − pi ( dh · 0 + dh / 2 − del5 ) / scale_p2 + del3 , dh ] ] ) , points_joined = false , label_orientation = ' vertical , color = red , label ( [ "h_D_" , − del2 , h_D_ / 2 ] ) , color = black , label ( [ "dh" , − 1 − del2 − pi ( dh · 0 + dh / 2 − del5 ) / scale_p2 , dh / 2 ] ) , points_joined = true , point_size = 0 . 1 , points ( [ [ − 1 , h_D_ ] , [ − 1 + del3 , h_D_ ] ] ) , /* copy right */ color = "#0e406e" , label_orientation = ' vertical , label ( [ "www.k123.org.ua " , 3 · B − 1 , H / 2 ] ) , label ( [ "Kopanytsia Y (c) 2025" , 3 · B − 0 . 5 , H / 2 ] ) , /* Results */ color = "#0e406e" , /* rectangle([0,y_draw-del4],[x_draw,y_draw]), */ label_orientation = ' horizontal , label ( [ hh , x_draw / 2 , y_draw − del3 ] ) , label ( [ "h_D [m]" , x_draw / 2 , y_draw − del1 / 2 ] ) , label ( [ pp , x_draw − del4 , y_draw − del3 ] ) , label ( [ "P [N]" , x_draw − del4 , y_draw − del1 / 2 ] ) /* key = "Force", xtics_secondary = true, ytics_secondary = true, xaxis_secondary = true, yaxis_secondary = true, xlabel_secondary="P[N]", ylabel_secondary="p[Pa]", yrange_secondary=[-49050.0,2/5*49050.0], xrange_secondary=[-P,P] */ ) $ |
Задача. Визначити силу тиску на плоску
прямокутну поверхню шириною B=3 м та
висотою H=7 м. На вільній поверхні рідини
атмосферний тиск . Прошарок води h1=1 м.
| (%i59) | kill ( all ) ; |
\[\operatorname{ }\ensuremath{\mathrm{done}}\]
| (%i5) | ro : 1000 ; g : 9 . 81 ; H : 7 ; B : 3 ; p_m : 10000 ; |
\[\operatorname{ }1000\]
\[\operatorname{ }9.81\]
\[\operatorname{ }7\]
\[\operatorname{ }3\]
\[\operatorname{ }10000\]
| (%i6) | h1 : 1 ; |
\[\operatorname{ }1\]
| (%i11) | del1 : H / 15 , numer ; del2 : H / 10 , numer ; del3 : H / 7 , numer ; del4 : H / 5 , numer ; del5 : H / 3 , numer ; |
\[\operatorname{ }0.4666666666666667\]
\[\operatorname{ }0.7\]
\[\operatorname{ }1\]
\[\operatorname{ }1.4\]
\[\operatorname{ }2.3333333333333335\]
| (%i12) | dh : H / 5 , numer ; |
\[\operatorname{ }1.4\]
| (%i14) | ' integrate ( ( ro · g · ( H − h + h1 ) ) · B , h , 0 , H ) ; integrate ( ( ro · g · ( H − h + h1 ) ) · B , h ) ; |
\[\operatorname{ }29430.0 \int_{0}^{7}{\left. 8\operatorname{-}hdh\right.}\]
\[\operatorname{ }29430.0 \left( 8 h\operatorname{-}\frac{{{h}^{2}}}{2}\right) \]
| (%i15) | pi ( h ) : = 9810 . 0 · ( H − h + h1 ) ; |
\[\operatorname{ }\operatorname{pi}(h)\operatorname{:=}9810.0 \left( H\operatorname{-}h\operatorname{+}\ensuremath{\mathrm{h1}}\right) \]
| (%i16) | P_h1 : integrate ( ro · g · ( H − h + h1 ) · B , h , 0 , H ) ; |
\[\operatorname{ }927045.0\]
| (%i17) |
if
P_h1
<
10
then
scale
:
3
elseif
P_h1
<
100
then
scale
:
20
elseif P_h1 < 1000 then scale : 200 elseif P_h1 < 10000 then scale : 2000 elseif P_h1 < 100000 then scale : 20000 elseif P_h1 < 1000000 then scale : 200000 elseif P_h1 < 10000000 then scale : 2000000 ; |
\[\operatorname{ }200000\]
| (%i20) | pi ( 0 ) ; pi ( 0 ) / scale ; pi ( h1 ) / scale ; |
\[\operatorname{ }78480.0\]
\[\operatorname{ }0.3924\]
\[\operatorname{ }0.34335\]
| (%i21) | mP_h1 : integrate ( ro · g · ( ( H − h + h1 ) · · 2 ) · B , h , 0 , H ) ; |
\[\operatorname{ }5012910.0\]
| (%i22) | h_D_h1 : mP_h1 / P_h1 ; |
\[\operatorname{ }5.407407407407407\]
| (%i23) | mP_h1_down : integrate ( ro · g · ( ( H − h + h1 ) · h ) · B , h , 0 , H ) ; |
\[\operatorname{ }2403450.0\]
| (%i24) | h_D_h1_down : mP_h1_down / P_h1 ; |
\[\operatorname{ }2.5925925925925926\]
| (%i25) | h_D_h1 + h_D_h1_down ; |
\[\operatorname{ }8.0\]
| (%i27) | x_draw : 3 · B ; y_draw : H + h1 + 2 ; |
\[\operatorname{ }9\]
\[\operatorname{ }10\]
| (%i29) | n : h_D_h1_down ; mod ( n , 1 ) ; |
\[\operatorname{ }2.5925925925925926\]
\[\operatorname{ }0.5925925925925926\]
| (%i30) | if floor ( n · 100 ) / 100 > 0 then n : floor ( n · 100 ) / 100 elseif floor ( n · 1000 ) / 1000 > 0 then n : floor ( n · 1000 ) / 1000 ; |
\[\operatorname{ }\frac{259}{100}\]
| (%i31) | n : n , numer ; |
\[\operatorname{ }2.59\]
| (%i32) | hh : sconcat ( n ) ; |
\[\operatorname{ }"2.59"\]
| (%i33) | pp : sconcat ( P_h1 ) ; |
\[\operatorname{ }"927045.0"\]
| (%i35) | scale_p : pi ( 0 ) / 2 ; scale ; |
\[\operatorname{ }39240.0\]
\[\operatorname{ }200000\]
| (%i36) |
draw2d
(
xrange
=
[
−
5
,
x_draw
]
,
yrange = [ 0 , y_draw ] , font = "Arial" , font_size = 16 , title = "Rectangle" , xlabel = "Presure, Pa" , ylabel = "h,m" , grid = true , proportional_axes = xy , line_type = solid , color = black , fill_color = "#cccccc" , line_width = 2 , rectangle ( [ 0 , 0 ] , [ B , H ] ) , line_width = 2 , color = blue , water : polygon ( [ [ − 3 , H + h1 ] , [ − 1 , H + h1 ] ] ) , water : polygon ( [ [ 0 , H + h1 ] , [ B , H + h1 ] ] ) , color = black , line_width = 1 , head_both = true , head_length = 0 . 2 , head_angle = 10 , vector ( [ 0 , H + h1 + del1 ] , [ B , 0 ] ) , label ( [ "B" , B / 2 , H + h1 + del3 ] ) , points_joined = true , point_size = 0 . 1 , points ( [ [ 0 , H + h1 ] , [ 0 , H + h1 + del2 ] ] ) , points ( [ [ B , H + h1 ] , [ B , H + h1 + del2 ] ] ) , points ( [ [ B , 0 ] , [ B + del4 , 0 ] ] ) , points ( [ [ B , H ] , [ B + del4 , H ] ] ) , vector ( [ B + del4 , 0 ] , [ 0 , H ] ) , points ( [ [ B , H + h1 ] , [ B + del4 , H + h1 ] ] ) , vector ( [ B + del4 , H ] , [ 0 , h1 ] ) , line_width = 2 , points ( [ [ 0 , 0 ] , [ 0 , H + del1 / 2 + h1 ] ] ) , points ( [ [ B , 0 ] , [ B , H + del1 / 2 + h1 ] ] ) , points_joined = false , label_orientation = ' vertical , label ( [ "H" , B + del2 , H / 2 ] ) , label ( [ "h1" , B + del2 , ( H + h1 / 2 ) ] ) , /* p_a */ color = black , label_orientation = ' horizontal , head_both = false , line_type = solid , head_length = 0 . 2 , head_angle = 10 , color = black , vector ( [ − 2 . 5 , ( H + h1 + del3 ) ] , [ 0 , − del3 ] ) , label ( [ "p_a" , − 2 . 5 − 0 . 5 + del3 , H + h1 + del3 ] ) , /* Epura */ line_width = 1 , color = blue , line_type = dashes , fill_color = white , poly : polygon ( [ [ − 1 , 0 ] , [ − 1 , H + h1 ] , [ − pi ( 0 ) / scale_p − 1 , 0 ] , [ 0 − 1 , 0 ] ] ) , line_type = solid , fill_color = lightblue , poly : polygon ( [ [ − 1 , 0 ] , [ − 1 , H ] , [ − pi ( H ) / scale_p − 1 , H ] , [ − pi ( 0 ) / scale_p − 1 , 0 ] , [ 0 − 1 , 0 ] ] ) , head_length = 0 . 3 , head_angle = 10 , color = blue , line_width = 2 , head_both = false , vector ( [ − pi ( dh · 0 ) / scale_p − 1 , H − 5 · dh ] , [ pi ( dh · 0 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 1 ) / scale_p − 1 , H − 4 · dh ] , [ pi ( dh · 1 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 2 ) / scale_p − 1 , H − 3 · dh ] , [ pi ( dh · 2 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 3 ) / scale_p − 1 , H − 2 · dh ] , [ pi ( dh · 3 ) / scale_p , 0 ] ) , vector ( [ − pi ( dh · 4 ) / scale_p − 1 , H − 1 · dh ] , [ pi ( dh · 4 ) / scale_p , 0 ] ) , transparent = true , line_width = 2 , color = black , points_joined = true , point_size = 0 . 1 , points ( [ [ − 2 , 0 ] , [ − 1 , 0 ] , [ − 1 , H + h1 + del1 / 2 ] ] ) , line_width = 2 , color = blue , color = red , label ( [ "Px" , − 1 − del4 , h_D_h1_down + del2 ] ) , label ( [ hh , − 1 + del2 , h_D_h1_down + del1 ] ) , line_type = solid , head_length = 0 . 3 , head_angle = 15 , line_width = 2 , point_type = filled_circle , point_size = 1 , vector ( [ − 1 − P_h1 / ( scale · 2 ) , h_D_h1_down ] , [ P_h1 / ( scale · 2 ) , 0 ] ) , points ( [ [ − 1 , h_D_h1_down ] ] ) , points ( [ [ B / 2 , h_D_h1_down ] ] ) , label_orientation = ' horizontal , label ( [ "D" , B / 2 + del1 , h_D_h1_down ] ) , /* h_D_h1_down */ color = black , line_width = 1 , head_both = true , head_length = 0 . 2 , head_angle = 10 , vector ( [ − 1 + del2 , 0 ] , [ 0 , h_D_h1_down ] ) , points_joined = false , label_orientation = ' vertical , label ( [ "h_D_" , − del2 , h_D_h1_down / 2 ] ) , points_joined = true , point_size = 0 . 1 , points ( [ [ − 1 , h_D_h1_down ] , [ − 1 + del3 , h_D_h1_down ] ] ) , /* copy right */ color = "#0e406e" , label_orientation = ' vertical , label ( [ "www.k123.org.ua " , 3 · B − 1 , H / 2 ] ) , label ( [ "Kopanytsia Y (c) 2025" , 3 · B − 0 . 5 , H / 2 ] ) , /* Results */ color = "#0e406e" , rectangle ( [ x_draw / 3 , y_draw − del4 ] , [ x_draw , y_draw ] ) , label_orientation = ' horizontal , label ( [ hh , x_draw / 2 , y_draw − del3 ] ) , label ( [ "h_D [m]" , x_draw / 2 , y_draw − del1 / 2 ] ) , label ( [ pp , x_draw − del4 , y_draw − del3 ] ) , label ( [ "P [N]" , x_draw − del4 , y_draw − del1 / 2 ] ) /* key = "Force", xtics_secondary = true, ytics_secondary = true, xaxis_secondary = true, yaxis_secondary = true, xlabel_secondary="P[N]", ylabel_secondary="p[Pa]", yrange_secondary=[-49050.0,2/5*49050.0], xrange_secondary=[-P,P] */ ) $ ; |
Triangle
| (%i37) | H : 7 ; |
\[\operatorname{ }7\]
| (%i38) | fB ( h ) : = ( B / H ) · ( H − h ) ; |
\[\operatorname{ }\operatorname{fB}(h)\operatorname{:=}\frac{B}{H} \left( H\operatorname{-}h\right) \]
| (%i40) | fB ( 0 ) ; fB ( H ) ; |
\[\operatorname{ }3\]
\[\operatorname{ }0\]
| (%i41) | P_tri : integrate ( ro · g · ( H − h ) · fB ( h ) , h , 0 , H ) ; |
\[\operatorname{ }480689.99999999994\]
| (%i42) | mP_tri : integrate ( ro · g · ( ( H − h ) · · 2 ) · fB ( h ) , h , 0 , H ) ; |
\[\operatorname{ }2523622.4999999995\]
| (%i43) | h_D_tri : mP_tri / P_tri ; |
\[\operatorname{ }5.25\]
| (%i44) | h_D_tri_down : H − h_D_tri ; |
\[\operatorname{ }1.75\]
| (%i45) | P_trap : integrate ( ro · g · ( H − h ) · fB ( h ) , h , 0 , H / 2 ) ; |
\[\operatorname{ }420603.74999999994\]
| (%i46) | mP_trap : integrate ( ro · g · ( ( H − h ) · · 2 ) · fB ( h ) , h , 0 , H / 2 ) ; |
\[\operatorname{ }2365896.0937499995\]
| (%i47) | h_D_trap : mP_trap / P_trap ; |
\[\operatorname{ }5.625\]
| (%i48) | mP_trap_down : integrate ( ro · g · ( ( H − h ) · h ) · fB ( h ) , h , 0 , H / 2 ) ; |
\[\operatorname{ }578330.1562499999\]
| (%i49) | h_D_trap_down : mP_trap_down / P_trap ; |
\[\operatorname{ }1.375\]
| (%i50) | R : 1 ; |
\[\operatorname{ }1\]
| (%i51) | fB_circle ( h ) : = 2 · sqrt ( R · · 2 − h · · 2 ) ; |
\[\operatorname{ }\operatorname{fB\_ circle}(h)\operatorname{:=}2 \sqrt{{{R}^{2}}\operatorname{-}{{h}^{2}}}\]
| (%i53) | fB_circle ( 0 ) ; fB_circle ( R ) ; |
\[\operatorname{ }2\]
\[\operatorname{ }0\]
| (%i54) | P_cir_up : integrate ( ro · g · ( R − h ) · fB_circle ( h ) , h , 0 , R ) ; |
\[\operatorname{ }19620.0 \left( \frac{\ensuremath{\pi} }{4}\operatorname{-}\frac{1}{3}\right) \]
| (%i55) | P_cir_up , numer ; |
\[\operatorname{ }8869.511965857935\]
| (%i56) | mP_cir_up : integrate ( ro · g · ( ( R − h ) · · 2 ) · fB_circle ( h ) , h , 0 , R ) ; |
\[\operatorname{ }19620.0 \left( \frac{5 \ensuremath{\pi} }{16}\operatorname{-}\frac{2}{3}\right) \]
| (%i57) | h_D_cir_up : mP_cir_up / P_cir_up , numer ; |
\[\operatorname{ }0.6969819738807302\]
| (%i62) | 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 ; |
\[\operatorname{ }0.5756\]
\[\operatorname{ }5646.636\]
\[\operatorname{ }\frac{\ensuremath{\pi} }{2}\]
\[\operatorname{ }8869.715087547827\]
\[\operatorname{ }0.1098\]
| (%i63) | h_D : h_c + I / ( h_c · w ) , numer ; |
\[\operatorname{ }0.6970399774252266\]
Created with wxMaxima.
The source of this Maxima session can be downloaded here.