\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| --> | kill(all); |
\[\]\[\tag{%o0} \ensuremath{\mathrm{done}}\]
| --> | load(draw); |
\[\]\[\tag{%o1} "C:/maxima-5.47.0/share/maxima/5.47.0/share/draw/draw.lisp"\]
| --> | ro:1000;g:9.81;h1:3;B:2;R:1;long_x:4; label_left:2.5; label_vert:1.5; label_URL:0.2; |
\[\]\[\tag{%o2} 1000\]
\[\]\[\tag{%o3} 9.81\]
\[\]\[\tag{%o4} 3\]
\[\]\[\tag{%o5} 2\]
\[\]\[\tag{%o6} 1\]
\[\]\[\tag{%o7} 4\]
\[\]\[\tag{%o8} 2.5\]
\[\]\[\tag{%o9} 1.5\]
\[\]\[\tag{%o10} 0.2\]
| --> | H1:R+h1; |
\[\]\[\tag{%o11} 4\]
| --> | x1:R+long_x; |
\[\]\[\tag{%o12} 5\]
| --> | fy(x):=sqrt(R··2−x··2); |
\[\]\[\tag{%o13} \mathop{fy}(x)\mathop{:=}\sqrt{{{R}^{2}}\mathop{-}{{x}^{2}}}\]
P_X
| --> | P_X:integrate(ro·g·(H1−h)·B,h,0,R); |
\[\]\[\tag{%o14} 68670.0\]
| --> | mP_X:integrate(ro·g·(H1−h)·B·h,h,0,R); |
\[\]\[\tag{%o15} 32700.0\]
| --> | h_D_:mP_X/P_X;h_D:H1−h_D_; |
\[\]\[\tag{%o16} 0.47619047619047616\]
\[\]\[\tag{%o17} 3.5238095238095237\]
| --> | h_C:H1−R/2,numer; |
\[\]\[\tag{%o18} 3.5\]
| --> | p_C:ro·g·h_C; |
\[\]\[\tag{%o19} 34335.0\]
| --> | w:R·B; |
\[\]\[\tag{%o20} 2\]
| --> | P_X_test:p_C·w; |
\[\]\[\tag{%o21} 68670.0\]
| --> | I_0:(B·R··3)/12,numer; |
\[\]\[\tag{%o22} 0.16666666666666666\]
| --> | h_D:h_C+(I_0)/(h_C·w); |
\[\]\[\tag{%o23} 3.5238095238095237\]
| --> | scale_L:P_X; |
\[\]\[\tag{%o24} 68670.0\]
| --> | scale_P_X:P_X/scale_L; |
\[\]\[\tag{%o25} 1.0\]
P_Z
| --> | W1:(R··2−((%pi·R··2)/4))·B,numer; |
\[\]\[\tag{%o26} 0.42920367320510344\]
| --> | W2:h1·R·B; |
\[\]\[\tag{%o27} 6\]
| --> | P_Z1:W1·ro·g;P_Z2:W2·ro·g;P_Z1+P_Z2; |
\[\]\[\tag{%o28} 4210.488034142065\]
\[\]\[\tag{%o29} 58860.0\]
\[\]\[\tag{%o30} 63070.488034142065\]
| --> | W:W1+W2; |
\[\]\[\tag{%o31} 6.429203673205103\]
| --> | P_Z:W·ro·g; |
\[\]\[\tag{%o32} 63070.48803414207\]
| --> | scale_P_Z:P_Z/scale_L; |
\[\]\[\tag{%o33} 0.9184576676007292\]
| --> | fi:atan(P_Z/P_X);fi_gr:fi·(180/%pi),numer; |
\[\]\[\tag{%o34} 0.7429196233894027\]
\[\]\[\tag{%o35} 42.56615893766137\]
| --> | x_z:h_D_/scale_P_Z; |
\[\]\[\tag{%o36} 0.5184675276699688\]
| --> | P:sqrt(P_Z··2+P_X··2);scale_P:P/scale_L; |
\[\]\[\tag{%o37} 93238.70098228985\]
\[\]\[\tag{%o38} 1.3577792483222637\]
title = "Сила тиску на криволінійну поверхню",
DRAW
| --> | R;h1;H1;x1;h_D_;x_z;scale_P;scale_P_Z;scale_P_X;P;P_X;P_Z; |
\[\]\[\tag{%o39} 1\]
\[\]\[\tag{%o40} 3\]
\[\]\[\tag{%o41} 4\]
\[\]\[\tag{%o42} 5\]
\[\]\[\tag{%o43} 0.47619047619047616\]
\[\]\[\tag{%o44} 0.5184675276699688\]
\[\]\[\tag{%o45} 1.3577792483222637\]
\[\]\[\tag{%o46} 0.9184576676007292\]
\[\]\[\tag{%o47} 1.0\]
\[\]\[\tag{%o48} 93238.70098228985\]
\[\]\[\tag{%o49} 68670.0\]
\[\]\[\tag{%o50} 63070.48803414207\]
| --> |
/* Definition of a block with local variables */ ds(r) := block([x, n], n:100, x:r·n, x:floor(x), x:x/100, return(x) )$ |
| --> | Pi_X:ds(P_X),numer; Pi_Z:ds(P_Z),numer; Pi:ds(P),numer; fi_gr:ds(fi_gr),numer; hi_D_:ds(h_D_),numer; |
\[\]\[\tag{%o52} 68670\]
\[\]\[\tag{%o53} 63070.48\]
\[\]\[\tag{%o54} 93238.7\]
\[\]\[\tag{%o55} 42.56\]
\[\]\[\tag{%o56} 0.47\]
| --> | xi_z:ds(x_z),numer; |
\[\]\[\tag{%o57} 0.51\]
| --> | if h1 < 1 then H2:H1+1 else H2:H1; |
\[\]\[\tag{%o58} 4\]
| --> | fy(x);xi0:0;yi0:0;xi1:x_z;yi1:h_D_; |
\[\]\[\tag{%o59} \sqrt{1\mathop{-}{{x}^{2}}}\]
\[\]\[\tag{%o60} 0\]
\[\]\[\tag{%o61} 0\]
\[\]\[\tag{%o62} 0.5184675276699688\]
\[\]\[\tag{%o63} 0.47619047619047616\]
| --> | fyL(x,h_D_,x_z):=(h_D_/x_z)·x; |
\[\]\[\tag{%o64} \mathop{fyL}\left( x\mathop{,}\ensuremath{\mathrm{h\_ D\_ }}\mathop{,}\ensuremath{\mathrm{x\_ z}}\right) \mathop{:=}\frac{\ensuremath{\mathrm{h\_ D\_ }}}{\ensuremath{\mathrm{x\_ z}}} x\]
| --> | fyL(0.73,h_D_,x_z); |
\[\]\[\tag{%o65} 0.6704740973485324\]
| --> | fxi(yi,x_z,h_D_):=x_z−(h_D_−yi)·((x_z)/(h_D_)); |
\[\]\[\tag{%o66} \mathop{fxi}\left( \ensuremath{\mathrm{yi}}\mathop{,}\ensuremath{\mathrm{x\_ z}}\mathop{,}\ensuremath{\mathrm{h\_ D\_ }}\right) \mathop{:=}\ensuremath{\mathrm{x\_ z}}\mathop{-}\left( \ensuremath{\mathrm{h\_ D\_ }}\mathop{-}\ensuremath{\mathrm{yi}}\right) \frac{\ensuremath{\mathrm{x\_ z}}}{\ensuremath{\mathrm{h\_ D\_ }}}\]
| --> | n:5;dx:(R−x_z)/n; |
\[\]\[\tag{%o67} 5\]
\[\]\[\tag{%o68} 0.09630649446600623\]
| --> | x_i:0.1;yiC:fy(x_i),numer;yiL:fyL(x_i,h_D_,x_z),numer; |
\[\]\[\tag{%o69} 0.1\]
\[\]\[\tag{%o70} 0.99498743710662\]
\[\]\[\tag{%o71} 0.09184576676007294\]
| --> | x_i:dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o72} 0.09630649446600623\]
\[\]\[\tag{%o73} 0.9953517263378153\]
\[\]\[\tag{%o74} 0.08845343828205063\]
| --> | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o75} 0.19261298893201245\]
\[\]\[\tag{%o76} 0.9812748017220643\]
\[\]\[\tag{%o77} 0.17690687656410126\]
| --> | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o78} 0.28891948339801865\]
\[\]\[\tag{%o79} 0.9573533998022997\]
\[\]\[\tag{%o80} 0.26536031484615186\]
| --> | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o81} 0.3852259778640249\]
\[\]\[\tag{%o82} 0.922822272151418\]
\[\]\[\tag{%o83} 0.3538137531282025\]
| --> |
coord_x(n,h_D_,x_z,R):=block ([dx,xi,yiC,yiL], dx:2·(R−x_z)/n, x_i:dx, for i:1 step 1 thru n do (yiC:fy(x_i),yiL:fyL(x_i,h_D_,x_z), if yiC>yiL then (x_i:x_i+dx) else (x_i:x_i)), return (x_i) ); |
\[\]\[\tag{%o84} \mathop{coord\_ x}\left( n\mathop{,}\ensuremath{\mathrm{h\_ D\_ }}\mathop{,}\ensuremath{\mathrm{x\_ z}}\mathop{,}R\right) \mathop{:=}\]
| --> | h_D_;x_z;R; |
\[\]\[\tag{%o85} 0.47619047619047616\]
\[\]\[\tag{%o86} 0.5184675276699688\]
\[\]\[\tag{%o87} 1\]
| --> | X:coord_x(30,h_D_,x_z,R);Y:fyL(X,h_D_,x_z); |
\[\]\[\tag{%o88} 0.738349790906048\]
\[\]\[\tag{%o89} 0.678143026829055\]
| --> | X:ds(X),numer; Y:ds(Y),numer; |
\[\]\[\tag{%o90} 0.73\]
\[\]\[\tag{%o91} 0.67\]
| --> | n:10;dx:2·(R−x_z)/n;x_i:dx; |
\[\]\[\tag{%o92} 10\]
\[\]\[\tag{%o93} 0.09630649446600623\]
\[\]\[\tag{%o94} 0.09630649446600623\]
| --> | for i:1 step 1 thru n do (yiC:fy(x_i),yiL:fyL(x_i,h_D_,x_z), if yiC>yiL then (x_i:x_i+dx,display (x_i, yiC,yiL)) else (x_i:x_i,display ("stop"))); |
\[\]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}0.19261298893201245 \]\[\ensuremath{\mathrm{yiC}}\mathop{=}0.9953517263378153 \]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.08845343828205063 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}0.28891948339801865 \]\[\ensuremath{\mathrm{yiC}}\mathop{=}0.9812748017220643 \]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.17690687656410126 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}0.3852259778640249 \]\[\ensuremath{\mathrm{yiC}}\mathop{=}0.9573533998022997 \]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.26536031484615186 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}0.48153247233003116 \]\[\ensuremath{\mathrm{yiC}}\mathop{=}0.922822272151418 \]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.3538137531282025 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}0.5778389667960374 \]\[\ensuremath{\mathrm{yiC}}\mathop{=}0.8764282503957341 \]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.44226719141025317 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}0.6741454612620437 \]\[\ensuremath{\mathrm{yiC}}\mathop{=}0.8161508000682767 \]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.5307206296923038 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}0.7704519557280499 \]\[\ensuremath{\mathrm{yiC}}\mathop{=}0.738598603478091 \]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.6191740679743545 \]\[\mbox{}\\"stop"\mathop{=}"stop" \]\[\mbox{}\\"stop"\mathop{=}"stop" \]\[\mbox{}\\"stop"\mathop{=}"stop"\]
\[\]\[\tag{%o95} \ensuremath{\mathrm{done}}\]
| --> |
draw2d( xrange = [0,x1], /* size picture x - x1 & y - H1 */ yrange = [0,H2], proportional_axes=xy, font = "Arial", font_size = 16, grid = true, line_width=4,color=black, title = "Pressure force on a curved surface", fill_color = light_blue, line_width=2, polygon([[0,0],[0,H1],[R,H1],[R,0]]), /* rectangle Body of presure */ color=black, fill_color = red, filled_func = true, explicit(fy(x),x,0,R), /* 1/4 circle */ fill_color = light_blue, line_width=1, head_angle = 180, vector([0,R],[R,0]), /* horizontal line between W1 &W2 */ color = navy, label(["W1",R−0.35,R−0.15]), label(["W2",R/2,H1−0.15]), label_orientation = vertical, color = "#654321", label(["Body presure",R−0.1,H1−1]), color = "black", fill_color = light_blue, line_width=2, head_angle = 15, head_length = 0.25, color=black,point_type = filled_circle, point_size = 2, points_joined = false, points([[0,0]]), points([[X,Y]]), points([[R,h_D_]]), label_orientation = horizontal, label(["P_x",R+0.5,h_D_+0.2]), label_orientation = vertical, label(["P_z",x_z−0.2,R+0.7]), line_width=1, line_type = dashes, head_angle = 180, vector([0,h_D_],[R,0]), /* horizontal line dot to vector P_x */ vector([x_z,R],[0,−R]), /* vertical line dot to vector P_z */ vector([0,0],[R,scale_P_Z·R]), /* direct angle line dot to vector P */ color = "blue", line_width=3, line_type = solid, head_angle = 15, head_length = 0.25, vector([R+scale_P_X,h_D_],[−scale_P_X,0]), /* horizontal vector P_x */ vector([x_z,R+scale_P_Z],[0,−scale_P_Z]), /* vertical vector P_y */ /* vector([x_z+scale_P_X,h_D_+scale_P_Z],[-scale_P_X,-scale_P_Z]), Full vector P */ vector([X+scale_P_X,Y+scale_P_Z],[−scale_P_X,−scale_P_Z]), /* Full vector P */ font = "Arial", font_size = 16, color = "#0e406e", label_orientation = horizontal, label(["www.k123.org.ua ", x1−long_x/2,H2−label_URL]), label(["Kopanytsia Y (c) 2026", x1−long_x/2,H2−3·label_URL]), label_orientation = horizontal, /* label([string(P_X), x1-0.8, R/2]) */ label_alignment = left, color = black, label([concat("Y=: ", string(Y)," m"), x1−label_left, R·1.6]), label([concat("X=: ", string(X)," m"), x1−label_left, R·1.4]), label([concat("h_D=: ", string(hi_D_)," m"), x1−label_left, R·1.2]), label([concat("x_z=: ", string(xi_z)," m"), x1−label_left, R]), label([concat("P_x=: ", string(Pi_X)," N"), x1−label_left, R·0.8]), label([concat("P_z=: ", string(Pi_Z)," N"), x1−label_left, R·0.6]), label([concat("P=: ", string(Pi)," N"), x1−label_left, R·0.4]), label([concat("phi=: ", string(fi_gr)," grad"), x1−label_left, R·0.2]), line_type = solid, color=black,line_width=1, head_both = true, head_length = 0.2, head_angle = 10, vector([R+scale_P_X,0],[0,h_D_]), /* h_D_ */ vector([0,R+0.3],[x_z,0]), /* x_z */ label_alignment = center, label_orientation = vertical, font_size = 10, label([concat("h_d=: ", string(hi_D_)," m"), R+0.8, h_D_/2]), label_orientation = horizontal, label([concat("x_z=: ", string(xi_z)," m"), x_z/2,R+0.5]) ); |
\[\]\[\tag{%o96} \]
Created with wxMaxima.
The source of this Maxima session can be downloaded here.