\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i1) | kill(all); |
\[\]\[\tag{%o0} \ensuremath{\mathrm{done}}\]
| (%i1) | load(draw); |
\[\]\[\tag{%o1} "C:/maxima-5.47.0/share/maxima/5.47.0/share/draw/draw.lisp"\]
| (%i10) | ro:1000;g:9.81;h1:2;B:2;R:1;long_x:4; label_left:2.5; label_vert:1.5; label_URL:0.2; |
\[\]\[\tag{%o2} 1000\]
\[\]\[\tag{%o3} 9.81\]
\[\]\[\tag{%o4} 2\]
\[\]\[\tag{%o5} 2\]
\[\]\[\tag{%o6} 1\]
\[\]\[\tag{%o7} 4\]
\[\]\[\tag{%o8} 2.5\]
\[\]\[\tag{%o9} 1.5\]
\[\]\[\tag{%o10} 0.2\]
| (%i13) | W1_:B·R·h1;W2_:((%pi·R··2)/4)·B,numer;W_:W1_+W2_; |
\[\]\[\tag{%o11} 4\]
\[\]\[\tag{%o12} 1.5707963267948966\]
\[\]\[\tag{%o13} 5.570796326794897\]
| (%i17) | mW1_:0.5·R·W1_;mW2_:0.4244·R·W2_;mW_:mW1_+mW2_;z_c_:mW_/W_; |
\[\]\[\tag{%o14} 2.0\]
\[\]\[\tag{%o15} 0.6666459610917541\]
\[\]\[\tag{%o16} 2.666645961091754\]
\[\]\[\tag{%o17} 0.478683083110666\]
| (%i18) | H1:R+h1; |
\[\]\[\tag{%o18} 3\]
| (%i19) | x1:R+long_x; |
\[\]\[\tag{%o19} 5\]
| (%i20) | fy(x):=R−sqrt((R)··2−x··2); |
\[\]\[\tag{%o20} \mathop{fy}(x)\mathop{:=}R\mathop{-}\sqrt{{{R}^{2}}\mathop{-}{{x}^{2}}}\]
| (%i21) | dx:0.1; |
\[\]\[\tag{%o21} 0.1\]
| (%i26) | ni:10;yi[0]:1;xi[0]:0;yi[1]:0;xi[1]:0; |
\[\]\[\tag{%o22} 10\]
\[\]\[\tag{%o23} 1\]
\[\]\[\tag{%o24} 0\]
\[\]\[\tag{%o25} 0\]
\[\]\[\tag{%o26} 0\]
| (%i27) | for i:2 step 1 thru ni do (yi[i]:fy(dx·i),xi[i]:dx·i,display(yi[i])); |
\[\]\[{{\ensuremath{\mathrm{yi}}}_2}\mathop{=}0.020204102886728803 \]\[{{\ensuremath{\mathrm{yi}}}_3}\mathop{=}0.04606079858305434 \]\[{{\ensuremath{\mathrm{yi}}}_4}\mathop{=}0.08348486100883201 \]\[{{\ensuremath{\mathrm{yi}}}_5}\mathop{=}0.1339745962155614 \]\[{{\ensuremath{\mathrm{yi}}}_6}\mathop{=}0.20000000000000007 \]\[{{\ensuremath{\mathrm{yi}}}_7}\mathop{=}0.285857157145715 \]\[{{\ensuremath{\mathrm{yi}}}_8}\mathop{=}0.40000000000000013 \]\[{{\ensuremath{\mathrm{yi}}}_9}\mathop{=}0.5641101056459328 \]\[{{\ensuremath{\mathrm{yi}}}_{10}}\mathop{=}1.0\]
\[\]\[\tag{%o27} \ensuremath{\mathrm{done}}\]
| (%i28) |
draw2d(proportional_axes=xy, color = black, fill_color = lightblue, line_width = 2, polygon([[xi[0],yi[0]], [xi[1],yi[1]], [xi[2],yi[2]], [xi[3],yi[3]], [xi[4],yi[4]], [xi[5],yi[5]], [xi[6],yi[6]], [xi[7],yi[7]], [xi[8],yi[8]], [xi[9],yi[9]], [xi[10],yi[10]]]), polygon([[0,R], [0,H1], [R,H1], [R,R]]), color = red, line_width = 8, /* explicit(f05(x),x,0,R), 1/4 circle */ explicit(fy(x),x,0,R) /* 1/4 circle */)$ |
P_X
| (%i29) | P_X:integrate(ro·g·(H1−h)·B,h,0,R); |
\[\]\[\tag{%o29} 49050.0\]
| (%i30) | mP_X:integrate(ro·g·(H1−h)·B·h,h,0,R); |
\[\]\[\tag{%o30} 22890.0\]
| (%i32) | h_D_:mP_X/P_X;h_D:H1−h_D_; |
\[\]\[\tag{%o31} 0.4666666666666667\]
\[\]\[\tag{%o32} 2.533333333333333\]
| (%i33) | h_C:H1−R/2,numer; |
\[\]\[\tag{%o33} 2.5\]
| (%i34) | p_C:ro·g·h_C; |
\[\]\[\tag{%o34} 24525.0\]
| (%i35) | w:R·B; |
\[\]\[\tag{%o35} 2\]
| (%i36) | P_X_test:p_C·w; |
\[\]\[\tag{%o36} 49050.0\]
| (%i37) | I_0:(B·R··3)/12,numer; |
\[\]\[\tag{%o37} 0.16666666666666666\]
| (%i38) | h_D:h_C+(I_0)/(h_C·w); |
\[\]\[\tag{%o38} 2.533333333333333\]
| (%i39) | scale_L:P_X; |
\[\]\[\tag{%o39} 49050.0\]
| (%i40) | scale_P_X:P_X/scale_L; |
\[\]\[\tag{%o40} 1.0\]
P_Z
| (%i41) | W1:(((%pi·(R··2))/4))·B,numer; |
\[\]\[\tag{%o41} 1.5707963267948966\]
| (%i42) | W2:h1·R·B; |
\[\]\[\tag{%o42} 4\]
| (%i45) | P_Z1:W1·ro·g;P_Z2:W2·ro·g;P_Z1+P_Z2; |
\[\]\[\tag{%o43} 15409.511965857935\]
\[\]\[\tag{%o44} 39240.0\]
\[\]\[\tag{%o45} 54649.511965857935\]
| (%i46) | W:W1+W2; |
\[\]\[\tag{%o46} 5.570796326794897\]
| (%i47) | P_Z:W·ro·g; |
\[\]\[\tag{%o47} 54649.511965857935\]
| (%i48) | scale_P_Z:P_Z/scale_L; |
\[\]\[\tag{%o48} 1.1141592653589794\]
| (%i50) | fi:atan(P_Z/P_X);fi_gr:fi·(180/%pi),numer; |
\[\]\[\tag{%o49} 0.8393432509285149\]
\[\]\[\tag{%o50} 48.09082584099392\]
| (%i51) | z_c:(0.5·R·W2+0.4244·R·W1)/W; |
\[\]\[\tag{%o51} 0.478683083110666\]
| (%i52) | x_z:z_c/scale_P_Z; |
\[\]\[\tag{%o52} 0.42963613730433364\]
| (%i54) | P:sqrt(P_Z··2+P_X··2);scale_P:P/scale_L; |
\[\]\[\tag{%o53} 73433.45053929067\]
\[\]\[\tag{%o54} 1.4971141802097996\]
title = "Сила тиску на криволінійну поверхню",
DRAW
| (%i66) | R;h1;H1;x1;h_D_;x_z;scale_P;scale_P_Z;scale_P_X;P;P_X;P_Z; |
\[\]\[\tag{%o55} 1\]
\[\]\[\tag{%o56} 2\]
\[\]\[\tag{%o57} 3\]
\[\]\[\tag{%o58} 5\]
\[\]\[\tag{%o59} 0.4666666666666667\]
\[\]\[\tag{%o60} 0.42963613730433364\]
\[\]\[\tag{%o61} 1.4971141802097996\]
\[\]\[\tag{%o62} 1.1141592653589794\]
\[\]\[\tag{%o63} 1.0\]
\[\]\[\tag{%o64} 73433.45053929067\]
\[\]\[\tag{%o65} 49050.0\]
\[\]\[\tag{%o66} 54649.511965857935\]
| (%i67) |
/* 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) )$ |
| (%i72) | 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; |
\[\]\[\tag{%o68} 49050\]
\[\]\[\tag{%o69} 54649.51\]
\[\]\[\tag{%o70} 73433.45\]
\[\]\[\tag{%o71} 48.09\]
\[\]\[\tag{%o72} 0.46\]
| (%i73) | xi_z:ds(x_z),numer; |
\[\]\[\tag{%o73} 0.42\]
| (%i74) | if h1 < 2 then H2:H1+4 else H2:H1; |
\[\]\[\tag{%o74} 3\]
| (%i79) | fy(x);xi0:1;yi0:1;xi1:x_z;yi1:h_D_; |
\[\]\[\tag{%o75} 1\mathop{-}\sqrt{1\mathop{-}{{x}^{2}}}\]
\[\]\[\tag{%o76} 1\]
\[\]\[\tag{%o77} 1\]
\[\]\[\tag{%o78} 0.42963613730433364\]
\[\]\[\tag{%o79} 0.4666666666666667\]
| (%i80) | fyL(x,h_D_,x_z):=R−(h_D_/(x_z))·x; |
\[\]\[\tag{%o80} \mathop{fyL}\left( x\mathop{,}\ensuremath{\mathrm{h\_ D\_ }}\mathop{,}\ensuremath{\mathrm{x\_ z}}\right) \mathop{:=}R\mathop{-}\frac{\ensuremath{\mathrm{h\_ D\_ }}}{\ensuremath{\mathrm{x\_ z}}} x\]
| (%i82) | fyL(0.69,h_D_,x_z);fy(0.69); |
\[\]\[\tag{%o81} 0.25052859375301895\]
\[\]\[\tag{%o82} 0.2761906328320971\]
| (%i83) | fxi(yi,x_z,h_D_):=x_z−(h_D_−yi)·((x_z)/(h_D_)); |
\[\]\[\tag{%o83} \mathop{fxi}\left( \ensuremath{\mathrm{yi}}\mathop{,}\ensuremath{\mathrm{x\_ z}}\mathop{,}\ensuremath{\mathrm{h\_ D\_ }}\right) \mathop{:=}\ensuremath{\mathrm{x\_ z}}\mathop{-}\left( \ensuremath{\mathrm{h\_ D\_ }}\mathop{-}\ensuremath{\mathrm{yi}}\right) \frac{\ensuremath{\mathrm{x\_ z}}}{\ensuremath{\mathrm{h\_ D\_ }}}\]
| (%i86) | fyL(0.683,h_D_,x_z);fy(0.683);fxi(fy(0.683),x_z,h_D_); |
\[\]\[\tag{%o84} 0.2581319268598723\]
\[\]\[\tag{%o85} 0.2695816267371145\]
\[\]\[\tag{%o86} 0.24819001885618402\]
| (%i87) | plot2d([fyL(x,h_D_,x_z),fy(x)],[x,0,R]); |
\[\]\[\tag{%o87} false\]
| (%i89) | n:10;dx:R/n,numer; |
\[\]\[\tag{%o88} 10\]
\[\]\[\tag{%o89} 0.1\]
| (%i92) | x_i:0.1;yiC:fy(x_i),numer;yiL:fyL(x_i,h_D_,x_z),numer; |
\[\]\[\tag{%o90} 0.1\]
\[\]\[\tag{%o91} 0.005012562893380035\]
\[\]\[\tag{%o92} 0.8913809556163795\]
| (%i95) | x_i:dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o93} 0.1\]
\[\]\[\tag{%o94} 0.005012562893380035\]
\[\]\[\tag{%o95} 0.8913809556163795\]
| (%i98) | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o96} 0.2\]
\[\]\[\tag{%o97} 0.020204102886728803\]
\[\]\[\tag{%o98} 0.7827619112327591\]
| (%i101) | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o99} 0.30000000000000004\]
\[\]\[\tag{%o100} 0.04606079858305434\]
\[\]\[\tag{%o101} 0.6741428668491386\]
| (%i104) | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o102} 0.4\]
\[\]\[\tag{%o103} 0.08348486100883201\]
\[\]\[\tag{%o104} 0.5655238224655181\]
| (%i107) | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o105} 0.5\]
\[\]\[\tag{%o106} 0.1339745962155614\]
\[\]\[\tag{%o107} 0.4569047780818978\]
| (%i110) | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o108} 0.6\]
\[\]\[\tag{%o109} 0.19999999999999996\]
\[\]\[\tag{%o110} 0.3482857336982773\]
| (%i113) | x_i:x_i+dx;yiC:fy(x_i);yiL:fyL(x_i,h_D_,x_z); |
\[\]\[\tag{%o111} 0.7\]
\[\]\[\tag{%o112} 0.285857157145715\]
\[\]\[\tag{%o113} 0.23966668931465696\]
| (%i114) |
coord_x(n,h_D_,x_z,R):=block ([dx,xi,yiC,yiL], dx:R/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 yiL>yiC then (x_i:x_i+dx) else (x_i:x_i)), return (x_i) ); |
\[\]\[\tag{%o114} \mathop{coord\_ x}\left( n\mathop{,}\ensuremath{\mathrm{h\_ D\_ }}\mathop{,}\ensuremath{\mathrm{x\_ z}}\mathop{,}R\right) \mathop{:=}\]
| (%i117) | h_D_;x_z;R; |
\[\]\[\tag{%o115} 0.4666666666666667\]
\[\]\[\tag{%o116} 0.42963613730433364\]
\[\]\[\tag{%o117} 1\]
| (%i119) | X:coord_x(500,h_D_,x_z,R);Y:fyL(X,h_D_,x_z); |
\[\]\[\tag{%o118} \frac{339}{500}\]
\[\]\[\tag{%o119} 0.2635628790790533\]
| (%i121) | X:ds(X),numer; Y:ds(Y),numer; |
\[\]\[\tag{%o120} 0.67\]
\[\]\[\tag{%o121} 0.26\]
| (%i124) | n:10;dx:R/n;x_i:dx; |
\[\]\[\tag{%o122} 10\]
\[\]\[\tag{%o123} \frac{1}{10}\]
\[\]\[\tag{%o124} \frac{1}{10}\]
| (%i125) | for i:1 step 1 thru n do (yiC:fy(x_i),yiL:fyL(x_i,h_D_,x_z), if yiL>yiC then (x_i:x_i+dx,display (x_i, yiC,yiL)) else (x_i:x_i,display ("stop"))); |
\[\]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}\frac{1}{5}\]\[\ensuremath{\mathrm{yiC}}\mathop{=}1\mathop{-}\frac{3 \sqrt{11}}{10}\]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.8913809556163795 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}\frac{3}{10}\]\[\ensuremath{\mathrm{yiC}}\mathop{=}1\mathop{-}\frac{2 \sqrt{6}}{5}\]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.7827619112327591 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}\frac{2}{5}\]\[\ensuremath{\mathrm{yiC}}\mathop{=}1\mathop{-}\frac{\sqrt{91}}{10}\]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.6741428668491387 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}\frac{1}{2}\]\[\ensuremath{\mathrm{yiC}}\mathop{=}1\mathop{-}\frac{\sqrt{21}}{5}\]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.5655238224655181 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}\frac{3}{5}\]\[\ensuremath{\mathrm{yiC}}\mathop{=}1\mathop{-}\frac{\sqrt{3}}{2}\]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.4569047780818978 \]\[\ensuremath{\mathrm{x\_ i}}\mathop{=}\frac{7}{10}\]\[\ensuremath{\mathrm{yiC}}\mathop{=}\frac{1}{5}\]\[\ensuremath{\mathrm{yiL}}\mathop{=}0.3482857336982773 \]\[\mbox{}\\"stop"\mathop{=}"stop" \]\[\mbox{}\\"stop"\mathop{=}"stop" \]\[\mbox{}\\"stop"\mathop{=}"stop" \]\[\mbox{}\\"stop"\mathop{=}"stop"\]
\[\]\[\tag{%o125} \ensuremath{\mathrm{done}}\]
| (%i126) |
draw2d( xrange = [−1,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 */ fill_color = white, line_width=1, line_type = dashes, polygon([[−0.5·R,0],[0,H1],[0,0],[−0.5·R,0]]), /* rectangle epura of presure P_x */ fill_color = gray90, line_type = solid, polygon([[−0.5·R,0],[−0.5·(R−R/H1),R],[0,R],[0,0],[−0.5·R,0]]), /* rectangle epura of presure P_x */ /* Epura */ color = "blue", line_width=1, line_type = solid, head_angle = 10, head_length = 0.15, vector([−0.5·(R−0.1·R/H1),0.1·R],[0.5·(R−0.1·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.2·R/H1),0.2·R],[0.5·(R−0.2·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.3·R/H1),0.3·R],[0.5·(R−0.3·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.4·R/H1),0.4·R],[0.5·(R−0.4·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.5·R/H1),0.5·R],[0.5·(R−0.5·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.6·R/H1),0.6·R],[0.5·(R−0.6·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.7·R/H1),0.7·R],[0.5·(R−0.7·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.8·R/H1),0.8·R],[0.5·(R−0.8·R/H1),0]), /* horizontal presure vector p */ vector([−0.5·(R−0.9·R/H1),0.9·R],[0.5·(R−0.9·R/H1),0]), /* horizontal presure vector p */ 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,R]]), points([[X,Y]]), points([[0,h_D_]]), /* point P_x */ label_orientation = horizontal, label(["P_x",−R+0.5,h_D_+0.2]), label_orientation = vertical, label(["P_z",x_z−0.2,R+0.9]), line_width=1, line_type = dashes, head_angle = 180, vector([−1,h_D_],[3·R,0]), /* horizontal line dot to vector P_x */ vector([x_z,R],[0,−R]), /* vertical line dot to vector P_z */ vector([X,Y],[−1.5·R,1.5·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,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]) ); |
\[\]\[\tag{%o126} \]
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origin D:\_j_kifnuba_2026\jMAXIMA\jh_Job_ex05_v3.wxmx
data 25.05.2026 22:20