\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i1) | kill(all); |
\[\]\[\tag{%o0} \ensuremath{\mathrm{done}}\]
| (%i4) | long_x:4; label_left:2.5; label_vert:1.5; label_URL:0.2; |
\[\]\[\tag{%o1} 4\]
\[\]\[\tag{%o2} 2.5\]
\[\]\[\tag{%o3} 1.5\]
\[\]\[\tag{%o4} 0.2\]
| (%i14) | ro:1000;g:9.81;x0:0;y0:0;x1:3;y1:2;x2:3;y2:3;B:1;h1:2; |
\[\]\[\tag{%o5} 1000\]
\[\]\[\tag{%o6} 9.81\]
\[\]\[\tag{%o7} 0\]
\[\]\[\tag{%o8} 0\]
\[\]\[\tag{%o9} 3\]
\[\]\[\tag{%o10} 2\]
\[\]\[\tag{%o11} 3\]
\[\]\[\tag{%o12} 3\]
\[\]\[\tag{%o13} 1\]
\[\]\[\tag{%o14} 2\]
| (%i16) | Hall:y2+h1;H:y2−y0; |
\[\]\[\tag{%o15} 5\]
\[\]\[\tag{%o16} 3\]
P_x
| (%i19) | h_C:(Hall−H/2);w:H·B;I:(B·H··3)/12; |
\[\]\[\tag{%o17} \frac{7}{2}\]
\[\]\[\tag{%o18} 3\]
\[\]\[\tag{%o19} \frac{9}{4}\]
| (%i20) | P_x:ro·g·h_C·B; |
\[\]\[\tag{%o20} 34335.0\]
| (%i22) | h_D:h_C+(I)/(h_C·w),numer;h_D_:Hall−h_D; |
\[\]\[\tag{%o21} 3.7142857142857144\]
\[\]\[\tag{%o22} 1.2857142857142856\]
P_z
| (%i23) | W1:(((x1−x0)·(y1−y0))/2)·B,numer; |
\[\]\[\tag{%o23} 3\]
| (%i24) | W2:((((x1−x0)+(x2−x1))/2)·(y2−y1))·B,numer; |
\[\]\[\tag{%o24} 1.5\]
| (%i26) | W:W1+W2;P_z:W·ro·g; |
\[\]\[\tag{%o25} 4.5\]
\[\]\[\tag{%o26} 44145.0\]
| (%i28) | P_z1:W1·ro·g; P_z2:W2·ro·g; |
\[\]\[\tag{%o27} 29430.0\]
\[\]\[\tag{%o28} 14715.0\]
| (%i30) | mP_z1:W1·ro·g·(1/3·(x1−x0)); mP_z2:W2·ro·g·(1/2·(x1−x0)); |
\[\]\[\tag{%o29} 29430.0\]
\[\]\[\tag{%o30} 22072.5\]
| (%i31) | if x0 = x1 and x1 =x2 then x_D=0 else x_D:(mP_z1+mP_z2)/(P_z); |
\[\]\[\tag{%o31} 1.1666666666666667\]
| (%i32) | P:sqrt(P_z··2+P_x··2); |
\[\]\[\tag{%o32} 55925.60460111272\]
| (%i34) | phi:atan(P_z/P_x);fi_gr:(180/%pi)·phi,numer; |
\[\]\[\tag{%o33} 0.9097531579442097\]
\[\]\[\tag{%o34} 52.1250163489018\]
| (%i35) | x1_:x1−x0+long_x; |
\[\]\[\tag{%o35} 7\]
| (%i37) | scale_L:P_x;scale_P_x:P_x/scale_L; |
\[\]\[\tag{%o36} 34335.0\]
\[\]\[\tag{%o37} 1.0\]
| (%i38) | scale_P_z:P_z/scale_L; |
\[\]\[\tag{%o38} 1.2857142857142858\]
| (%i39) | scale_P:P/scale_L; |
\[\]\[\tag{%o39} 1.6288220358559113\]
| (%i51) | h1;Hall;H;x1;h_D_;x_D;scale_P;scale_P_z;scale_P_x;P;P_x;P_z; |
\[\]\[\tag{%o40} 2\]
\[\]\[\tag{%o41} 5\]
\[\]\[\tag{%o42} 3\]
\[\]\[\tag{%o43} 3\]
\[\]\[\tag{%o44} 1.2857142857142856\]
\[\]\[\tag{%o45} 1.1666666666666667\]
\[\]\[\tag{%o46} 1.6288220358559113\]
\[\]\[\tag{%o47} 1.2857142857142858\]
\[\]\[\tag{%o48} 1.0\]
\[\]\[\tag{%o49} 55925.60460111272\]
\[\]\[\tag{%o50} 34335.0\]
\[\]\[\tag{%o51} 44145.0\]
| --> | /* Definition of a block with local variables */; |
| (%i52) |
ds(r) := block([x, n], n:100, x:r·n, x:floor(x), x:x/100, return(x) )$ |
| (%i58) | 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;xi_D:ds(x_D),numer; |
\[\]\[\tag{%o53} 34335\]
\[\]\[\tag{%o54} 44145\]
\[\]\[\tag{%o55} 55925.6\]
\[\]\[\tag{%o56} 52.12\]
\[\]\[\tag{%o57} 1.28\]
\[\]\[\tag{%o58} 1.16\]
| (%i63) | x0;x1;y0;y1;h1; |
\[\]\[\tag{%o59} 0\]
\[\]\[\tag{%o60} 3\]
\[\]\[\tag{%o61} 0\]
\[\]\[\tag{%o62} 2\]
\[\]\[\tag{%o63} 2\]
| (%i64) | fyL1(y1,x1,x):=(y1/x1)·x; |
\[\]\[\tag{%o64} \mathop{fyL1}\left( \ensuremath{\mathrm{y1}}\mathop{,}\ensuremath{\mathrm{x1}}\mathop{,}x\right) \mathop{:=}\frac{\ensuremath{\mathrm{y1}}}{\ensuremath{\mathrm{x1}}} x\]
| (%i65) | plot2d(fyL1(y1,x1,x),[x,0,x1]); |
\[\]\[\tag{%o65} false\]
| (%i67) | x_v:xi_D;y_v:hi_D_; |
\[\]\[\tag{%o66} 1.16\]
\[\]\[\tag{%o67} 1.28\]
| (%i69) | x0_v:x_v−scale_P_x;y0_v:y_v+scale_P_z; |
\[\]\[\tag{%o68} 0.15999999999999992\]
\[\]\[\tag{%o69} 2.565714285714286\]
| (%i70) | (y0_v−y_v)/(x_v−x0_v)=(y−y_v)/(x_v−x); |
\[\]\[\tag{%o70} 1.2857142857142858\mathop{=}\frac{y\mathop{-}1.28}{1.16\mathop{-}x}\]
| (%i71) | fyV(x_v,y_v,x0_v,y0_v,x):=(x_v−x)·((y0_v−y_v)/(x_v−x0_v))+y_v; |
\[\]\[\tag{%o71} \mathop{fyV}\left( \ensuremath{\mathrm{x\_ v}}\mathop{,}\ensuremath{\mathrm{y\_ v}}\mathop{,}\ensuremath{\mathrm{x0\_ v}}\mathop{,}\ensuremath{\mathrm{y0\_ v}}\mathop{,}x\right) \mathop{:=}\left( \ensuremath{\mathrm{x\_ v}}\mathop{-}x\right) \frac{\ensuremath{\mathrm{y0\_ v}}\mathop{-}\ensuremath{\mathrm{y\_ v}}}{\ensuremath{\mathrm{x\_ v}}\mathop{-}\ensuremath{\mathrm{x0\_ v}}}\mathop{+}\ensuremath{\mathrm{y\_ v}}\]
| (%i72) | fyV(x_v,y_v,x0_v,y0_v,1); |
\[\]\[\tag{%o72} 1.4857142857142858\]
| (%i73) | plot2d(fyV(x_v,y_v,x0_v,y0_v,x),[x,0,x1]); |
\[\]\[\tag{%o73} false\]
| (%i74) | plot2d([fyV(x_v,y_v,x0_v,y0_v,x),fyL1(y1,x1,x)],[x,0,x1]); |
\[\]\[\tag{%o74} false\]
| (%i75) |
coord_x(n,x_v,y_v,x0_v,y0_v,y1,x1):=block ([dx,xi,yiC,yiL], dx:x1/n, x_i:dx, for i:1 step 1 thru n do (yiL:fyV(x_v,y_v,x0_v,y0_v,x_i),yiC:fyL1(y1,x1,x_i), if yiL>yiC then (x_i:x_i+dx) else (x_i:x_i)), return (x_i) ); |
\[\]\[\tag{%o75} \mathop{coord\_ x}\left( n\mathop{,}\ensuremath{\mathrm{x\_ v}}\mathop{,}\ensuremath{\mathrm{y\_ v}}\mathop{,}\ensuremath{\mathrm{x0\_ v}}\mathop{,}\ensuremath{\mathrm{y0\_ v}}\mathop{,}\ensuremath{\mathrm{y1}}\mathop{,}\ensuremath{\mathrm{x1}}\right) \mathop{:=}\]
| (%i81) | x_v;y_v;x0_v;y0_v;y1;x1; |
\[\]\[\tag{%o76} 1.16\]
\[\]\[\tag{%o77} 1.28\]
\[\]\[\tag{%o78} 0.15999999999999992\]
\[\]\[\tag{%o79} 2.565714285714286\]
\[\]\[\tag{%o80} 2\]
\[\]\[\tag{%o81} 3\]
| (%i83) | X:coord_x(500,x_v,y_v,x0_v,y0_v,y1,x1),numer;Y:fyL1(y1,x1,X),numer; |
\[\]\[\tag{%o82} 1.422000000000001\]
\[\]\[\tag{%o83} 0.9480000000000006\]
| (%i85) | Xi:ds(X),numer; Yi:ds(Y),numer; |
\[\]\[\tag{%o84} 1.42\]
\[\]\[\tag{%o85} 0.94\]
| (%i86) | H2:y2+h1+3; |
\[\]\[\tag{%o86} 8\]
| (%i87) | x_z:x_v; |
\[\]\[\tag{%o87} 1.16\]
| (%i88) | b:(2/Hall)·(Hall−0.1·y2); |
\[\]\[\tag{%o88} 1.8800000000000001\]
| (%i90) | −(2/Hall)·(Hall−1·y2);y2; |
\[\]\[\tag{%o89} \mathop{-}\left( \frac{4}{5}\right) \]
\[\]\[\tag{%o90} 3\]
| (%i91) | if h1 < 2 then Hall_add:Hall+5 else Hall_add:Hall; |
\[\]\[\tag{%o91} 5\]
| (%i92) |
draw2d( xrange = [−2,x1_], /* size picture x - x1 & y - H1 */ yrange = [0,Hall_add], proportional_axes=xy, font = "Arial", font_size = 16, grid = true, line_width=1, color=black, title = "Pressure force on a cinclined flat surface", fill_color = light_blue, polygon([[x0,y0],[x1,y1],[x2,y2],[x2,Hall],[x0,Hall],[x0,y0]]), /* rectangle Body of presure */ line_width=4, line_type = solid, points_joined = true, color=red, points([[x0,y0],[x1,y1],[x2,y2]]), /* inclined flat surface */ line_width=1, color=black, line_type = dashes, points_joined = true, fill_color = white, polygon([[−2,0],[0,Hall],[0,y0],[−2,0]]), /* rectangle epura of presure P_x */ fill_color = gray90, line_type = solid, polygon([[−2,0],[−(2/Hall)·(Hall−1·y2),y2],[0,y2],[0,0],[−2,0]]), /* rectangle epura of presure P_x */ /* Epura */ color = "blue", line_width=1, line_type = solid, head_angle = 10, head_length = 0.15, vector([−(2/Hall)·(Hall−0.1·y2),0.1·y2],[(2/Hall)·(Hall−0.1·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.2·y2),0.2·y2],[(2/Hall)·(Hall−0.2·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.3·y2),0.3·y2],[(2/Hall)·(Hall−0.3·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.4·y2),0.4·y2],[(2/Hall)·(Hall−0.4·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.5·y2),0.5·y2],[(2/Hall)·(Hall−0.5·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.6·y2),0.6·y2],[(2/Hall)·(Hall−0.6·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.7·y2),0.7·y2],[(2/Hall)·(Hall−0.7·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.8·y2),0.8·y2],[(2/Hall)·(Hall−0.8·y2),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.9·y2),0.9·y2],[(2/Hall)·(Hall−0.9·y2),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,y1],[x1,0]), /* horizontal line between W1 &W2 */ color = navy, label(["W1",x1·0.7,y1−0.2]), label(["W2",x1·0.7,H−0.2]), label_orientation = vertical, color = "#654321", label(["Body presure",x1/2,H−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 = 1.5, points_joined = false, points([[x_z,y2]]), /* point P_z */ points([[X,Y]]), /* point P */ points([[0,h_D_]]), /* point P_x */ label_orientation = horizontal, label(["P_x",x0−0.5,h_D_+0.3]), label_orientation = vertical, label(["P_z",x_z−0.4,y2+0.9]), line_width=1, line_type = dashes, head_angle = 180, vector([−1,h_D_],[3·y1,0]), /* horizontal line dot to vector P_x */ vector([x_z,y2],[0,−y2]), /* vertical line dot to vector P_z */ vector([X,Y],[−1.5·x1,1.5·scale_P_z·x1]), /* direct angle line dot to vector P */ color = "blue", line_width=3, line_type = solid, head_angle = 15, head_length = 0.25, vector([x0−1,h_D_],[+scale_P_x,0]), /* horizontal vector P_x */ vector([x_z,y2+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,Hall_add−label_URL]), label(["Kopanytsia Y (c) 2026", x1_−long_x/2,Hall_add−3·label_URL]), label_orientation = horizontal, /* label([string(P_X), x1-0.8, R/2]) */ label_alignment = left, color = black, label([concat("Y=: ", string(Yi)," m"), x1_−label_left, y1·1.6]), label([concat("X=: ", string(Xi)," m"), x1_−label_left, y1·1.4]), label([concat("h_D=: ", string(hi_D_)," m"), x1_−label_left, y1·1.2]), label([concat("x_z=: ", string(x_z)," m"), x1_−label_left, y1]), label([concat("P_x=: ", string(Pi_x)," N"), x1_−label_left, y1·0.8]), label([concat("P_z=: ", string(Pi_z)," N"), x1_−label_left, y1·0.6]), label([concat("P=: ", string(Pi)," N"), x1_−label_left, y1·0.4]), label([concat("phi=: ", string(fi_gr)," grad"), x1_−label_left, y1·0.2]), label([concat("(", string(Xi)," ,", string(Yi)," )"), X+0.1, Y−0.1]), line_type = solid, color=black,line_width=1, head_both = true, head_length = 0.2, head_angle = 10, vector([x1+scale_P_x,0],[0,h_D_]), /* h_D_ */ vector([0,y1+0.3],[x_z,0]), /* x_z */ label_alignment = center, label_orientation = vertical, font_size = 10, label([concat("h_d=: ", string(hi_D_)," m"), x1+0.8, h_D_/2]), label_orientation = horizontal, label([concat("x_z=: ", string(x_z)," m"), x_z/2,y1+0.5]) ); |
\[\]\[\tag{%o92} \]
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