\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i1) | kill(all); |
\[\]\[\tag{%o0} \ensuremath{\mathrm{done}}\]
| (%i1) | load("draw")$ |
| (%i2) | fileName:"jh_Job_ex08a_v4.wxmx"; |
\[\]\[\tag{%o2} "jh\_ Job\_ ex08a\_ v4.wxmx"\]
| (%i7) | x_right:9; label_left:3; label_vert:1.5; label_URL:0.2; delta_x:4; |
\[\]\[\tag{%o3} 9\]
\[\]\[\tag{%o4} 3\]
\[\]\[\tag{%o5} 1.5\]
\[\]\[\tag{%o6} 0.2\]
\[\]\[\tag{%o7} 4\]
| (%i15) | ro:1000;g:9.81;x0:2;y0:1;x1:x0+delta_x;y1:3;B:1;h1:0; |
\[\]\[\tag{%o8} 1000\]
\[\]\[\tag{%o9} 9.81\]
\[\]\[\tag{%o10} 2\]
\[\]\[\tag{%o11} 1\]
\[\]\[\tag{%o12} 6\]
\[\]\[\tag{%o13} 3\]
\[\]\[\tag{%o14} 1\]
\[\]\[\tag{%o15} 0\]
| (%i18) | Hall:y1−y0+h1;H:y1−y0;Hwater:y1+h1; |
\[\]\[\tag{%o16} 2\]
\[\]\[\tag{%o17} 2\]
\[\]\[\tag{%o18} 3\]
VARIANT # 1 (standart)
P_x
| (%i20) | alpha:atan((y1−y0)/(x1−x0)),numer;grad:(180/%pi)·alpha,numer; |
\[\]\[\tag{%o19} 0.4636476090008061\]
\[\]\[\tag{%o20} 26.56505117707799\]
| (%i23) | h_C_x:(Hall−H/2);w_x:H·B;I:(B·H··3)/12,numer; |
\[\]\[\tag{%o21} 1\]
\[\]\[\tag{%o22} 2\]
\[\]\[\tag{%o23} 0.6666666666666666\]
| (%i24) | p_c:ro·g·h_C_x; |
\[\]\[\tag{%o24} 9810.0\]
| (%i25) | P_x:p_c·w_x; |
\[\]\[\tag{%o25} 19620.0\]
| (%i27) | h_D_x:h_C_x+(I)/(h_C_x·w_x),numer;h_D_x:Hall−h_D_x+y0; |
\[\]\[\tag{%o26} 1.3333333333333333\]
\[\]\[\tag{%o27} 1.6666666666666667\]
| (%i28) | P:P_x/sin(alpha); |
\[\]\[\tag{%o28} 43871.65371854587\]
| (%i29) | P_z:P_x·(1/tan(alpha)); |
\[\]\[\tag{%o29} 39240.0\]
| (%i30) | Ptest:sqrt(P_x··2+P_z··2); |
\[\]\[\tag{%o30} 43871.65371854587\]
| (%i34) | H30:(y1−y0)/sin(alpha);w30:H30·B;P30:p_c·w30; if (abs(P − P30) < 0.1) then display ("OK") else display ("ERROR!"); |
\[\]\[\tag{%o31} 4.47213595499958\]
\[\]\[\tag{%o32} 4.47213595499958\]
\[\]\[\tag{%o33} 43871.65371854587 \]\[\mbox{}\\"OK"\mathop{=}"OK"\]
\[\]\[\tag{%o34} \ensuremath{\mathrm{done}}\]
| (%i35) | x1_:x1+x_right; |
\[\]\[\tag{%o35} 15\]
| (%i38) | scale_L:P_x;scale_P_x:P_x/scale_L;scale_P_z:P_z/scale_L; |
\[\]\[\tag{%o36} 19620.0\]
\[\]\[\tag{%o37} 1.0\]
\[\]\[\tag{%o38} 2.0\]
| (%i51) | h1;Hall;Hwater;H;x1;h_D_x;h_D;scale_P_x;scale_P_z;scale_P_x;P;P_x;P_z; |
\[\]\[\tag{%o39} 0\]
\[\]\[\tag{%o40} 2\]
\[\]\[\tag{%o41} 3\]
\[\]\[\tag{%o42} 2\]
\[\]\[\tag{%o43} 6\]
\[\]\[\tag{%o44} 1.6666666666666667\]
\[\]\[\tag{%o45} {h_D}\]
\[\]\[\tag{%o46} 1.0\]
\[\]\[\tag{%o47} 2.0\]
\[\]\[\tag{%o48} 1.0\]
\[\]\[\tag{%o49} 43871.65371854587\]
\[\]\[\tag{%o50} 19620.0\]
\[\]\[\tag{%o51} 39240.0\]
| (%i53) | W1:(((x1−x0)·(y1−y0))/2)·B;mW1:W1·((1/3)·(x1−x0)+x0); |
\[\]\[\tag{%o52} 4\]
\[\]\[\tag{%o53} \frac{40}{3}\]
| (%i55) | W2:(((x1−x0)·h1))·B;mW2:W2·(0.5·(x1−x0)+x0); |
\[\]\[\tag{%o54} 0\]
\[\]\[\tag{%o55} 0\]
| (%i56) | X:(mW1+mW2)/(W1+W2),numer; |
\[\]\[\tag{%o56} 3.3333333333333335\]
| (%i58) | P1:(((y1−y0+h1)/2)·ro·g)·((y1−y0+h1)·B);mP1:P1·(((y1−y0+h1)·(1/3))); |
\[\]\[\tag{%o57} 19620.0\]
\[\]\[\tag{%o58} 13080.0\]
| (%i60) | P2:(((h1)/2)·ro·g)·((h1)·B);mP2:P2·(Hall−(2/3·h1)); |
\[\]\[\tag{%o59} 0\]
\[\]\[\tag{%o60} 0\]
| (%i62) | Y:(mP1−mP2)/(P1−P2);Y:h_D_x; |
\[\]\[\tag{%o61} 0.6666666666666666\]
\[\]\[\tag{%o62} 1.6666666666666667\]
| --> | /* X:x0+(x1-x0)/3; Y:h_D_x; h1:0 */; |
| --> | /* Definition of a block with local variables */; |
| (%i63) |
ds(r) := block([x, n], n:100, x:r·n, x:floor(x), x:x/100, return(x) )$ |
| (%i67) | h_C_x:ds(h_C_x),numer; w_x:ds(w_x),numer; I:ds(I),numer;p_c:ds(p_c),numer; |
\[\]\[\tag{%o64} 1\]
\[\]\[\tag{%o65} 2\]
\[\]\[\tag{%o66} 0.66\]
\[\]\[\tag{%o67} 9810\]
| (%i71) | P_x:ds(P_x),numer; P_z:ds(P_z),numer; P:ds(P),numer; hi_D_x:ds(h_D_x),numer; |
\[\]\[\tag{%o68} 19620\]
\[\]\[\tag{%o69} 39240\]
\[\]\[\tag{%o70} 43871.65\]
\[\]\[\tag{%o71} 1.66\]
| (%i72) | grad_:ds(grad),numer; |
\[\]\[\tag{%o72} 26.56\]
| (%i74) | X:ds(X),numer; Y:ds(Y),numer; |
\[\]\[\tag{%o73} 3.33\]
\[\]\[\tag{%o74} 1.66\]
| (%i75) | H2:y1+h1+3; |
\[\]\[\tag{%o75} 6\]
| (%i76) | b:(2/Hall)·(Hall−0.1·y1); |
\[\]\[\tag{%o76} 1.7\]
| (%i78) | −(2/Hall)·(Hall−1·y1);y1; |
\[\]\[\tag{%o77} 1\]
\[\]\[\tag{%o78} 3\]
| (%i79) | if h1 < 7 then Hall_add:Hall+7 else Hall_add:Hall; |
\[\]\[\tag{%o79} 9\]
| (%i83) | x1_;Hall;Hall_add;x_left:2; |
\[\]\[\tag{%o80} 15\]
\[\]\[\tag{%o81} 2\]
\[\]\[\tag{%o82} 9\]
\[\]\[\tag{%o83} 2\]
| (%i84) | x1_; |
\[\]\[\tag{%o84} 15\]
| (%i85) |
draw2d( xrange = [−x_left,x1_], /* size picture x - x1 & y - H1 */ yrange = [0,Hall_add], proportional_axes=xy, font = "Arial", font_size = 12, grid = true, line_width=1, color=black, title = "TEST OBJECT OF single operations of the K123", line_width=1, color=black, line_type = dashes, points_joined = true, fill_color = "#ddddee", polygon([[x0,y0],[x1,y1],[x1,Hwater],[x0,Hwater],[x0,y0]]), /* body of presure P_z */ line_width=10, line_type = solid, points_joined = true, color=black, points([[x0,y0],[x0,y1]]), /* VERTICAL reflect of inclined flat surface */ color=red, points([[x0,y0],[x1,y1]]), /* inclined flat surface */ line_width=1, color=green, point_type = filled_circle, point_size = 1.5, points_joined = false, points([[x0,y0],[x0,y1]]), /* inclined flat surface */ color=green, points([[x0,y0],[x1,y1]]), line_width=1, color=black, line_type = dashes, points_joined = true, fill_color = white, polygon([[−2,y0],[0,Hall],[0,y0],[−2,y0]]), line_width=4, line_type = solid, points_joined = true, color=red, points([[x0,y0],[x1,y1],[x1,Hwater]]),/* inclined flat surface */ line_width=1, color=black, line_type = dashes, points_joined = true, fill_color = white, polygon([[−2,y0],[0,Hall+y0],[0,y0],[−2,y0]]), /* rectangle epura of presure P_x */ fill_color = gray90, line_type = solid, polygon([[−2,y0],[((−2/(Hall))·(h1)),y1],[0,y1],[0,y0],[−2,y0]]), /* 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·H),0.1·H+y0],[(2/Hall)·(Hall−0.1·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.2·H),0.2·H+y0],[(2/Hall)·(Hall−0.2·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.3·H),0.3·H+y0],[(2/Hall)·(Hall−0.3·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.4·H),0.4·H+y0],[(2/Hall)·(Hall−0.4·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.5·H),0.5·H+y0],[(2/Hall)·(Hall−0.5·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.6·H),0.6·H+y0],[(2/Hall)·(Hall−0.6·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.7·H),0.7·H+y0],[(2/Hall)·(Hall−0.7·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.8·H),0.8·H+y0],[(2/Hall)·(Hall−0.8·H),0]), /* horizontal presure vector p */ vector([−(2/Hall)·(Hall−0.9·H),0.9·H+y0],[(2/Hall)·(Hall−0.9·H),0]),/* horizontal presure vector p */ color = "black", fill_color = light_blue, line_width=2, head_angle = 15, head_length = 0.25, color=red, point_type = filled_circle, point_size = 1.5, points_joined = false, points([[x0,h_D_x]]), /* point D_{x} on vertical reflect */ color=blue, label_orientation = horizontal, label(["P_x",X−0.8,Y+0.4]),/* point P_x */ line_width=1, line_type = dashes, head_angle = 180, vector([−1,Y],[3·y1,0]), /* horizontal line dot to vector P */ color = "blue", line_width=3, line_type = solid, head_angle = 15, head_length = 0.25, vector([X−scale_P_x,Y],[+scale_P_x,0]), /* horizontal vector P_x */ label_orientation = horizontal, label_alignment = left, /* Input data */ color = "#0e406e", label([concat("file:", string(fileName)), x0, Hall_add−1.5]), label([concat("x0=", string(x0)), x0, Hall_add−2]), label([concat("y0=", string(y0)), x0, Hall_add−2.5]), label([concat("x1=", string(x1)), x0, Hall_add−3.0]), label([concat("y1=", string(y1)), x0, Hall_add−3.5]), label([concat("alpfa=", string(grad_)), x0, Hall_add−4.0]), label([concat("h_{1}=: ", string(h1)," m"), x0, Hall_add−4.5]), color = black, label([concat("h_{C_{x}}=: ", string(h_C_x)," m"), x1_−label_left, y1·2]), label([concat("w_{x}=: ", string(w_x)," m"), x1_−label_left, y1·1.8]), label([concat("p_{c}=: ", string(p_c)," Pa"), x1_−label_left, y1·1.6]), label([concat("I=: ", string(I)," m"), x1_−label_left, y1·1.4]), label([concat("h_D_{coord}=: ", string(hi_D_x)," m"), x1_−label_left, y1·1.2]), label([concat("P_{x}=: ", string(P_x)," N"), x1_−label_left, y1·1]), label([concat("P_{z}=: ", string(P_z)," N"), x1_−label_left, y1·0.8]), color=red, label([concat("P=: ", string(P)," N"), x1_−label_left, y1·0.6]), label([concat("X=: ", string(X)," m"), x1_−label_left, y1·0.4]), label([concat("Y=: ", string(Y)," m"), x1_−label_left, y1·0.2]), line_type = solid, color=black, line_width=1, head_both = true, head_length = 0.2, head_angle = 10, vector([x1+scale_P_x+0.1,0],[0,h_D_x]),/* h_D_x */ label_alignment = center, label_orientation = vertical, font_size = 12, label([concat("h_{D_{crd}}=: ", string(hi_D_x)," m"), x1+0.7, h_D_x·0.6]), /* Input data */ line_type = solid, color=blue, line_width=4, head_angle = 180, vector([−x_left,Hwater],[x1+x_left,0]), /* horizontal line dot to vector P_x */ line_width=1, line_type = dashes, head_angle = 180, vector([x0,y1],[x1+x_left,0]), /* horizontal line dot size H */ line_type = solid, color=black, line_width=1, line_type = solid, head_both = true, head_length = 0.2, head_angle = 10, vector([x1+1.5·x_left−0.2,y0],[0,H]), /* vertical line size H */ vector([x1+1.5·x_left−0.2,y1],[0,h1]), /* vertical line size h1 */ vector([x1+2·x_left−0.2,y0],[0,Hall]), /* vertical line size Hall */ label_alignment = center, label_orientation = vertical, font_size = 10, label([concat("H=: ", string((y1−y0))," m"), x1+1.5·x_left−0.5, (y0+(y1−y0)/2)]), /* vertical size H */ label([concat("h_{1}=: ", string((h1))," m"), x1+1.5·x_left−0.5, (y1+(h1)/2)]), /* vertical size H */ label([concat("Hall=: ", string(Hall)," m"), x1+2·x_left−0.5, Hall·0.6]), /* vertical size Hall */ line_type = solid, color=blue, line_width=1, line_type = solid, head_both = false, head_length = 0.2, head_angle = 10, vector([x0−x_left/2,Hwater+0.5],[0,−0.4]), /* vector p_a */ font_size = 12, color = "#0e406e", label_orientation = horizontal, label(["p_{a} ", x0−x_left/2−0.4,Hwater+0.5]), label(["D_{x} ", x0+0.5,hi_D_x−0.2]), /* Vector P */ font_size = 12, label_alignment = 'left, color = red, label([concat("D ( ", string(X),", ",string(Y),") "), X+0.3,Y−0.2]), color=black, point_type = filled_circle, point_size = 1.5, points_joined = false, points([[X,Y],[x0,y0],[x1,y1]]), /* VECTOR P */ line_type = solid, color=red, line_width=3, line_type = solid, head_both = false, head_length = 0.3, head_angle = 10, vector([X−scale_P_x,Y+scale_P_z],[scale_P_x,−scale_P_z]), /* vectorP */ color = red, label_orientation = horizontal, label(["P ", X−1.2,Y+0.9]), /* Vector P_z */ color = blue, label_orientation = vertical, label(["P_{z} ", X−0.3,Y+0.8]), vector([X,Y+scale_P_z],[0,−scale_P_z]), /* vector P_z */ line_width=1, color=black, line_type = short_long_dashes, points_joined = true, polygon([[X,0],[X,Hwater+0.3]]), line_type = dots, polygon([[x1,0],[x1,y1]]), polygon([[X−scale_P_x,y0],[X−scale_P_x,Hall]]), polygon([[x0,Y+scale_P_z],[X+0.3,Y+scale_P_z]]), polygon([[x1,Hwater],[x1+4,Hwater]]), polygon([[−x_left,y0],[x1_,y0]]), color = red, line_width=2, ellipse(x0, y0, 0.75, 0.75, 0, grad), label_orientation = horizontal, label([concat("alpfa= ", string(grad_)), x0+1.1,y0+0.3]), font = "Arial", font_size = 12, color = "#0e406e", label_orientation = horizontal, label(["www.k123.org.ua ", x1_−x_right/2,Hall_add−label_URL]), label(["Kopanytsia Y (c) 2026", x1_−x_right/2,Hall_add−3·label_URL]) ); |
\[\]\[\tag{%o85} \]
Created with wxMaxima.
The source of this Maxima session can be downloaded here.