MathPlotAI Logo MathPlotAI

Continuity Equation Demonstration

Continuity Equation Demonstration
Loading the math board and drawing, please wait…
2016-12-06 12:41
FunctionSolid GeometryCalculusGeometric Construction
This example demonstrates the principle of mass conservation in fluid dynamics through the continuity equation at varying pipe diameters. It involves core mathematical concepts such as linear functions, secant lines, parallelograms, real numbers, and the sine function, along with calculus-based continuity principles. The construction utilizes GeoGebra commands like Segment, Point, Line, OrthogonalLine, Mirror, Distance, Intersect, If, Textfield, Ellipse, Polygon, Sequence, PolyLine, Vector, and Midpoint. It is suitable for high school students and enthusiasts studying the intersection of fluid mechanics and calculus.

GeoGebra Commands & Parameters

  1. Segment(M_9, D_{12}) → h_4
  2. Point(h_4) → F_9
  3. Line(F, G) → h
  4. Segment(F, L_9) → i
  5. Point(i) → H
  6. OrthogonalLine(H, h) → k
  7. Line(F_9, k) → b_3
  8. Mirror(I, k) → I'
  9. Distance(I, I') → distanceII'
  10. Mirror(H_9, b_3) → I_9
  11. Distance(H_9, I_9) → distanceH9I9
  12. Point(xAxis) → T_2
  13. OrthogonalLine(T_2, xAxis) → l
  14. Point(xAxis) → U_2
  15. OrthogonalLine(U_2, xAxis) → m
  16. Line(B, C) → f
  17. Segment(B, C) → g
  18. Point(g) → D
  19. OrthogonalLine(D, f) → j
  20. OrthogonalLine(E, f) → n
  21. Intersect(m, n) → K
  22. Segment(E, K) → s
  23. OrthogonalLine(E, s) → p_1
  24. OrthogonalLine(S_9, p_1) → j_5
  25. Intersect(j_5, l) → T_9
  26. Mirror(E, j) → E'
  27. Distance(E, E') → distanceEE'
  28. OrthogonalLine(C_1, p_1) → h_5
  29. Intersect(h_5, m) → K_{10}
  30. Intersect(k, l) → W
  31. OrthogonalLine(I, h) → p
  32. Intersect(l, p) → L
  33. Segment(L, I) → d
  34. OrthogonalLine(I, d) → q_1
  35. Intersect(k, q_1) → B_1
  36. OrthogonalLine(E', m) → q
  37. Intersect(m, q) → N
  38. OrthogonalLine(I', i) → r
  39. Intersect(l, r) → O
  40. Segment(N, O) → f_1
  41. Line(I_9, b_3) → d_3
  42. Intersect(l, d_3) → K_9
  43. Line(H_9, k) → c_3
  44. Intersect(c_3, l) → J_9
  45. Segment(J_9, K) → f_4
  46. Intersect(f_4, f_1) → N_9
  47. Segment(W, H) → t_3
  48. Point(t_3) → N_8
  49. Intersect(j, m) → V
  50. Segment(D, V) → s_3
  51. Point(s_3) → W_8
  52. If(time > t1 + (8 * timelag), t1, If[time - (8 * timelag) < 0, 0, time - (8 * timelag)]) → time1J3
  53. If(time > t1 + ttrans + (8 * timelag), ttrans, If[time - t1 - (8 * timelag) < 0, 0, time - t1 - (8 * timelag)]) → timetransJ3
  54. If(time > t1 + ttrans + t2 + (8 * timelag), t2, If[time - (t1 + (8 * timelag) + ttrans) < 0, 0, time - (t1 + (8 * timelag) + ttrans)]) → time2J3
  55. If(time > t1 + ttrans + t2 + (9 * timelag), t2, If[time - (t1 + (9 * timelag) + ttrans) < 0, 0, time - (t1 + (9 * timelag) + ttrans)]) → time2R2
  56. If(time > t1 + ttrans + (9 * timelag), ttrans, If[time - t1 - (9 * timelag) < 0, 0, time - t1 - (9 * timelag)]) → timetransR2
  57. If(time > t1 + (9 * timelag), t1, If[time - (9 * timelag) < 0, 0, time - (9 * timelag)]) → time1R2
  58. If(time > t1 + (10 * timelag), t1, If[time - (10 * timelag) < 0, 0, time - (10 * timelag)]) → time1S2
  59. If(time > t1 + ttrans + (10 * timelag), ttrans, If[time - t1 - (10 * timelag) < 0, 0, time - t1 - (10 * timelag)]) → timetransS2
  60. If(time > t1 + ttrans + t2 + (10 * timelag), t2, If[time - (t1 + (10 * timelag) + ttrans) < 0, 0, time - (t1 + (10 * timelag) + ttrans)]) → time2S2
  61. If(time > t1 + ttrans + t2 + (7 * timelag), t2, If[time - (t1 + (7 * timelag) + ttrans) < 0, 0, time - (t1 + (7 * timelag) + ttrans)]) → time2K3
  62. If(time > t1 + ttrans + (7 * timelag), ttrans, If[time - t1 - (7 * timelag) < 0, 0, time - t1 - (7 * timelag)]) → timetransK3
  63. If(time > t1 + (7 * timelag), t1, If[time - (7 * timelag) < 0, 0, time - (7 * timelag)]) → time1K3
  64. If(time > t1 + (5 * timelag), t1, If[time - (5 * timelag) < 0, 0, time - (5 * timelag)]) → time1J
  65. If(time > t1 + ttrans + (5 * timelag), ttrans, If[time - t1 - (5 * timelag) < 0, 0, time - t1 - (5 * timelag)]) → timetransJ
  66. If(time > t1 + ttrans + t2 + (5 * timelag), t2, If[time - (t1 + (5 * timelag) + ttrans) < 0, 0, time - (t1 + (5 * timelag) + ttrans)]) → time2J
  67. If(time > t1 + ttrans + (4 * timelag), ttrans, If[time - t1 - (4 * timelag) < 0, 0, time - t1 - (4 * timelag)]) → timetransA
  68. If(time > t1 + ttrans + t2 + (4 * timelag), t2, If[time - (t1 + (4 * timelag) + ttrans) < 0, 0, time - (t1 + (4 * timelag) + ttrans)]) → time2A
  69. If(time > t1 + (4 * timelag), t1, If[time - (4 * timelag) < 0, 0, time - (4 * timelag)]) → time1A
  70. If(time > t1 + (6 * timelag), t1, If[time - (6 * timelag) < 0, 0, time - (6 * timelag)]) → time1O2
  71. If(time > t1 + ttrans + (6 * timelag), ttrans, If[time - t1 - (6 * timelag) < 0, 0, time - t1 - (6 * timelag)]) → timetransO2
  72. If(time > t1 + ttrans + t2 + (6 * timelag), t2, If[time - (t1 + (6 * timelag) + ttrans) < 0, 0, time - (t1 + (6 * timelag) + ttrans)]) → time2O2
  73. If(time > t1 + ttrans + (3 * timelag), ttrans, If[time - t1 - (3 * timelag) < 0, 0, time - t1 - (3 * timelag)]) → timetransS
  74. If(time > t1 + ttrans + t2 + (3 * timelag), t2, If[time - (t1 + (3 * timelag) + ttrans) < 0, 0, time - (t1 + (3 * timelag) + ttrans)]) → time2S
  75. If(time > t1 + (3 * timelag), t1, If[time - (3 * timelag) < 0, 0, time - (3 * timelag)]) → time1S
  76. If(time > t1 + (2 * timelag), t1, If[time - (2 * timelag) < 0, 0, time - (2 * timelag)]) → time1R
  77. If(time > t1 + ttrans + (2 * timelag), ttrans, If[time - t1 - (2 * timelag) < 0, 0, time - t1 - (2 * timelag)]) → timetransR
  78. If(time > t1 + ttrans + t2 + (2 * timelag), t2, If[time - (t1 + (2 * timelag) + ttrans) < 0, 0, time - (t1 + (2 * timelag) + ttrans)]) → time2R
  79. If(time > t1 + ttrans + t2 + timelag, t2, If[time - (t1 + timelag + ttrans) < 0, 0, time - (t1 + timelag + ttrans)]) → time2U
  80. If(time > t1 + ttrans + timelag, ttrans, If[time - t1 - timelag < 0, 0, time - t1 - timelag]) → timetransU
  81. If(time > t1 + timelag, t1, If[time - timelag < 0, 0, time - timelag]) → time1U
  82. If(time > t1 + ttrans, ttrans, If[time - t1 < 0, 0, time - t1]) → timetrans
  83. If(time > t1 + ttrans + t2, t2, If[time - (t1 + ttrans) < 0, 0, time - (t1 + ttrans)]) → time2
  84. If(time > t1, t1, time) → time1
  85. Textfield(r1) → InputBox1
  86. Textfield(r2) → InputBox2
  87. Intersect(h, i) → M
  88. Segment(E', N) → t_1
  89. Segment(O, I') → b
  90. Segment(L, K) → e
  91. Ellipse(E, E', P) → c_1
  92. Polygon(E, K, K_9, N, E', L, I, I', O, N_9, J_9, H_9, I_9) → poly1, i_1, m_4, p_4, q_4, r_4, k_1, l_1, n_1, e_1, i_4, j_4, k_4, l_4
  93. Ellipse(I, I', Q) → d_1
  94. Ellipse(E, E', P) → g_1
  95. Ellipse(I, I', Q) → h_1
  96. Sequence((xstart2, ylow2 + (space2 * i)), i, 1, 5) → list2
  97. Sequence((xstart1 + (v1 * t), ylow1 + (space1 * i)), i, 1, 5) → list3
  98. Sequence(xstart1 - (spacex1 * i), i, 0, 5) → list1
  99. Sequence((list1(i) + (v1 * t), ylow1 + space1), i, 1, 5) → list4
  100. OrthogonalLine(R, xAxis) → a
  101. OrthogonalLine(S, xAxis) → c
  102. OrthogonalLine(T, xAxis) → j_1
  103. OrthogonalLine(U, xAxis) → m_1
  104. Intersect(c_1, q_1) → A_1,
  105. Line(E_1, xAxis) → s_1
  106. Line(D_1, xAxis) → a_1
  107. Line(F_1, xAxis) → b_1
  108. Line(G_1, xAxis) → f_2
  109. Line(J_1, xAxis) → g_2
  110. Line(K_1, xAxis) → h_2
  111. Line(I_1, xAxis) → i_2
  112. Line(H_1, xAxis) → j_2
  113. Intersect(m, s_1) → M_1
  114. Intersect(a_1, m) → N_1
  115. Intersect(b_1, m) → O_1
  116. Intersect(f_2, m) → P_1
  117. Intersect(i_2, l) → Q_1
  118. Intersect(j_2, l) → R_1
  119. Intersect(g_2, l) → S_1
  120. Intersect(h_2, l) → T_1
  121. PolyLine(E_1, M_1, Q_1, I_1) → r_1
  122. PolyLine(D_1, N_1, R_1, H_1) → k_2
  123. PolyLine(F_1, O_1, S_1, J_1) → l_2
  124. PolyLine(G_1, P_1, T_1, K_1) → m_2
  125. Intersect(j_1, k_2) → Z
  126. Intersect(j_1, r_1) → L_1
  127. PolyLine(C_1, K_{10}, T_9, S_9) → n_2
  128. Intersect(j_1, n_2) → U_1
  129. Intersect(j_1, l_2) → V_1
  130. Intersect(j_1, m_2) → W_1
  131. Intersect(m_1, r_1) → Z_1
  132. Intersect(m_1, k_2) → A_2
  133. Intersect(m_1, n_2) → B_2
  134. Intersect(m_1, l_2) → C_2
  135. Intersect(m_1, m_2) → D_2
  136. Intersect(a, m_2) → E_2
  137. Intersect(a, l_2) → F_2
  138. Intersect(a, n_2) → G_2
  139. Intersect(a, k_2) → H_2
  140. Intersect(a, r_1) → I_2
  141. Intersect(c, r_1) → J_2
  142. Intersect(c, k_2) → K_2
  143. Intersect(c, n_2) → L_2
  144. Intersect(c, l_2) → M_2
  145. Intersect(c, m_2) → N_2
  146. OrthogonalLine(O_2, xAxis) → p_2
  147. OrthogonalLine(A, xAxis) → q_2
  148. OrthogonalLine(J, xAxis) → r_2
  149. OrthogonalLine(R_2, xAxis) → s_2
  150. OrthogonalLine(S_2, xAxis) → t_2
  151. Intersect(p_2, m_2) → P_2
  152. Intersect(p_2, l_2) → U_3
  153. Intersect(p_2, n_2) → V_2
  154. Intersect(p_2, k_2) → W_2
  155. Intersect(p_2, r_1) → Z_2
  156. Intersect(r_2, r_1) → Q_2
  157. Intersect(r_2, k_2) → A_3
  158. Intersect(r_2, n_2) → B_3
  159. Intersect(r_2, l_2) → C_3
  160. Intersect(r_2, m_2) → D_3
  161. Intersect(q_2, m_2) → E_3
  162. Intersect(q_2, l_2) → F_3
  163. Intersect(q_2, n_2) → G_3
  164. Intersect(q_2, k_2) → H_3
  165. Intersect(q_2, r_1) → I_3
  166. If(time > t1 + ttrans + (11 * timelag), ttrans, If[time - t1 - (11 * timelag) < 0, 0, time - t1 - (11 * timelag)]) → timetrans11
  167. OrthogonalLine(K_3, xAxis) → d_2
  168. Intersect(d_2, r_1) → L_3
  169. Intersect(d_2, k_2) → M_3
  170. Intersect(d_2, n_2) → N_3
  171. Intersect(d_2, l_2) → O_3
  172. Intersect(d_2, m_2) → P_3
  173. Intersect(timetrans11, r_1) → Q_3
  174. Intersect(timetrans11, k_2) → R_3
  175. Intersect(timetrans11, n_2) → S_3
  176. Intersect(timetrans11, l_2) → T_3, T_4
  177. Intersect(timetrans11, m_2) → V_3
  178. Intersect(s_2, r_1) → W_3
  179. Intersect(s_2, k_2) → Z_3
  180. Intersect(s_2, n_2) → A_4
  181. Intersect(s_2, l_2) → B_4
  182. Intersect(s_2, m_2) → C_4
  183. Intersect(t_2, r_1) → D_4
  184. Intersect(t_2, k_2) → E_4
  185. Intersect(t_2, m_2) → F_4
  186. Intersect(t_2, n_2) → G_4
  187. Intersect(t_2, l_2) → H_4
  188. If(time > t1 + (11 * timelag), t1, If[time - (11 * timelag) < 0, 0, time - (11 * timelag)]) → time111
  189. If(time > t1 + (12 * timelag), t1, If[time - (12 * timelag) < 0, 0, time - (12 * timelag)]) → time112
  190. If(time > t1 + (13 * timelag), t1, If[time - (13 * timelag) < 0, 0, time - (13 * timelag)]) → time113
  191. If(time > t1 + (14 * timelag), t1, If[time - (14 * timelag) < 0, 0, time - (14 * timelag)]) → time114
  192. If(time > t1 + (15 * timelag), t1, If[time - (15 * timelag) < 0, 0, time - (15 * timelag)]) → time115
  193. If(time > t1 + (16 * timelag), t1, If[time - (16 * timelag) < 0, 0, time - (16 * timelag)]) → time116
  194. If(time > t1 + ttrans + t2 + (11 * timelag), t2, If[time - (t1 + (11 * timelag) + ttrans) < 0, 0, time - (t1 + (11 * timelag) + ttrans)]) → time211
  195. If(time > t1 + ttrans + t2 + (12 * timelag), t2, If[time - (t1 + (12 * timelag) + ttrans) < 0, 0, time - (t1 + (12 * timelag) + ttrans)]) → time212
  196. If(time > t1 + ttrans + t2 + (13 * timelag), t2, If[time - (t1 + (13 * timelag) + ttrans) < 0, 0, time - (t1 + (13 * timelag) + ttrans)]) → time213
  197. If(time > t1 + ttrans + t2 + (14 * timelag), t2, If[time - (t1 + (14 * timelag) + ttrans) < 0, 0, time - (t1 + (14 * timelag) + ttrans)]) → time214
  198. If(time > t1 + ttrans + t2 + (15 * timelag), t2, If[time - (t1 + (15 * timelag) + ttrans) < 0, 0, time - (t1 + (15 * timelag) + ttrans)]) → time215
  199. If(time > t1 + ttrans + t2 + (16 * timelag), t2, If[time - (t1 + (16 * timelag) + ttrans) < 0, 0, time - (t1 + (16 * timelag) + ttrans)]) → time216
  200. If(time > t1 + ttrans + (12 * timelag), ttrans, If[time - t1 - (12 * timelag) < 0, 0, time - t1 - (12 * timelag)]) → timetrans12
  201. If(time > t1 + ttrans + (13 * timelag), ttrans, If[time - t1 - (13 * timelag) < 0, 0, time - t1 - (13 * timelag)]) → timetrans13
  202. If(time > t1 + ttrans + (14 * timelag), ttrans, If[time - t1 - (14 * timelag) < 0, 0, time - t1 - (14 * timelag)]) → timetrans14
  203. If(time > t1 + ttrans + (15 * timelag), ttrans, If[time - t1 - (15 * timelag) < 0, 0, time - t1 - (15 * timelag)]) → timetrans15
  204. If(time > t1 + ttrans + (16 * timelag), ttrans, If[time - t1 - (16 * timelag) < 0, 0, time - t1 - (16 * timelag)]) → timetrans16
  205. OrthogonalLine(I_4, xAxis) → a_2
  206. OrthogonalLine(J_4, xAxis) → b_2
  207. If(time > t1 + ttrans + (19 * timelag), ttrans, If[time - t1 - (19 * timelag) < 0, 0, time - t1 - (19 * timelag)]) → timetrans19_1
  208. OrthogonalLine(L_4, xAxis) → e_2
  209. OrthogonalLine(M_4, xAxis) → f_3
  210. OrthogonalLine(N_4, xAxis) → g_3
  211. OrthogonalLine(J_3, xAxis) → h_3
  212. Intersect(e_2, r_1) → O_4
  213. Intersect(e_2, k_2) → P_4
  214. Intersect(e_2, n_2) → Q_4
  215. Intersect(e_2, l_2) → R_4
  216. Intersect(e_2, m_2) → S_4
  217. Intersect(timetrans19_1, r_1) → T_4
  218. Intersect(timetrans19_1, k_2) → U_4
  219. Intersect(timetrans19_1, n_2) → V_4
  220. Intersect(timetrans19_1, l_2) → W_4, W_5
  221. Intersect(timetrans19_1, m_2) → Z_4
  222. Intersect(f_3, r_1) → A_5
  223. Intersect(f_3, k_2) → B_5
  224. Intersect(f_3, n_2) → C_5
  225. Intersect(f_3, l_2) → D_5
  226. Intersect(f_3, m_2) → E_5
  227. Intersect(b_2, r_1) → F_5
  228. Intersect(b_2, k_2) → G_5
  229. Intersect(b_2, n_2) → H_5
  230. Intersect(b_2, l_2) → I_5
  231. Intersect(b_2, m_2) → J_5
  232. Intersect(a_2, r_1) → K_5
  233. Intersect(a_2, k_2) → L_5
  234. Intersect(a_2, n_2) → M_5
  235. Intersect(a_2, l_2) → N_5
  236. Intersect(a_2, m_2) → O_5
  237. Intersect(g_3, r_1) → P_5
  238. Intersect(g_3, k_2) → Q_5
  239. Intersect(g_3, n_2) → R_5
  240. Intersect(g_3, l_2) → S_5
  241. Intersect(g_3, m_2) → T_5
  242. Intersect(h_3, r_1) → U_5
  243. Intersect(h_3, k_2) → V_5
  244. Intersect(h_3, n_2) → W_5
  245. Intersect(h_3, l_2) → Z_5
  246. Intersect(h_3, m_2) → A_6
  247. If(time > t1 + (17 * timelag), t1, If[time - (17 * timelag) < 0, 0, time - (17 * timelag)]) → time117
  248. If(time > t1 + (18 * timelag), t1, If[time - (18 * timelag) < 0, 0, time - (18 * timelag)]) → time118
  249. If(time > t1 + (19 * timelag), t1, If[time - (19 * timelag) < 0, 0, time - (19 * timelag)]) → time119
  250. If(time > t1 + (20 * timelag), t1, If[time - (20 * timelag) < 0, 0, time - (20 * timelag)]) → time120
  251. If(time > t1 + (21 * timelag), t1, If[time - (21 * timelag) < 0, 0, time - (21 * timelag)]) → time121
  252. If(time > t1 + (22 * timelag), t1, If[time - (22 * timelag) < 0, 0, time - (22 * timelag)]) → time122
  253. If(time > t1 + (23 * timelag), t1, If[time - (23 * timelag) < 0, 0, time - (23 * timelag)]) → time123
  254. If(time > t1 + (24 * timelag), t1, If[time - (24 * timelag) < 0, 0, time - (24 * timelag)]) → time124
  255. If(time > t1 + (25 * timelag), t1, If[time - (25 * timelag) < 0, 0, time - (25 * timelag)]) → time125
  256. If(time > t1 + ttrans + (17 * timelag), ttrans, If[time - t1 - (17 * timelag) < 0, 0, time - t1 - (17 * timelag)]) → timetrans17
  257. If(time > t1 + ttrans + (18 * timelag), ttrans, If[time - t1 - (18 * timelag) < 0, 0, time - t1 - (18 * timelag)]) → timetrans18
  258. If(time > t1 + ttrans + (19 * timelag), ttrans, If[time - t1 - (19 * timelag) < 0, 0, time - t1 - (19 * timelag)]) → timetrans19
  259. If(time > t1 + ttrans + (20 * timelag), ttrans, If[time - t1 - (20 * timelag) < 0, 0, time - t1 - (20 * timelag)]) → timetrans20
  260. If(time > t1 + ttrans + (21 * timelag), ttrans, If[time - t1 - (21 * timelag) < 0, 0, time - t1 - (21 * timelag)]) → timetrans21
  261. If(time > t1 + ttrans + (22 * timelag), ttrans, If[time - t1 - (22 * timelag) < 0, 0, time - t1 - (22 * timelag)]) → timetrans22
  262. If(time > t1 + ttrans + (23 * timelag), ttrans, If[time - t1 - (23 * timelag) < 0, 0, time - t1 - (23 * timelag)]) → timetrans23
  263. If(time > t1 + ttrans + (24 * timelag), ttrans, If[time - t1 - (24 * timelag) < 0, 0, time - t1 - (24 * timelag)]) → timetrans24
  264. If(time > t1 + ttrans + (25 * timelag), ttrans, If[time - t1 - (25 * timelag) < 0, 0, time - t1 - (25 * timelag)]) → timetrans25
  265. If(time > t1 + ttrans + t2 + (17 * timelag), t2, If[time - (t1 + (17 * timelag) + ttrans) < 0, 0, time - (t1 + (17 * timelag) + ttrans)]) → time217
  266. If(time > t1 + ttrans + t2 + (18 * timelag), t2, If[time - (t1 + (18 * timelag) + ttrans) < 0, 0, time - (t1 + (18 * timelag) + ttrans)]) → time218
  267. If(time > t1 + ttrans + t2 + (19 * timelag), t2, If[time - (t1 + (19 * timelag) + ttrans) < 0, 0, time - (t1 + (19 * timelag) + ttrans)]) → time219
  268. If(time > t1 + ttrans + t2 + (20 * timelag), t2, If[time - (t1 + (20 * timelag) + ttrans) < 0, 0, time - (t1 + (20 * timelag) + ttrans)]) → time220
  269. If(time > t1 + ttrans + t2 + (21 * timelag), t2, If[time - (t1 + (21 * timelag) + ttrans) < 0, 0, time - (t1 + (21 * timelag) + ttrans)]) → time221
  270. If(time > t1 + ttrans + t2 + (22 * timelag), t2, If[time - (t1 + (22 * timelag) + ttrans) < 0, 0, time - (t1 + (22 * timelag) + ttrans)]) → time222
  271. If(time > t1 + ttrans + t2 + (23 * timelag), t2, If[time - (t1 + (23 * timelag) + ttrans) < 0, 0, time - (t1 + (23 * timelag) + ttrans)]) → time223
  272. If(time > t1 + ttrans + t2 + (24 * timelag), t2, If[time - (t1 + (24 * timelag) + ttrans) < 0, 0, time - (t1 + (24 * timelag) + ttrans)]) → time224
  273. If(time > t1 + ttrans + t2 + (25 * timelag), t2, If[time - (t1 + (25 * timelag) + ttrans) < 0, 0, time - (t1 + (25 * timelag) + ttrans)]) → time225
  274. OrthogonalLine(B_6, xAxis) → i_3
  275. OrthogonalLine(C_6, xAxis) → j_3
  276. OrthogonalLine(D_6, xAxis) → k_3
  277. OrthogonalLine(E_6, xAxis) → l_3
  278. Point(xAxis) → F_6
  279. OrthogonalLine(F_6, xAxis) → m_3
  280. OrthogonalLine(G_6, xAxis) → n_3
  281. OrthogonalLine(H_6, xAxis) → p_3
  282. OrthogonalLine(I_6, xAxis) → q_3
  283. OrthogonalLine(J_6, xAxis) → r_3
  284. OrthogonalLine(K_4, xAxis) → c_2
  285. Intersect(c_2, r_1) → K_6
  286. Intersect(c_2, k_2) → L_6
  287. Intersect(c_2, n_2) → M_6
  288. Intersect(c_2, l_2) → N_6
  289. Intersect(c_2, m_2) → O_6
  290. Intersect(k_3, r_1) → P_6
  291. Intersect(k_3, k_2) → Q_6
  292. Intersect(k_3, n_2) → R_6
  293. Intersect(k_3, l_2) → S_6
  294. Intersect(k_3, m_2) → T_6
  295. Intersect(r_3, m_2) → U_6
  296. Intersect(r_3, l_2) → V_6
  297. Intersect(r_3, n_2) → W_6
  298. Intersect(r_3, k_2) → Z_6
  299. Intersect(r_3, r_1) → A_7
  300. Intersect(n_3, r_1) → B_7
  301. Intersect(n_3, k_2) → C_7
  302. Intersect(n_3, n_2) → D_7
  303. Intersect(n_3, l_2) → E_7
  304. Intersect(n_3, m_2) → F_7
  305. Intersect(i_3, r_1) → G_7
  306. Intersect(i_3, k_2) → H_7
  307. Intersect(i_3, n_2) → I_7
  308. Intersect(i_3, l_2) → J_7
  309. Intersect(i_3, m_2) → K_7
  310. Intersect(j_3, r_1) → L_7
  311. Intersect(j_3, k_2) → M_7
  312. Intersect(j_3, n_2) → N_7
  313. Intersect(j_3, l_2) → O_7
  314. Intersect(j_3, m_2) → P_7
  315. Intersect(p_3, r_1) → Q_7
  316. Intersect(p_3, k_2) → R_7
  317. Intersect(p_3, n_2) → S_7
  318. Intersect(p_3, l_2) → T_7
  319. Intersect(p_3, m_2) → U_7
  320. Intersect(q_3, r_1) → V_7
  321. Intersect(q_3, k_2) → W_7
  322. Intersect(q_3, n_2) → Z_7
  323. Intersect(q_3, l_2) → A_8
  324. Intersect(q_3, m_2) → B_8
  325. Intersect(l_3, r_1) → C_8
  326. Intersect(l_3, k_2) → D_8
  327. Intersect(l_3, n_2) → E_8
  328. Intersect(l_3, l_2) → F_8
  329. Intersect(l_3, m_2) → G_8
  330. Vector(E, C_1) → u
  331. Vector(C_1, E) → v
  332. Vector(I, B_1) → w
  333. Vector(B_1, I) → u_1
  334. Midpoint(B_1, I) → H_8
  335. Midpoint(C_1, E) → I_8
  336. Intersect(f, xAxis) → J_8
  337. Intersect(h, xAxis) → K_8
  338. Vector(D, J_8) → v_1
  339. Vector(J_8, D) → w_1
  340. Vector(H, K_8) → u_2
  341. Vector(K_8, H) → v_2
  342. Midpoint(D, J_8) → L_8
  343. Midpoint(H, K_8) → M_8
  344. Segment(V, W) → a_3
  345. Polygon(P_8, Q_8, R_8, S_8, T_8, U_8, V_8) → poly2, p_8, q_8, r_8, s_8, t_8, u_8, v_8
  346. Polygon(O_8, Z_8, A_9, B_9, C_9, D_9, E_9) → poly3, o_8, z_8, a_9, b_9, c_9, d_9, e_9
  347. Intersect(b_3, l) → G_9
  348. Segment(V, G_9) → e_3
  349. Segment(K_9, N) → g_4
  350. Ellipse(H_9, I_9, O_9) → c_4
  351. Segment(H_9, J_9) → n_4
  352. Segment(J_9, N_9) → s_4
  353. Intersect(p_4, q_4) → P_9
  354. Segment(P_9, K_9) → t_4
  355. Segment(K_9, I_9) → a_4
  356. Segment(J_9, N_9) → b_4
  357. Ellipse(H_9, I_9, O_9) → d_4
  358. Segment(N_9, J_9) → e_4
  359. Intersect(e_1, i_4) → Q_9
  360. Segment(N_9, Q_9) → f_5
  361. Intersect(l_4, b_3) → R_9
  362. OrthogonalLine(Z_9, p_1) → i_5
  363. Intersect(i_5, m) → L_{10}
  364. OrthogonalLine(U_9, l) → k_5
  365. Intersect(k_5, n_2) → V_9
  366. Intersect(l, k_5) → W_9
  367. PolyLine(Z_9, L_{10}, W_9, U_9) → l_5
  368. Intersect(k_5, l_5) → A_{10}, C_{10}
  369. Intersect(k_5, l_5) → E_{10}, F_{10}
  370. Intersect(k_5, l_5) → G_{10}, H_{10}
  371. Intersect(k_5, l_5) → I_{10}, J_{10}
  372. Intersect(k_5, l_5) → M_{10}, N_{10}
  373. Intersect(p_2, l_5) → P_{10}
  374. Intersect(d_2, l_5) → Q_{10}
  375. Intersect(h_3, l_5) → R_{10}
  376. Intersect(s_2, l_5) → S_{10}
  377. Intersect(k_5, l_5) → U_{10}, V_{10}
  378. Intersect(k_5, l_5) → W_{10}, Z_{10}
  379. Intersect(k_5, l_5) → A_{11}, B_{11}
  380. Intersect(k_5, l_5) → C_{11}, D_{11}
  381. Intersect(k_5, l_5) → E_{11}, F_{11}
  382. Intersect(k_5, l_5) → G_{11}, H_{11}
  383. Intersect(k_5, l_5) → I_{11}, J_{11}
  384. Intersect(k_5, l_5) → K_{11}, L_{11}
  385. Intersect(f_3, l_5) → N_{11}
  386. Intersect(b_2, l_5) → O_{11}
  387. Intersect(a_2, l_5) → P_{11}
  388. Intersect(g_3, l_5) → Q_{11}
  389. Intersect(t_2, l_5) → R_{11}
  390. Intersect(k_5, l_5) → S_{11}, T_{11}
  391. Intersect(k_3, l_5) → V_{11}
  392. Intersect(l_3, l_5) → W_{11}
  393. Intersect(j_3, l_5) → Z_{11}
  394. Intersect(i_3, l_5) → A_{12}
  395. Intersect(e_2, l_5) → B_{12}
  396. Intersect(c_2, l_5) → C_{12}
  397. Textfield(r3) → InputBox4
  398. Textfield(v1) → InputBox3
  399. Segment(G_9, F_9) → g_5
  400. Vector(R_9, H_9) → w_2
  401. Vector(H_9, R_9) → u_3
  402. Intersect(j_1, l_5) → E_{12}
  403. Intersect(m_1, l_5) → D_{10}
  404. Intersect(a, l_5) → O_{10}
  405. Intersect(c, l_5) → M_{11}
  406. Intersect(q_2, l_5) → T_{10}
  407. Intersect(r_2, l_5) → U_{11}
  408. Intersect(p_3, l_5) → F_{12}
  409. Intersect(l_5, l_5) → G_{12}, H_{12}, I_{12}, J_{12}
  410. Intersect(q_3, l_5) → K_{12}
  411. Intersect(n_3, l_5) → L_{12}
  412. Intersect(r_3, l_5) → M_{12}
  413. Midpoint(R_9, H_9) → N_{12}
  414. Vector(O_{12}, F_9) → v_3
  415. Vector(F_9, O_{12}) → w_3
  416. Midpoint(F_9, O_{12}) → P_{12}
  417. Midpoint(I_9, K_9) → Q_{12}

AI Drawing Prompt Reference

Draw a fluid dynamics mass conservation continuity equation demonstration, showing pipes with varying diameters, incorporating linear functions, secant lines, parallelograms, and sine functions. Use lines and orthogonal lines to construct pipe cross-sections, and employ mirroring and distance calculations to illustrate fluid flow geometry. Include vectors and midpoints for assistance, resulting in a complete figure with multiple geometric shapes and mathematical concepts.
The prompt above was compiled from the original drawing commands and is for reference only.