MathPlotAI Logo MathPlotAI

Continuity Equation Demonstration by Dr.Lakshman Chaudhari

Continuity Equation Demonstration by Dr.Lakshman Chaudhari
Loading the math board and drawing, please wait…
2016-01-31 23:49
VectorFunctionInequalityGeometric ConstructionGraphing
This example graphically illustrates the continuity equation in fluid mechanics in a 2D plane. It involves core mathematical concepts such as vector fields, streamlines, inequalities, and geometric transformations. The construction uses commands like Sequence, Point, Segment, and Vector in GeoGebra. Suitable for high school students and above studying fluid dynamics or vector calculus.

GeoGebra Commands & Parameters

  1. Sequence(y = i, i, (-r_1), r_1, (2 * r_1 / 10)) → list1
  2. Point(list1) → A
  3. Point(list1) → B
  4. Point(list1) → C
  5. Point(list1) → D
  6. Point(list1) → E
  7. Point(list1) → F
  8. Point(list1) → G
  9. Point(list1) → H
  10. Point(list1) → I
  11. Point(list1) → J
  12. Point(list1) → K
  13. Point(list1) → L
  14. Point(list1) → M
  15. Point(list1) → N
  16. Point(list1) → O
  17. Point(list1) → P
  18. Point(list1) → Q
  19. Point(list1) → R
  20. Sequence(y = i, i, (-r_2), r_2, (2 * r_2 / 10)) → list3
  21. Point(list3) → S
  22. Point(list3) → T
  23. Point(list3) → U
  24. Point(list3) → V
  25. Point(list3) → W
  26. Point(list3) → Z
  27. Point(list3) → A_1
  28. Point(list3) → B_1
  29. Point(list3) → C_1
  30. Point(list3) → D_1
  31. Point(list3) → E_1
  32. Point(list1) → F_1
  33. Point(list1) → G_1
  34. Point(list1) → H_1
  35. Point(list1) → I_1
  36. Segment(A, S) → a
  37. Segment(B, T) → b
  38. Segment(C, U) → c
  39. Segment(D, V) → d
  40. Segment(E, W) → e
  41. Segment(F, Z) → f
  42. Segment(G, A_1) → g
  43. Segment(H, B_1) → h
  44. Segment(I, C_1) → i
  45. Segment(H_1, D_1) → j
  46. Segment(I_1, E_1) → k
  47. Segment(J, A) → l
  48. Segment(K, B) → m
  49. Segment(L, C) → n
  50. Segment(M, D) → p
  51. Segment(N, E) → q
  52. Segment(O, F) → r
  53. Segment(P, G) → s
  54. Segment(Q, H) → t
  55. Segment(R, I) → a_1
  56. Segment(F_1, H_1) → b_1
  57. Segment(G_1, I_1) → c_1
  58. Point(list3) → J_1
  59. Point(list3) → K_1
  60. Point(list3) → L_1
  61. Point(list3) → M_1
  62. Point(list3) → N_1
  63. Point(list3) → O_1
  64. Point(list3) → P_1
  65. Point(list3) → Q_1
  66. Point(list3) → R_1
  67. Point(list3) → S_1
  68. Point(list3) → T_1
  69. Vector(T, K_1) → v
  70. Vector(U, L_1) → w
  71. Vector(W, N_1) → u_1
  72. Vector(V, M_1) → v_1
  73. Vector(Z, O_1) → w_1
  74. Vector(A_1, P_1) → d_1
  75. Vector(B_1, Q_1) → e_1
  76. Vector(D_1, S_1) → g_1
  77. Segment(S, J_1) → i_1
  78. Segment(C_1, R_1) → f_1
  79. Segment(E_1, T_1) → h_1
  80. Vector(C_1, R_1) → u