messing around with a testvolume and visualization

of the change in height that comes with different
flow patterns

.gitignore

@@ -1 +1,2 @@
 2bignored.txt
+functions/__pycache__/

Messy_NB.ipynb

@@ -9,13 +9,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1.21.5\n"
+      "11\n"
      ]
     }
    ],
    "source": [
     "import numpy as np\n",
-    "print(np.__version__)"
+    "import plotly\n"
    ]
   }
  ],

functions/visualize_parameters.py

@@ -0,0 +1 @@
+import plotly

functions/volume_change.py

@@ -0,0 +1,117 @@
+                                     
+import numpy as np
+# Testvolume                                            
+# Depth of the whole structure is constant and given by the variable d
+#                                           
+#                                  
+#        { x_1*d*h                                                      for       h <= h_1
+# V(h) = { x_1*d*(h-h_1)+(x_2-x_1)*d*(h-h_1)**2/(2*(h_2-h_1) + V(h_1))  for h_1 < h <= h_2
+#        { x_2*d*(h-h_2)+(x_3-x_2)*d*(h-h_2)**2/(2*(h_3-h_2) + V(h_2))  for h_2 < h <= h_3
+#        { x_3*d*(h-h_3) + V(h_3)                                       for h_3 < h                           
+#
+#
+#       { V/(x_1*d)                                                     for       V <= V_1
+#h(V) = { (-b_2+sqrt(b_2**2-4*a_2*c_2)/(2*a_2))                         for V_1 < V <= V_2
+#       { (-b_3+sqrt(b_3**2-4*a_3*c_3)/(2*a_3))                         for V_2 < V <= V_3
+#       { (V-V_3)/(x_1*d)                                               for V_3 < V                           
+#
+# with
+#     a_2 = 0.5*((x_2-x_1)*d)/(h_2-h_1)                                      
+#     a_3 = 0.5*((x_3-x_2)*d)/(h_3-h_2)  
+#                                           
+#     b_2 = x_1*d-((x_2-x_1)*d*h_1)/(h_2-h_1)                                       
+#     b_3 = x_2*d-((x_3-x_2)*d*h_2)/(h_3-h_2)                                       
+#                                           
+#     c_2 = ((x_2-x_1)*d*h_1**2)/(h_2-h_1)-h_1*x_1*d-(V-V_1)                                         
+#     c_3 = ((x_3-x_2)*d*h_2**2)/(h_3-h_2)-h_2*x_2*d-(V-V_2)                                         
+#                                           
+#                                           
+#                                           
+#                                           
+#                                           
+#                    _____                      
+#                   |     |                      |       
+#                   |     |                      |       
+#                   |     |                      | h_4 - h_3     
+#                   |     |                     _|_      
+#                 __| _ _ |__                    |      
+#                /    x_3    \                   |     
+#               /             \                  |     
+#              /               \                 |    
+#             /                 \                | h_3 - h_2  
+#            /                   \               |    
+#           /                     \              |     
+#          /                       \             |     
+#         /                         \            |      
+#        /                           \          _|_      
+#       <----------------------------->          | 
+#        \            x_2            /           | h_2 - h_1  
+#         \                         /            |  
+#          \ _ _ _ _ _ _ _ _ _ _ _ /            _|_
+#           |         x_1         |              | 
+#           |                     |              | h_1  
+#           |                     |              |   
+#           |_____________________|             _|_
+
+
+
+
+
+
+h_1 = 10
+h_2 = 5     + h_1
+h_3 = 5     + h_2
+
+x_1 = 100
+x_2 = 101
+x_3 = 30
+
+d = 5
+
+V_1 = x_1*d*h_1
+V_2 = x_1*d*(h_2-h_1)+(x_2-x_1)*d*(h_2-h_1)**2/(2*(h_2-h_1)) + V_1
+V_3 = x_2*d*(h_3-h_2)+(x_3-x_2)*d*(h_3-h_2)**2/(2*(h_3-h_2)) + V_2
+
+def V_h(h):
+    if h <= h_1:
+        V = x_1*d*h
+    elif (h_1 < h) and (h <= h_2):
+        V = x_1*d*(h-h_1)+(x_2-x_1)*d*(h-h_1)**2/(2*(h_2-h_1)) + V_1
+    elif (h_2 < h) and (h <= h_3):
+        V = x_2*d*(h-h_2)+(x_3-x_2)*d*(h-h_2)**2/(2*(h_3-h_2)) + V_2
+    elif (h_3 < h):
+        V = x_3*d*(h-h_3) + V_3
+
+    return V
+
+a_2 = 0.5*((x_2-x_1)*d)/(h_2-h_1)                                      
+a_3 = 0.5*((x_3-x_2)*d)/(h_3-h_2)  
+                                        
+b_2 = x_1*d-((x_2-x_1)*d*h_1)/(h_2-h_1)                                       
+b_3 = x_2*d-((x_3-x_2)*d*h_2)/(h_3-h_2)                                       
+                                        
+c_2 = ((x_2-x_1)*d*h_1**2)/(2*(h_2-h_1))-h_1*x_1*d                                        
+c_3 = ((x_3-x_2)*d*h_2**2)/(2*(h_3-h_2))-h_2*x_2*d
+
+
+def h_V(V):
+    if V <= V_1:
+        h = V/(x_1*d)
+    elif (V_1 < V) and (V <= V_2):
+        h = (-b_2+(b_2**2-4*a_2*(c_2-(V-V_1)))**0.5)/(2*a_2) 
+    elif (V_2 < V) and (V <= V_3):
+        h = (-b_3+(b_3**2-4*a_3*(c_3-(V-V_2)))**0.5)/(2*a_3)
+    elif (V_3 < V):
+        h = (V-V_3)/(x_3*d)+h_3
+    return h
+
+
+def show_parameters():
+    print('h_1: ', h_1)
+    print('h_2: ', h_2)
+    print('h_3: ', h_3)
+    print('x_1: ', x_1)
+    print('x_2: ', x_2)
+    print('x_3: ', x_3)
+    
+