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messing around with a testvolume and visualization

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of the change in height that comes with different
flow patterns
This commit is contained in:
Brantegger Georg
2022-05-16 15:44:03 +02:00
parent b633dfd584
commit 44f4d77524
6 changed files with 2088142 additions and 2 deletions
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functions/volume_change.py Normal file
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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)