air_standard.txt

1.8658892   
2.6044703
3.7317784
3.8483965
4.159378
4.2371235
4.664723
5.1311955
5.7531586
6.1030126
6.686103
7.1525755
7.308066
7.6190476
8.08552
8.590865
9.718173
9.912537
10.379008
11.856171
13.216715
14.305151
16.015549
16.793003

theory.py

import numpy as np
import sympy 
import matplotlib.pyplot as plt
from math import pi, sqrt

sympy.init_printing(use_unicode=True)

RHO_AIR = 1.225
RHO_WATER = 1000.0
D = 0.0254
R = D/2
A = pi*(D**2)/4
g = 9.8
MU = 8.9e-4
SIGMA = 7.28e-2
ALPHA = 0.67
Co = 1.2

AIR_EXPT = np.loadtxt("./data/air_standard.txt")
print(AIR_EXPT)
water_arr = np.array([])

Q_air = AIR_EXPT/(RHO_AIR * 3600)
# print(QG)

QF = sympy.symbols("QF")


Bo = ((RHO_WATER)*g*D**2/(SIGMA))
v_ts_dash = 0.352 * (1 - 3.18 * (Bo ** -1) - 14.77 * (Bo ** -2))
v_ts = v_ts_dash*sqrt(g*D)

temp = 0
for QG in Q_air:

    left = QF + (1.34*pi*R)*((Co*(QG+QF)/A)+v_ts)*\
           ((MU*QF/(A*SIGMA*(1-(QG/(Co*(QF+QG)+(A*v_ts))))))**(sympy.S("2/3")))

    right = pi*(R**2)*((Co*(QF+QG)/A) + v_ts)

    equation = sympy.Eq(left, right)

    Q_water = sympy.solveset(equation, QF)

    water = list(Q_water)[0]

    temp = water*3600*RHO_WATER
    # print(temp)

    water_arr = np.append(water_arr, temp)    

print(water_arr)