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import numpy as np
import matplotlib.pyplot as plt

from sympy.abc import rho
from sympy.interactive import printing
from sympy import Eq, Derivative, Function
from sympy import symbols, integrate, lambdify, dsolve

printing.init_printing()


    

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t, z, g = symbols('t z g', nonzero=True, constant=True)
w = Function('w')(t)
p = Function('p')


    

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dwdt = Eq(Derivative(w, t), -1/rho*Derivative(p(z), z) - g)
dwdt


    

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dwdt = dwdt.subs(w, 0).doit()


    

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P = integrate(dwdt, (z, -z, 0))
P


    

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P = P.subs(p(0), 0)
P


    

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P = Eq(p(-z), rho*g*z)
P


    

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depth = -np.linspace(0, 11e3, 100)
subs = [(g, -9.8), (rho, 1023)]

func = P.subs(subs)
func = lambdify(z, func.rhs, "numpy")
pressure = func(depth)


    

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fig, ax = plt.subplots(figsize=(4, 4))
ax.grid(True)
ax.plot(pressure, depth/1e3)
ax.set_xlabel(r'Pressão [Pa ou N m$^{-2}$]')
ax.set_ylabel(r'Profundidade [km]')