21.11: Confined phreatic flow with precipitation

This notebook shows the Bruggeman solution for:

Confined phreatic aquifer with horizontal 1D-flow. Flow caused by precipitation through an infinite strip of width 2b, bounded at both sides by open water with equal level H.

import matplotlib.pyplot as plt
from numpy import linspace

from bruggeman.flow1d import bruggeman_21_11

bruggeman_21_11

\[\displaystyle h = \sqrt{H^{2} + \frac{p \left(b^{2} - x^{2}\right)}{k}}\]

bruggeman_21_11?

# aquifer parameters
b = 50.0
k = 1.0
H = 1.0
p = 5e-3  # constant precipitation flux

x = linspace(-b, b, 100)

fig, ax = plt.subplots(figsize=(12, 3), layout="tight")

h = bruggeman_21_11(x, b, k, H, p)
ax.plot(x, h)

ax.grid(True)
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Head (m)")
ax.set_title("Bruggeman 21.11")
ax.set_ylim(0.0);