Merge pull request #7 from dbrakenhoff/eq_21_11

add phreatic equation with rainfall

Author: dbrakenhoff

bruggeman/flow1d.py

@@ -5,6 +5,43 @@
 from bruggeman.general import ierfc, latexify_function
 
 
+@latexify_function(identifiers={"bruggeman_21_11": "h"}, reduce_assignments=True)
+def bruggeman_21_11(
+    x: float | NDArray[float64],
+    b: float,
+    k: float,
+    H: float,
+    p: float = 1.0,
+) -> float | NDArray[float64]:
+    """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
+
+    From Bruggeman 21.11
+
+    Parameters
+    ----------
+    x : float or ndarray
+        Distance from the center of the strip [m]
+    b : float
+        Half-width of the strip [m]
+    k : float
+        Hydraulic conductivity [m/d]
+    H : float
+        Head in the open water [m]
+    p : float
+        Arbitrary constant precipitation [m/d]
+
+    Returns
+    -------
+    head: float
+        Hydraulic head at distance x [m]
+    """
+
+    return sqrt(H**2 + p / k * (b**2 - x**2))
+
+
 @latexify_function(identifiers={"bruggeman_123_02": "varphi"}, reduce_assignments=True)
 def bruggeman_123_02(
     x: float | NDArray[float64],

docs/examples/bruggeman_21_11.ipynb

@@ -0,0 +1,106 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "4b9445a0",
+   "metadata": {},
+   "source": [
+    "# 21.11: Confined phreatic flow with precipitation\n",
+    "\n",
+    "This notebook shows the Bruggeman solution for:\n",
+    "\n",
+    "Confined phreatic aquifer with horizontal 1D-flow. \n",
+    "Flow caused by precipitation through an infinite strip of width `2b`, bounded at both sides by open water with equal level `H`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f6114c5c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "from numpy import linspace\n",
+    "\n",
+    "from bruggeman.flow1d import bruggeman_21_11"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3e31ee8a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bruggeman_21_11"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4682c73d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bruggeman_21_11?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "06b5a222",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# aquifer parameters\n",
+    "b = 50.0\n",
+    "k = 1.0\n",
+    "D = 1.0\n",
+    "p = 5e-3  # constant precipitation flux"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c42d5b22",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = linspace(-b, b, 100)\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(12, 3), layout=\"tight\")\n",
+    "\n",
+    "h = bruggeman_21_11(x, b, k, D, p)\n",
+    "ax.plot(x, h)\n",
+    "\n",
+    "ax.grid(True)\n",
+    "ax.set_xlabel(\"Distance (m)\")\n",
+    "ax.set_ylabel(\"Head (m)\")\n",
+    "ax.set_title(\"Bruggeman 21.11\")\n",
+    "ax.set_ylim(0.0);"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "CWGI25",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.13.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

docs/examples/index.rst

@@ -9,6 +9,7 @@ Below you can find examples.
     :hidden:
     :glob:
 
+    bruggeman_21_11
     bruggeman_123_05
     bruggeman_126_33
     bruggeman_128_0x
@@ -20,6 +21,8 @@ Below you can find examples.
 Flow1D
 ------
 
+`21.11 Confined phreatic aquifer with precipitation`_
+
 `123.05 Constant pumping in a confined aquifer`_
 
 `126.33 Step head change in a semi-confined aquifer - steady state`_
@@ -30,6 +33,7 @@ Flow1D
 
 `Edelman sudden change in water level in a confined aquifer`_
 
+.. _21.11 Confined phreatic aquifer with precipitation: bruggeman_21_11.html
 .. _123.05 Constant pumping in a confined aquifer: bruggeman_123_05.html
 .. _126.33 Step head change in a semi-confined aquifer - steady state: bruggeman_126_33.html
 .. _128.0x Tidal fluctuation of open water: bruggeman_128_0x.html