{ "cells": [ { "cell_type": "code", "execution_count": null, "id": "2e3c4da4", "metadata": { "tags": [ "remove-input" ] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from myst_nb import glue\n", "%config InlineBackend.rc = {'figure.dpi': 300}\n", "%config InlineBackend.figure_format = 'svg'\n", "import sys\n", "sys.path.append(\"../py_figures\")\n", "import diagrams" ] }, { "cell_type": "markdown", "id": "c2a31558", "metadata": {}, "source": [ "(content:chap4:steady_1D_flow)=\n", "# Steady one-dimensional flow in coastal aquifers\n", "The salinity ($C_s$) of groundwater in coastal aquifers ranges from almost zero for freshwater to $C_s = 36$ g/L for intruded seawater. Because freshwater has a lower density ($\\rho_f = 1000$ kg/m$^3$) than seawater ($\\rho_s = 1025$ kg/m$^3$), fresh groundwater tends to float on top of saline groundwater. The water density $\\rho$ at 20$^\\circ$ may be computed from the salinity using the empirical formula\n", "\n", "$$\n", "\\rho = \\rho_f + 0.7C_s\n", "$$(eq_rho_rhof4.0)\n", "\n", "where both $C_s$ and $\\rho$ are in kg/m$^3$. This approximation is reasonable for salt concentrations up to the salinity of seawater. \n", "
      In coastal aquifers, the freshwater is separated from the saltwater by a brackish transition zone. When the transition zone is relatively thin, that is, much thinner than the thickness of the freshwater lens, it can be approximated by an interface. An interface is a boundary between fluids that do not mix. Replacing the transition zone (in which there is mixing) by an interface greatly simplifies the mathematical treatment of variable-density flow problems and provides a means to develop analytical solutions for coastal aquifer flow. The location where the interface is at the top of the aquifer is called the tip of the interface, while the point where the interface is at the bottom of the aquifer is called the toe of the interface ({numref}`Figure %s `)." ] }, { "cell_type": "code", "execution_count": 2, "id": "3bcd020a", "metadata": { "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "application/papermill.record/image/png": 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", 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DW7ZskXWkmSqKvn37EhMTI5vmbaooRowYwfr162XT7k0V94QJE9iwYYNs2r2p4n7wwQeNVQxvVB6lpaXGGeX1ODs//PBD7r333lYpj/Xr11NRUSGZou/o6Mi///1vFi9ebHUudyLXnaKvVqv55ptvyMnJAepP89Zqtaxbt47z588D9ad5W87Cm1qJQ/NR5AUFBbKOtOYiD9PoifqiIcA8eqK+aAgwTx8PDg5mxowZso400/Tx9u3b88gjj8g60kzTx52cnHjyySdl7bQqlYpPP/3UmJlYXxmEhsrjRlP0jx49Wm/afUuWh4ODg9FsJRR5/bTIxZdjYmIIDQ3FycnJ6P02TYf+5ptv6NmzJ46OjvTo0YNPP/3U7PfPPfccISEhODs706VLF1566SVqamoa1YczZ84wfvx4XF1dad++PXPnzjWGq33xxRf4+/tTW1tr9ptJkyYxf/5847Zh1uPo6EiXLl1Yvny5WLxDIBA0mgYrco1OQWWNlorqGorLylm5ag35RSU8NPNh/PzN05UrqmuM/8oq1Xy3/gdSLl5m8gPT6BrS3cxGa9q2XF3Nxs1bOXTkGPePi6JPWD8rh1t2djazZs3i0UcfJTk5mb179/LAAw8YbXtfffUVy5Yt4/XXXyc5OZk33niDl156iejoaOM+3NzcWLlyJWfOnOHDDz/kq6++4j//+U+DL1p2djbDhw8nLCyMI0eOsGPHDnJycozRLw899BD5+flmcb1FRUXs3LnTWON6586dzJkzhyVLlnDmzBm++OILVq5cyeuvvy57XIONtlqjNbtulvIICKiTh2VbS3l0714njxqLtpbyCO9XJw/LthXVNez6dS+7ft3LkHuHM3zECKONVqrt7wlH+XHTFkLD+hE1YYLRRmvZ34rqGk6cTua7dT/QJaQ70x6azqVLl4iJiaHKol1FdQ0XU9P45tvV+Pp35OHZcyguLmbNmjWUV1Zatc24msPXK6Np69mOOfPmYWtrS3R0NMWlpVZt8wqL+fqbaHRKW+bMm0e7du2Ijo4mNy/fqq2pPGY+PNuYzp+WnmHVtqzyxlL09+/fz9Fjx6z2ayqPYcNHGG3m+/btk2xrkEff8H5MnDiRo0ePsnXrVsrV1bLy6BbSnRkzZhjlUVaplpWHn39H5s6da5RHcVm5rDzcvdpZFdbS6XSUl5cb/4H+rcf0szs5w7PBppXey76V/W5oNz8G6dKNdsApX+2jskZ6Zjkg0IdxbUqMdtnHfkikqEJ6MPfy92JuJx1Hjx41huYdO3aM/v37k5qaKrkKS6dOnXj77beZNWuW8bPXXnuNbdu2ceDAAcnjGBILjhw5Ivm9pWnl5Zdf5tChQ+zcudPYJiMjg44dO3Lu3DlCQkKYPHky7dq143//+x8AX375Jf/85z/JyMhAqVQSERHBuHHjeOGFF4z7WL16Nc8++6yx0JGlaeWTTz5BrVaT1T6MHWcyJPsKsHvpZLb9tIHc3FxKOg9kyynreiAGtj0zmd9/2cH58+ep7DKITaezZdtu/PNEzh3RO9c0XQexMVk+dvf7J8ZTdOkMe/bsQRPYj40p8suRrXjsfuxKstm8eTPV/r3YdFl+ibNP5o7Ez6ZCbz/16sLmDPk3mPdmRtDb045Vq1ZR7NyerTnSr/4Arz04hHs7exAdHc1VnTPbCq1XtTGwbOLdTOwdQHR0NKmqWraXykdN/HVsP2bfHcyaNWs4k13Ejgpvs+9rq9Uk/3sRUL9pJSHlCs7O+u8qKsoZGKIf+zt27OCX34+wraajbB9mDurOi5MGERcXx45f97G5Rr7O+aTwLrwxbRiJiYn8uGkLG2sCZduO7tWJ/zw8wmgzX1vZSbbt0G5+fPHIaKPNfK3KD41O2mwT3qkdq/5vPMnJyaxfv55RU6bj4OxiPGc5TK9Ra+Eu/4YtstGoOHI5bGxsmD1zNmvWrGHVqlXU6gLkGysUTJs2jZiYGH3GWG2XevcdFRVltt23b1/uu+8+QkNDGTNmDPfffz/Tpk3Dw8ODvLw80tPTeeyxx3j88ceNv9FoNGYhSjExMXzwwQdcuHDBWNGuTZs2DT7fo0ePsmfPHklb6sWLFwkJCWH27NksWrSITz/9FAcHB9asWcPMmTONs4yjR4+SkJBgNgPXarVUVVVRUVEhuTzW/PnziY6O5sLFC4CjbP/s/4ieWLNmDYfPpQDyg9sQPRETE8MPZ84B8tfBEM0C8O2hc0D9MdAGe+znu48BnvW2Ndjd39+4B2hXb1tD9MRb38UC9Q90Q/TEayt+uGYfDNETr331Xb3toC6d/40vV1+zrSGa5b3/rYHrXGt53pc7sbHX25Vrq+smPl17hZFTVsW2xGsvTBwREUFZtZbNe9Jl2yjQK9fw8HCqNLVs/Om0fNs/7OcGeayNPijb1sZG//JvkMf3n+4CpBW54R7RKPWhhs/9sJ/CBry4mF6j1sKp1+c1qF2DZ+QvvfIqDo6OoNMxa9Ys/DrUOR+UChsc7JR16cpZV3F0cqSyopIHHniAbsHdjG1tFAoc7WyN0RNnzp3HxdWFstIyxkdF0bdvH6u2hoQgAzqdjgMHDvDzzz+zceNGrl69yqFDh3B2dsbX15fVq1ebZZiBfnAEBQVx8OBBhg0bZqzZ0LZtW9auXct7770nG+5kOSMfN24czs7OvP3221Zt/fz8cHFxobKykvbt27Ny5UoGDhxI586dSUhIMBb5d3JyYvny5TzwwANW++jSpQs2NjZWM3LQO71WrIympLQMpa2SWm2tlTyc7GxRKBT6cK7Va8jOlpeHo60tNjYKvQN0/Q+cO39BVh6Gtjqdjk1btnL0WCLuHu4UFxUTERHB0GF160862CpR/nHz/rp3H3v27jO2DQ8PZ8zYMUaZmrZNOHqMzVu24tbGjXJVOd2CuzFlylSUSv339koltn/8febsWdb/sAEnZyeqKqvw9fVlxowZ2DvYW7VNS0/n29XfYaO0QavR4ubmxuzZs3Fx1T/k7JRK7P5om5OXx8pvV6HR6MPrbG2VzJ49G09PT6u2JaVlfBP9LWVl0vKws7HBzlavmCoqK1m15nuuXq2Tx9ixYxl89wCg/hl5z799aabIDbP4hJQrhHcJYNPWWBITpeVha2OD/R990Ol07N6zT7/kn4Q8LNsePHKMbbGxkvIw3PcGTpxO5scff5SUh2Xbi6lpfP/995LyMNz38ceT2f3TenbVdKCo1h5djXypXACFnX2rS9NvqCJvsI3cVqFDq65kUtQ4ugZ2wtnezvjPICAHBwdmzpwJ2hqqVGUMHzaEPr16mrV1tNO/BCiVSh588EFsdFoqy0oJvasHgwf2l2xrKRyFQsHQoUNZvnw5iYmJ2Nvbs3HjRtq3b4+/vz+XLl2iW7duZv+CgoIAfdxt586dWbZsGQMGDCA4OJgrV6409DIA0K9fP06fPk1gYKDVcQyRBU5OTjzwwAOsWbOG77//npCQEKMSN+zj3LlzVr/v1q2bcfYihaurK7NnzaS2Rk1NZYWkPIwK0sGBObPql4eNjcIoj+kPTatXHoa2CoWCyRMnYKvQoSouwtvTndEjR5i1VZqcw8gRw/H2dEdVXIStQsfUSRNwcbCXbDuwfz9C7+pBZVkpNjotsx6ahpuTg7GtQTED3NWjB8OHDaFKVQbaGuY+PBN3NxfJtp06dmRS1DhqKiuorVEz9+GZeHu6G9vambRt7+3NzGkPoqmqQFNVwcxpDxLg216ybds2bsx9WF4eBiUO4OzkxNyHzeURepf1QtiNRam0YeokeXnYm/RBoVAweuQIWXlYth08sL+sPEwVM0CfXj1l5WHZtmtgJ1l5GO57UxQKBTb2DvX+a21KvDE0Ompl9+7dskXytVqtcTUSgEOHDknWawb90960allKSopkvWZLDh06xBtvvMGRI0dIS0vjxx9/JC8vz7hKyiuvvMKbb77Jhx9+SEpKCidPnuSbb77h/fffB6Bbt26kpaWxdu1aLl68yEcffcTGjRsbfP4ATz31FIWFhcyaNYvDhw9z6dIlfv75Zx599FGzjLfZs2cTGxvLihUrmDNnjtk+Xn75Zb799lteeeUVTp8+TXJyMuvWrePFF1+s99hqtZpNmzYZt5tKHr/99pvx76KiIsl65gYSExPNFrIw/a0llsfdsWOHrBMrMzOTQ4cOGbe3bNkiuxhCQUEBu3fvNm5v2rRJtha4SqVi69atxu2tW7fKZhzeqDxMF364EVqzPATXplGKfM6cObLpypaLEDz//POy6cqWGYIvvviibPo4YJad1qZNG+Li4hg/fjwhISG8+OKLvPfee4wbNw7Qx+t+/fXXrFy5ktDQUIYPH87KlSuNM/LJkyfzzDPPsHjxYsLCwjhw4AAvvfRSYy4DHTp0ID4+Hq1Wy5gxY+jduzdPP/00bdu2NZtNjxw5Ek9PT86dO2e1JNWYMWPYunUru3btYuDAgdxzzz28//77kg5cA6aJJgsXLmTp0qVNJg9DcsnLL79c7+IUpokmL7/8cr3p46aJJi+++GK96eOmiSbPP/98vYshmCaaLF26lIULF8qmj5sm/ixevJjFixfLpo/fDHkYYrFvhNYsD0HDaHRCkJubm1Vqslz9aqnUZLk0b7l9GAZpYwpmtVZWrFhhlSEolSp+O+Rhmlwitw+5+tVS+5CrXy21D7n61VL7kKsnLrUPuXriUvuQq+/eWHmsWLGCJ598Erg+G/lXP2wi83Riq5THr4eO8duOLeyq6UCxrnU5MRvKTXd2mmZ2mg7WOXPmsGfPHtk0b9MBP2fOHJKSkmTTvC0H/NWrV+tNK77TeOuttyTTvJuDPCyVByCpNAyYKg9fX19JpWHAVHmEhYWxevVq2TRvU+URGRnJ6tWrZdPuTZXH5MmTWbt2rWzavakCmjlzJps2bZJNu2+MPAoLC43Huh5F/uTzrzBjXOuUx4qV0VSoyoQibwDXnaKvUqlYsWKF0dZWX5q3Wq1m9erVxhXF60vztiy+L5R4HZmZmbJp981BHpbp/NdK8zZNH69vEQIwTx8PCAgwmvmkME0f9/Dw4NFHH5VNuzdNH7e3t2fRokWyafcFBQV8+eWXxoWG6yuD0FB5NDRFv74Z+cJpkyT70NLlobS1RavRCEXeAK47Rd/JyckYoQHIDn7Q3yCmdZd9fHxk2yqVSrPvfX19r7eLrY76ynU2B3koFAqzhRI6dOhQbySB6b58fHxklYZlHz08PCTLmRowPXcXFxdjXXEpTK+pra1tvfWwXV1dsbWti6i4WfK4Ebw85WPuW7o8bGzkjy8w57oUuWGWlp2dzaRJk4zpylLeesOs4OTJk4wdO7be1cdBPyswFMWvb/Vx0M8Kli9fztatW9m6dasxHFGKlJQUXnvtNdatW8eePXtYvny5pIMH9LOCt956ixUrVnDo0CHjMaReXgoKCnj//ff55JNPSExMNB5DyluvUqn45JNPeP/99zlx4oTxGFIOHoP99K233uLEiRO8//77svWam5M8DPVj+vfvz5YtW+qVh2F19YiICONxpDBdXX3s2LGcPHlSdjV4gwmkXbt2TJo0iezsbNnV4A0mEDc3N6ZOnYpWq5V1uBlMUlqtlqlTpxp9RTdDHjfCr7/+0mrlUVsrHfEisKbRitzSbhoeHi67+rilnW7QoEGyq4+DuZ0uMjJSdvVxsHa6yK0GD9ZOF8P+pbz1lk6XQYMGyXrrLR034eHhsquPWzrB+vTpI7v6uKUjrU+fPrKrjwt5tGx53OjCwQEBAa1WHv2GjLiha3Mn0ShFLud9lyq+L+c5lyu+L+U5l1sMQcpzLrcYgpz3Xar4vpz3Xar4vpz3Xar4vlw0hFTxfbloCKni+0IeLV8e9cV7N4TIyMhWK4+2nvWXVBDU0Shnp4+PDwUFBbKrqxsEUlVVhbe3N5cvX5Z1pJneIIGBgZw7d07WkWZ6g4SEhJCcnCzruDFVWD179iQlJUXW+w51Cqt79+6kpqbKet+h7gYJCgoiLy8PR0dH2XUGDTeIn58f5eXlaDQa2XUfDTeIu7s7oF8ZRW61e8MNYmtri4uLC9nZ2UIeLVgeo0ePZuhQfSr99afo+7dKeZim6AtnZ/00akaem5tLVFSUbDSEq6sr8+bNQ6VScfnyZYYOHSobDWGYCarVas6dO0f37t1loyEMM0GtVmtcCFbO+26YebRp04bk5GS0Wm293veIiAi6d+/OuXPnUKvVsoMU9DOPoUOHcvnyZVQqFfPmzZN1joWEhBAVFUVGRgZFRUXMmTNH1uHl7+/P9OnTycnJMZbDlYuG8PLyYs6cORQVFZGRkSHk0cLl0bdvX8m2jaG1y0NwbRptIz9w4IBsurJOp2Pfvn3G7RMnTsimKwNm6bypqamyDjfDvgyoVCrj6jZSnD9/3qyPpr+1JDMzk9TUVMk+WVJQUGC2r3379sk6q1QqlVnZ3D179simK6vVavbu3Wvc3rt3r2yGm1arNatzLuTReuXRGFqzPATXplGKfPr06bLpypY22PrSlcHcBltf+jiY2/yWLVtGSEiIbPSE4ZUtJCSEZcuW1ZuubJlWXF+6smVacX3pypZp3vWlK1umedeXrmyZ5l1f+riQR8uQx5o1a6zOrbG0ZnkIGkajFLm7u7ukt17KkSa3+jhYO9LkHG5g7bixtbWVjZ6wdNzY2trKeuulHDdyq49LOW7kVh+XctzIrT4u5UiTW31cypEmt/q4kEfLkseNcD7lfKuVh0ZmcRqBNdeV2WkquHnz5rFv3z7ZNG9LwZ0+fVo2zdvyRsrNzZVNK7a8kQDZtGLLG8mgoOQcN6aKrVevXpLedwOmim348OF8++23smnepjfSxIkTWbt2rWyat+mNNHPmTLZs2SKb5i3k0XLlkZOTY0zEud4U/XFDW6c8vvx6BSVFBcLZ2QCuO0W/oKCAlStXGmcd9aV5G5SHYXHi+tK8jYtTpOtXMakvrdgyfby+tGLLdOWOHTvW67gxTVdu166drPcdzNOVXV1dWbBggazjxjRd2dbWlgULFsg60jIzM1m5cqVxQeb60u6FPOpoSfK40RT9D7/5nj/Pn9Eq5WFjo6S2VntLFPnAoPZ8s3AMg//1PWVVjVt4/XZyy1P0PT098fauW38wODhYtq2rq6uxjCxAr169ZNs6ODiYfR8WFiabVqxUKs28/n379pX1visUCsLCwsz6UN9rrWkfgoKC6k3dNj13b29v40oyUpiWqXVycqo35d3X19csnbm+ErdCHnW0NHncCN1CglutPGzt7WTbNZZvHruf58YPMG4npuUx/M31zVqJN4brUuSGp7chhKq+dGXQP70TEhIYOHBgvenKoH9679ixg9DQUAICAli9erVs9ERKSgoxMTEEBwcTHBxMTEyMbLpyZmYmq1evJiAggNDQUHbs2CGbjGGaVjxw4EASEhJk05VN04oNoVdy6cqG2a3B3lhRUSHr4DHMpioqKox2a7n0cSGPOlqiPG6EnTt3tlp51NzC2uQabS0Fqqpbtv/bTaMVuaU9bdSoUbLpymBuTxs/frysww3M7WlTp05lzpw5stETpva0GTNmMGPGDNn0cVP75pw5c5g6daqst97ScTN+/HhZb72lvXnUqFGy3npLe3NkZKRsurKlfTMyMlI2fVzIo2XLY//+/dwInh4erVYefQcNu6FrY+C1B4cwsIsvc4fexanX53Hq9XlMDu/Kqdfn4eaon/VPDu/KgRdnMrJnR7Y+M4Wjr8zmq0dG4dvWehH05kijFLlcmrect14qzVsuekIqrVguekIqrVgufVzK+y6XriyXVizlrZdLK5by1suleUt56+XSvKWiJ4Q8Wr485GayDeX+++9vtfJo5+vHzeCtrQkkXcnlh4QUhr+5nuFvrudqSblVOyc7JYtGhLIsZj9zv9yOi4Md785oGSW0G+Xs7NatGxcuXJB13JgKOigoiISEBFlHmqmg+/TpQ3x8vKwjzVTQgwYNIj4+Xjat2PTGGzp0KIcOHZL1vpveeEOHDuXEiROy3neoU4QDBw7k8uXLst53qFOEoaGhFBUVkZeXJ5vmbbjxunTRO7YuXbokm+ZtuPG8vb3x8PDg5MmTQh4tWB733HMPY8eOBa4/RT+0U/tWKY+bmaL/zWP3cza7kLe3HQGsnZ2Tw7vy+rShzPpsGycz9EEAQe3asOWZKcz8LJZTGTcncaux3BJn54ULFxg7dqxsNIRh5pGfn2+0wcpFQxhmgmVlZcTHxxMUFCQbDWGaPh4XF4ezs7Os990w83B2diYuLq7etGLDzCMoKIj4+HjKysrq9b5HREQYbYL5+fmygxT0Mw9Dic+MjAzmzJkjGw0REhLCtGnTOH/+POfPn2fatGmy0RD+/v7MmTOHjIwMYylaIY+WK49hw27cfNDa5XG7qNHWcjqzTmFfzi+lpFJNF2/5uvPNhUbbyE+fPl3vAqmnT582/m2ouSCHaRpxXl4ehYWFsm2vXLli/LuyspKrV6/Ktr169SqVlZWSv7WksLCQvLw8yT5ZYqiRYcD0XC1Rq9Vm3yclJcmmK2u1Wo4fP27cPn78uGyGm06nIykpyawPQh56Wps8GkNrlsftRIdEH5q+W9ekUYp8ypQp9a52bWqDrS9dGcxtsH/9619xdHSUjZ4wLXr/97//HT8/P9n0ccOrrp+fH3//+9/rXQzB8Krr6OjIX//613rTlS3TiutLV7ZM864vXdkyzbu+dGVLG+y1Vh8X8mj+8rgZKfqtWR43ixptLTY29as7O6UNvfzr3iAC27WhrZMDl/JLbkmfbiaNUuQ+Pj6y3npLR5qcgwesHWlubm6y0ROWjhtnZ2fZ9HFLx43hFVPKW2/puHFzc5NNV5Zy3MilK0s5buTSlaUcaXLpylKONLn0cSGPliWPGyE9PaPVyqNWW3tD18aUzGIVfTq2o4O7C+7ODpImwxqNln9MuJvQgHb07ODJaw8MISktr8ns442h0aYVqcEqFQ0B0t56qWgIkI6ekCt6LxU9IVf0XspbL+d9l/LWy3nfwdpbL+d9B2tvvUajkYyGAOvoCY1GIxkNIeTR8uUxe/bseu+3a/Hrr7+0WnmcSPj9hq6NKSt/O422Vsempyezf9kM/Nq6WLWprNGyIu4070y/lzX/N44qjZa/r7uxqKLbxXWn6BsGhmFGUV+at2FglJWVAfWneVumj9eXVmyZPl5fWrFlunJ9acWW6cqGGaqc48Y0XdnBwUE2GgLM05VtbGyYMWOGrCMtJSWFdevWUVurn5nUl3Yv5FFHS5LHjabov/XZCv72+LxWKQ8UCtDpGhW14uJgRy9/Lw5fkvcRSDE5vCvPRQ1kyGtrG/W7W80tT9H39/cnMDDQuD1o0CDZtl5eXvTp08e4PXz4cNm0YldXV4YMGWLcjoyMlE0rdnBwYMSIEcbtESNGyKYVK5VKIiMjjdtDhgyR9b4rFAqGDx9u3O7Tp0+9Re9Nzz0wMLBe77vpdXB1da03dTs4ONisj6a/tUTIo46WJo8boV+/fq1WHg4Ojlbfe7k4smrRWEID2pl97tvWhb+N7c/uZx/k47mRtHG0lz1Ga+S6FXlcXJxxJZn60pVB/5Q1hLS5urry7bffynrrU1JSiI2NJSAgAA8PD1avXi2bPp6Zmcn69etp37497du3Z/369bLpygUFBaxevRoPDw8CAgKIjY2VTVdWqVR8++23xpok8fHxsunKpmnFhpVU5JI8DLMepVJJz549KS0tlXXwGGY9paWl9OzZE6VSWW+9ZiEPPS1RHjfCzp93tlp5qKsqzb63U9rwwewRBHi6klWsH6+9/b14Z/q97Fg6lakDurHuUAoT/vMTpVXVksdorVyXIje1+c2cOVPWwQPmjrS5c+eyYMEC2egJUxvsggULePTRR2XTx01tfo888giPPPKIbPq4qc3v0UcfZcGCBbLpyqY2vwULFjB37lxZb72lzW/mzJmy3npLR9r06dNlvfWWjjRDe7noCSGPlisP0zDH68He1r7VyqNn+ECzNi9NGkQvfy+eWbOPPh29WblwDGufjCI0oB3vbDvCqHc28MHPx8gtNX8ANIRNiRebnVmlMTRakUs5buS89VKONLnoCSlHmlz6uJTjRi59XMpxI5euLOW4kUtXlnPcSHnr5dK8pbz1cmnectETQh4tWx6xsbGNvQXNGDd+XKuVh3/nugqdswf34IEBwWw/mcrr04by3zmRKG0U/GXNXqL+8xPfHTxLZfWduxBFo5yd4eHhJCYmyjpuTAdQr1692LFjh6wjzXQADRkyhNjYWNm0YtMBNGrUKLZt2yabVmw6gMaPH8/u3btl04pNB1BUVBQHDhyQTSs2vaHHjh3L6dOnZRchgLobOiIigtzcXNlFCMBcwQKyixCAuYL18fEhLi5OyKMFy6NXr1489NBDwPWn6Pfw82yV8jCk6GtChrJ85n3UaGqxVSrYdSqN6PgzxlT61swtWVgCwLdbKB26h8m2Ky/O51z8dgA8OgQSGDZM1pFWVV7Cmb16D7WLeztCBt+PwkbacVOjruTk7hgAbO0d6BU5FaWtdL1iraaG03s2oqnWz3xCR03DzsFJsq2uVkvK7z9TXqwfFHeNmISji3RKrk6nIzVpP0VZqQB0HzoOF/d2km0Bss4lcfXCSQC6DoykrU+AbNv8tAukndSHW3UKHUy7Tt1k25bkZnAxQR8FIOTRsuXh270fM4brHXzXo8g/2Pw7Xfx8WqU80jPSyDu+j78//wLODnXOy2qNlspqDZXVGr7cd5L1h6Vt+a2Bm6/I//Ua1IqFUQWCm0l1dTVvvPEGcP1LvflYB3e0GjQ6BWk+YXi6t0GhUOBsb4uTvS1Odvr/953N4FRm80/YuV4aqshtG7pD3YBZUNN6CrELBM0BXVUF8Mb1/z4kEl09oX8tmcRzZ8gqLqMysxgyi5u6O82aBityHN30/wQCwc3D1roudqNwbgtu3tdu1wLJKNeiboSKupO57jhygUAguFVUVatR19xZseA3glDkAoGg2VFYXNzUXWhRCEUuEAiaHQUlxU3dhRaFUOQCgaDZkV9c1NRdaFEIRS4QCJoVFVVVFJY2/8UcmhNCkQsEgmbFmUvyy8kJpBGxPQKBoNlQWq4iNUu6QqNAHjEjFwgEzQKdTkdi8mnZEhICecSMXCAQNAvOp6WSJ5yc14WYkQsEgiansKSEkxdab/GrW80NKXKdTseW95by9uTuLB/ZnqsXTt2sfhn56e0lrH1p/k3fr0AgaB5UVlURn3QUaFD9PoEEN6TILxz+laSd63j49dUsjTmJT1CPm9WvJuWDWQM4GPNFU3dDIGj11Ghq2J90hGpNDQ2rwyqQ4oZs5EVZqbh5tqdj74GS32trqlHa3VmLoJpyp5+/QFAfGq2W/YlHKVWpxFz8BrluRf7T20s4vnMdAMtHtqdt+464+3bEJ7AHSjs7jv/8Az6B3VnwwU/kpZ7j58+Xc+XE79g7OdO1/wjGPPUqzm315TfP7NvCvm//TWFmKnaOTvh2683Mf0Wb1WY+sO5Tfv/hM7SaGnpFTmHsU/9CaWvHoR+/5ljsKp743z4Azu7fxrqXH2Hckje5e8qjAKx+dga+waGMevxFCjNT+fmzl8lIPkp1ZQXenUO4b+E/6NJfvyr4ymemUpKTzs5PX2bnpy8D8M9fcwBIP5XA7q9eI+tcEs5tPekxbBz3LVxm7OcHswbQb/zDFGalcnb/NnoMHceU5/97vZdYIGi11Gg07E88IlLxbxLXbVoZ+9RrjHjkOdp4d2BpzEke/2wHAMd/XoeN0pZHP9rChL++S1lBDiufmYpvt14s+vxnZr+1FlVRHj8sfxyAsoIcNrz2J8LGzuKplb8x//0f6XlvlNmxUpPiKcxKZf77PzLluY84vnMtSTv0C6UGhg0hN/UcFSX64vKpx3/Hua0XV47rV3ep1WpIP51AYN8hAFRXldNt0CjmvvsD//flL3QdMILvl82jJCcDgBnLV9DGuwMjHnmOpTEnWRqjX8Ek59IZVj83g573judPX+9h2ktfknbyMNs/+odZXw+s/xSfwB4s+nwXEXP/er2XVyBotairq4k7ephCocRvGtc9I3d0bYODkwsKGyWunj7Gzz39gxj9fy8bt/d88zZ+waHct3CZ8bPJz37Af2aEU5B+kerKcmq1GnreG4W7b0cA2ne5y+JY7oxf8iY2SiXtOgUTPGg0lxN/o/+EufgE9cS5jSepx3/nrogJXDl+gMEP/YmDG/Q27syziWiq1XQKHQSAb9de+HbtZdz3yMde4Oz+7Zw7sJO7pz6GUxsPFDZKHJxczM7rwLpP6X3fA9wz7f8A8Arowrg/v87KZ6YQ9czb2Nrrl2kJChvGkBlPXu9lFQhaNaqKCn5LTKCiqkqYU24iNz2O3C+kr9l2dsoJLifF88b4IKu2hVmpdB0wgqB+9/LZwhF0GxBJlwHDuWv4RJzc3I3tfAK7Y2OyALCrlw+5l5IBUCgUdO5zD6lJ8XTpdy+5qeeYP2k+B9Z/Rt6VFFKPH8AvONRo/qiuLGfft++RcnAXZflXqdVq0FRXUZJbfzZZdsoJCrMuc3L3BpNPdehqaynKTsO7s37RWL/ufaV3IBDc4eQWFvD7iUQ0Wi0NXGFS0EBuuiK3d3Q229bpauk++H5GLXrJqq2rpw82SiVz3/2B9NMJXDyyl8M//Y9fV7zJwk+24+HXGQAbW/NuKlCYDYTOfYdwLHYVV04cxLdrLxxd29K5zz1cOf47V5IO0DlsqLHtri9e5WLCHkb/6RU8/QOxc3Bi/SuPob1GEXudrpb+E+Yy6IHHrb5r61O3Srjl+QsEdzo6nY4L6Vc4kXJWv93E/WmN3PLMTt/gUJLjYnH37YiNUvpwCoWCTr3vplPvuxk+dykfzOrP2f3bGfzQnxp0jMCwIez45EWS47bS+Q9beOe+g7l0LI700wlmyjft5EH6jp1Jz3vHA/oZevHVdDCZSCvt7KitrTU7hl9wKHmp5/D0t36zEAgE0lTX1HA0+RSZuTlN3ZVWzS3P7Lx78qNUlhWx4V9/IjP5GEVZqVxM2Mumd56mVqslI/kov635gKxzSZTkZJD8WywVJQW06xTc4GMY7OQndm8gMEyvyAPDhnJ2/3Zq1FVG+ziAZ4cgzv4Wy9ULp7h68TQbXvsTOp250nZv35G0E79TmpdtdKIOnbmY9DNHif3wea5eOEVBxiXOxe9g20cv3ISrJBC0PvKLi9h1cD9Zt1CJn3p9HiN7drxl+28p3PIZuVs7Xx79aCu7v/wXq5+biaamGvf2AXQdGInCxgYHZzeunDjIwQ1foi5X4d4+gPv/9ArBg+5r8DEUCgWd+w7m7P7tdA69B9A7TB1d2+Dh1xkHl7pFo8c89Sqb3vkL//vzBJzbejJ05mLUFSqz/UU+8ixb3/87H80ZhLZGzT9/zaF9114s+M9Gfv3fm3zz9CR0Oh2eHQLpFTn55lwogaCVoK2tJfnSBc6mXkLB7TOldHB34ee/P8iDH2/hXPatq9ny2oNDcHO05+k1e2/ZMRqLQtdAr8Mre3JvdV8EgjuO6spy3ozqAsALsZfMcidMv+v5ty+xsXcAoLZaTfK/FwHwxNokfHz8bnOv5SksLSHh1AnKKspvy/FOvT6PJav38GtyeotT5LZKGzTa2nrbnHp9XsP2dUM9EQgEAkCj0XD60gXOp6XSmCq0o3t14omRfenk5UZVjZbkrEKWrN5DZY2G3v5ePH1/OD38PLFV2nA2u5B3th0hOatQcl8///1BADYsnghAwqWrvLH1MBsWTyTizfUUV6hp42jP/mUz2HX6CkvXxgGwMKI3I3p2ZM4X27FRKHhlyj3c3cWXdm5OZBeXs+7QOVb/rnfUPjmyL1P6dQPqlOwjX+8k4XIOPm2ceHbcQAYH+6HTwbEruby19TBZxfqHmuEBcDI9n4cH96BGW8uYf//Y+IstgVDkAoHgutHpdGTl5ZB49gxV1dV/fNaw37Zzc+KdGRG8v+Mov5xJw8XBjn6B7eGPB4Gzgx2bjl3kzawEAOYPu4vP5t3H+Pc3UlGtsdrfzE9jWftkFI/972cu5BZTo62ltLKa4ko1A4Las/t0Gv2D2hu3DQzs4suRy3o7vo0Cckor+NvaOIoq1IR18uafU+4hr6ySnaeu8M3+03TxbouLox0vbogHoKSyGkc7JSseG8Ox1BwWfLUTba2ORSNC+XzBKB747xbjzPuern6Uq2t4/JtdKLh5dddFGVuBQHBdlJar+O1YAr+fSDIq8cbg7eaEndKG3WfSyCou53xOMesOnaPyDyV9+NJVth6/zKW8Ei7llbD8p4M42ikZaKKETSksrwKguFJNgaqK0kp9n45ezmFgkC8AA4Pas/nYRRQKBV2826K0URDWyZuEy1cB0NTq+OSX45zKLCCzSEXs8ctsOnaRMaGBAFRWa6jSaKjWaClQVVGgqkKjrWVcnyBqdTpe3vg753OKuZRXwos/HsCvrQt3m/S3slrDyxt/52JuCRdyixt9zeQQM/JbzJUTB3Fya4tPUM+m7opAcFNQV1eTfPkCF9LTbmg1n3PZRfx+IZuNf55I/PksDlzIZtepK5RW6RWwp4sji0f15e4ufni5OqJUKHC0s8XX3bVRx0m4nMO0gfoouAFB7fl4dxL+Hq4MDGqPm6MdDrZKEq/U+QCn3x3CgwO64efuiqOtEjulDWev1m9zv6uDJ5083Tj88iyzzx1slXT0dAOyATifU3RNu/j1IBT5LeaHVxdRXphDz4iJjJi/VCh0QYtFq9VyPv0KyZcvUqvVAtxQhmatTsfj3+wivJM3Q4I7MHtwD5aMDuPhz7eTWaTitQeH4OniyNuxCWQVq6jW1LLmT+OwUzbOkJBw+SrPRw2ko6cbwT7uHE3NpaOnGwOC2uPmaM+ZrAKjqWZM7848O34A724/yvG0PMrVNTxyby/6dGxX7zFsFArOZBXw3Pr9Vt8V/fGmAEiahG4GTaLIz+7fxs+fL6f4ahp3T3kM32692fHJSzy/pfWtnl2r1eDQKZQLJw6T/NgIodAFLY7a2lpSszM5ffE86uswoVyLxLQ8EtPy+OzXE/z89we4766OfBufTP/A9ry2+RC/pejLZ/i2dcbTxVF2PzV/zHSVFm8J53OKKa5U83+RoZy7WkS5uoYjl3NYOLw3bZwcjPZxgH6B7UlKy2PdoXPGz/QzavPjKG3Mj3Emq5CxoYEUlldRrq65vgtxAzSJjXzrf/7OXRETeGZtIpGPPn/bj5+aFM/yke2pUpXcluM5BYbjt/BzPMf+mQsnDvPZYyNY/8pCci8n35bjCwTXg06n40p2JjsO/Max5NM3XYmHBrTj8eG96eXvhW9bF0b16oSniyOX8vT3ZVpBGRPDutDFuy2hAe1466F7jfZzKQrLq6is1jAsxB8vF0dcHeyM3x29nMOEvl1I+ENpn7tahJ1SyaAuvsbPANILSunl78WQbh3o7OXG4lFh9A7wMjtOVpGKkPYeBLZrg7uzA7Y2CmKPX6KoQs1/50TSr7MP/h6uDAhsz/NRA2nf5taX7bjtM/LqynLKi/LpOjASt3a+t/vwN5WslONUltRvOzPUcFEo7XDrOwbX3iNRnfqVCwfXixm6oFlSW1tLes5Vzlw6T3ll5S07Trm6hv6B7ZkzpCeuDvZkFat4d/sR9qdkAfDSjwd4Zco9/PDUBLJLyvnw52P8bdwA2f1pa3W8FXuYP0X25an7+nIsNZdH/vczAIcvX2V0785GpybA0dQchncP4JiJfXzd4RS6+3ny75kR6NCx/UQq6w6dY1hIXT2lmITzDAzyZd2TUbg42BnDD+d/tYO/junPB7NH4GJvR25pBQcvZaO6DTP025oQlJoUT/RfHzD7bP77P1J8Nd3KtJKwaSW/r/+UkrwsPHw7ce+cZ+h7/0MA7PzsnxSmX2TWG6sBOBjzBTs/fZlZb6wm5J7RAHw8bwj3PPQnBkw0D6gvvprGhw+br2jUd8wMpjz3EZpqNbu+WM6pPT+hLlfRoXtfxjz5Kv49wq3OpbK0iHemNGxpO88xT+EWNs7sM51Wg+rUL5QdXE9NsbCh36k0p4QgbW0tadmZJF++SEVV1bV/ILjlNMuEoI69BrI4+gAfzx/C9FdW0LH3QJzc3PVFq0xI/m0bOz55kbFP/Ysu/SJIObiLTe88TRtvP4LChxHYdwiJ275DV1uLwsaGKyaLSYTcMxpVYS4FGRcJ7DvYqg9tvP2Z/soK1r/yKIujD+Dg4masJb7ry1dJjotlynP/xb19APHrPmH1czNZsuogTm08zPaj+WOm7TXuaRwD6ytda4PSzcvqU4XS9o8Z+n1/zNDXiRm6oEmo0Wi4nJnOuSuXb4kNXHDrua2KXGlnj4uH3vvr1MbdbOEGU35f/ylhY2YwcPIjAAzu2JWMM0f5ff1nBIUPo3OfwVRXqsi+cBK/4D5cOXmIIdOfIPm3WAAuJ+7HxcNbsvCWjVKJUxt3AFw82uHo2hbQz36ObI5mynMfGuu8TFz6HpeO7OPYtu8YOvMpyb7auLhj20b6PBqCXqHfb2JyqVPok5/9AAfnxoVaCQQNpVJdxYX0NC6mX0HzRxSKoGXSLBOC8tLO07H33Wafdew9kLy0FEC/OpFv196kJh0g99IZFDYK+k+cR86lM6grVKQePyA5G6+PoqxUajU1dOxVd1ylrR3+PcLJ/+O4txKF0haXHkNx7jkCgJSDP1OSk17/jwSC66CotJTDp06wbf8+UlIvCSXeCmi2ceRWiQY6nVlKa+ewIVxJikdpa0dgnyE4ubnj3bk76acOcyXpAIMeXNSo4xkcBZbH1aGjUcUjroNadTmlRzajOrIJtDUMeuBxhs76M25e0hlsAkFjqa2tJSsvl/NpqRSUFKNQKMQqPa2IZqnIvTsFk3byEH3vn278LP30Edp1rjOVGOzkNkpbgvpHAPrFJE7t+UnWPm5AaWsPYExqAPDsEIjSzp60U4cIbR8AgFZTQ9a549xTz0Oh5LfVqI5tlT8ZhYK2Q2bh0KG71VeWCnzAxHlCgQtuKlVqNZezMriYfoWq6mrjVEgo8dZFs1TkQ2Y8yQ+vLsIvuA9B/e4l5fefSf4tlnn//sHYxmAnP/f7z8ZY9MCwIaz/52M4u3vhHWitOA20bR8ACgUpB3cRPOg+7BycsHdyYcDE+ez6/FWc3Dxo6+NP/LpPqFFXEj7+Yat9uLi3o//E+caFJ+Q4d+BnqvzvMlPktVUqSo9uEQpccEvQ6XTkFxdxMSONzNwcM6V9J6nvbx67n7PZhby97UirP3azVOQ9ho1n7FOvcWDdJ2z/eBkevp2Y/OyHBJqsveno2gbfbqGU5GYYlXbn0HvQ6WoJ7DOk3v238fZjxIJn+eWr19j0ztP0vX86U577iFGLXkSnq2Xjm/rFJjp078uct9eaLQRtwEapZMIz71zzXN6Zepfxb6HABbcSdXU1V7KzuJSRhqqyQphPrpOG1AlvboiFJW4x70y9C7vuw1HYOwkFLrDiRuPI//R9EtjacTkzg8y8nDtGcbd1cmDZxLvpF+hDWycH0gvL+GrfSbafSAX0tb8NdcMN3P/uBmNtcFN2/u0BNhw5TycvN+67qxO/nkln2YZ4wjp585f7+9E7wIvicjW/nEnjg58TqazRZ5fOGNSdeUN64tvWBZW6mqOpufz1+32NOva1aJZx5HcqpYd/RGnnIBS44Kbz+4ljaBTKO2727WBnw5msAv732ynKq2qI6B7Am9OGkVGo4mRGPm9tTSDQqw3nc4v5eHcSAEXlatn9PXJvL77Yc4Iv9pwEILi9O18sGMV/dyfx8sYDeLo48o+Jd/OPiXfz0o8H6OXvxQtRA3khZj9JaXm0dXKgf6A+DLmxx74ZCEV+i+k1fCJKWzuhwAXXhZOTE71790Zjp0QqVae6RoONvfKOUuIAuaWVrNx/xrj93cGzDAvpwJjenTmZkY9KXUONtpaqag0FqmtnqR6+dNVsf29MG0rs8cusPqCvh5RWUMabWxNYufB+/rX5IH5tXais0bDvbAYV1Rqyi8s5m61fuaixx74ZCEV+i4n6y9tN3QVBC8XORkFSUhIhISGk5hUz7ZNYqmpEzDfoy8YuHN6bsaGB+LRxxl5pg52t8rrLxJ7ONA9auKuDF5283JjQN6juQwUobWwI8HDjwIUssovL2fG3B4hPyWT/+Sx+OZPWZPIRivwOYuUzU/Ht2ouxi19r6q4IGkB7NztCQgIBCPR2p1t7d05l1B8ldacwf9hdzB3Sk7djEzifU0xFtYbnowY2ula5AcsHgI0CfjicYlyr05TsknI02loe+mQrA4N8GdLNj8X3hfHkyL7M/CyWsqrbX8ZWKHKBoAmxc3TmhdhLAKhrIS09jav5uVRVV+Nga8OEHm508mpDan4JF3KKAVDY2dPzb18a/74T6R/ow57kdLYevwzoc/Y6ebkZS+CCvm64jc31KfYzWYV0be9OemGZbBttrY6DF7M5eDGbz349wYGXZjKoix+7z6Td0LGvB6HITdi78l3Oxm/nT1/92tRduen89PYSrhw/wJXjBzj041cAPP1dAsU5Gez6fDk5l87g5OZO3/unM/KxF7BR6oeGTqfjwLpPOLIlGlVBLl4BXYiY+1fuGj6xKU+n1aCqrCDj6lXSrmZRVlGOAvNY7wf+u4Vu7d25kFNsfG1XKBQo/ohguVNJKyhjdK/OhHXyprSymnlD76Kdm5OZIs8sVtGnYzs6uLtQUa2hpFLd4IWhV8SdYs2fxrNs4t3EHDlPZbWGLt5tGdytA29uPczw7v4EeLpxJDWH0spqIkL8sVHA5fySGz729SAU+R3C2KdeoyD9Ij5BPYh85DlAn9n63QsP03fMTKa+8DH5aefZ8t7fsLV3ZMSCvwPw64o3OfvbNqL+8g5e/kFcOXGQH994Cmd3LwL71h+vL5CmrKKcjJyrpF/NprRcZaa8Le/1qhrtNc0pjw/vzdP397P6/J1tCXwb3zoXL/l8zwn8PVz5YsEoqmo0/JBwnl/PpOPqWLeYxMrfTvP6tGFsenoyTva2jQoBTMkp5pGvd7JkdDjfPj4WBZBeWMaOk6kAlFbVMOquTjw5si/2tkrSCkp5dt1vXMwtueFjXw/NLo487dRhfv36DTLPJWFrZ49/j3AefOkLnNzcr1kvvFarZcv7S0lN3I+qMI+2Pv4MmLzALMU+NSmeXV+8St6Vc9go7fAJ7M4Dyz4jNSmeTe88bdaXyc9+SNjYmbflvG8HljbyX/73BslxsTy1cr+xxkzCpm/Y/eW/eH7LBWrUlbw79S7mvRdDx151Ndw3//sZaqoqefDFz5vkPFoipeUqMnNySM/JorT85t7Qzva2ONnXzcmeGNmXe0P8mfflDnJKK27qsQS3lxYZR371wim+XTqN8HGzGPvn17GxUZKaFI+uVv9Kea164TpdLW28OzDt5a9wbutJ+ukEtr7/N9y82tNrxGRqtRrWvrSAflFzePDFL9Bqqsk8m4hCoaBX5GRyL5/lQsKvzPt3DAAOLm71dbfFk3/lPB3vGmBWKKxj77upriynNC8LVVEemuoqVv19utnvtJoa/Lr1vt3dbVHodDqKy0rJzM0hI+eqPtOSW5MiX1GtMTrrnhjZh3tD/Fnw9U5ySiu4p6sfwe3dWXWgdc7MBXqalSKPX/sxHbr3NQvZ8wnSr8LTkHrhSls7Ihc8a/yth19n0k8f4fTezfQaMRl1eRnq8lJCBo/G0z8QAO/OIcb29k4u2ChtZeuktzp0OrAs7Gh4QVMo0On0acoPv7mGNu3MV6FR3qFOtvqora0lv7iIrLxcMnKuUlWtNkvUudWR3k+M7MOUft1Y8PVOsv94jTc44wStm2alyK9ePC3rRGtovfAjm6M5tm0NJTkZ1Kgr0Wpq8O3aCwCnNh6EjZnJ6mdn0rV/BEH9I+g1YvIdk6ijtLWjtrYuzrVdYAjJcbHodDrjrDz9dAL2zq60aeeHo2tblHYOlORkCnu4DDUaDTkF+WTl5ZKVl4NGqzVX3rcpUUdKiQN8Nv8+3t12xMwJKGh9NCtFbvfHkmtSNKRe+Om9m9j56cvc/8QrBNw1AAdnV+LXfUJm8jFj+8nPfcjdDyzkQsKvnN6ziT0r3mLuu+sJuEt+UdfWgrtvRzKTj1F8NQ17JxcGTnqEQxu+ZPtH/+DuqY+Sn36BvSvfZfC0P6GwscHB2ZUh059g56cvo9PV0qn3INQVZXpl7+RC2JgZTX1KTUJFVSXZeXlk5uWQV1RofBDebuVtQE6JA3T2cuNKQelt7Y/g9tOsFHn7Lndx+dhvZuYRAw2pF37lxEE69hpgXCIO9DN5S/yCQ/ELDuXeh5/mf4vHc/KXHwm4awBKOzujPb41MmT6k/z09p/55JEINOpKnv4ugYff/I5dny/n88dX4+TmTvi4WUTMfcb4m8hHn8fFox37v/uIouwrOLq2wS+4D/c+/HQ9R2pd6HQ6CkuKyc7PIysvx+isNIs2aaIU+UUjQpl1Tw+e+vZXqjVavFz1k6HSymoc/sh01NbeWen7dyLNSpEPe3gJny0cQewHzzFg4jyUdvZcToyn14iJOLf1uma9cE//IE7s+oELCXvw8O3E8V0/kHUuCXffTgAUZV/h6NZVdB8yBjcvXwrSL1KQcYk+o/XOPHffjhRlp3H1winaePth7+SKbSuK1/Xq2JXHPt5m9pm7byce/2yn7G8UCgWDHnicQQ88fqu716yorqkmp6CA7PxcsvPzqNForApTNQf1+Mi9vXBztOf7J8abfT7rs23Y2iiMSUSC1k2zUuReHbsy5511/Pr1G3z15DjsHBzx79mP0PumAlyzXviAifPJuXCamFcXoVAo6D1yKgMmLeDCYX2Cj52DEwVpF1j/83oqS4tw9WzPwCmPMmCiPsSn570TSP5tG9F/fYAqVUmrCz8UyGOIMrlakE92Xi6FpXqbclOaTBrC4H+tlf3uoYHBQpHfITS7OHKB4Hahrq4mpzCfq/n5XC3Io7qm5paFCDYFL0QN5MDFbPadzWjqrgiukxYZRy4Q3Epqa2spKCkmp7CAq/m5FJfp62jczhDB28mbsQlN3QXBbUIocoEku796jX7j5xjj7VsiOp0OVUUFOYX55BTkk1tYgLa21trW3QxNJgJBYxCKXCBJ4vbvUNrZS0YQNWfU1dXkFhboZ90FeVSp9SuzNIcIE4HgViEUuUAS/+7hZJ1NbOpuXBONRkNecZFeeRfkU1quAmiWESYCwa1CKHKBJB16hHN449dmWZ/NAW1tLYUlxUbFXVRagg4JxS1m3YI7CKHIBZIE9OzHvugiirKuNKmdvLa2lsLSEvKKCsktLKCguIhai0xKEIpbcGcjFLlAkg7dwwDIPHsUG6UNK5ZMYtHnP9/ygmK1tbUUlZUaFXd+cRG1tbVWYYFCcQsEdQhFLjDjxK4Yrpz4nQnPvItHh0Ayko9RWVpMeXE+9k4uN/14hhl3flEhuUWFRsVtiVDbAoE8QpELzHDzas+xbWtw9fQhoGc/ss4mUZqbRUDP/jdFkWu1WgpKiskvLiKvqJCC4mJqddYzboFA0HCEIheYEdTvXkY+9gK/fv0GYeNmkZVyAntHJwaZrLLUGKprav5Q3IXkFRZSVFaqd6Ci0Feu/AOhxAWC60cocoEVw2YtITvlBKf3/EStppoqVTVd+t3boN9WqqvILy4iv6iIvKKCukqBVuGAQnULBDcLocgFVigUCiY/+yFfPzmW/LTzxgU8LNHpdJSWqygoLiK/uJi8ogIqDQk4IqpEILhtCEUukMTB2ZWZ/4rmk0eG4erli9LOHo1WS2FJsdHGXVBchEarr98uFLdA0HQ0XJFXlUFN1S3siqC54eXehrnLv+JsZga7f9lk9b0rmK/52XzyhgSCO4oGK3LFkbVQq7mVfRE0Q7oAXXwBspq4JwKBQI6Gz8hrNUydOhVvb2+0Wi2//PILaWlpDBs2jBMnTlBdXc2ECRNwd3c3+5lOp2P//v0kJyczePBgLl26RGFhIVFRUfj4WCeXHDt2jCNHjhAeHk5RURFpaWmMHj2azp07W7U9e/YscXFx9OzZE4Dk5GQiIiLo0aOHVdsrV66wa9cuOnXqhIeHB4mJiQwYMIB+/fpZtc3NzSU2NhZPT0+6dOnC77//Ts+ePRk2bJhVunpxcTFbt27F3t6ePn36sH//fjp16sR9992HUqk0a1tRUcHWrVuprq5m0KBB7N+/H09PT8aNG4e9vfmq9NXV1Wzfvp3CwkKGDRvGoUOHsLe3Z8KECTg7O5u1FfIQ8mit8nBr25Y+gyKwtTNXVZoaDYkH9qEqK6FHn/6cP3McW1s7+g8bgYOjk1nbWm0tJxJ+pyAnix5hA7hy/iwaTQ39h0Xi4upmIQ84e/womakXCQkNJycjDVVZCf2GjKCtp6fVtbh07gyXkk8R1P0uykpKKMjJou+gYbTz9bNqm3nlMsmJCfgHdtFvp16iZ/hA/DsHWbXNv5rN8UP7rT6Xo1E2cm9vb3x8fIiJiSE9PZ0ZM2YQEhLCwIEDiY6OZvv27cyfPx8vLy9AP0hjY2NJTk5m0qRJhIeHo1arWbNmDdu3b2fu3Ln4+/sb9x8XF8eRI0eIjIwkIiICrVZLTEwMu3fvZvr06YSEhBjbJiYmEhcXR//+/YmKigIgNjaWuLg43N3dCQ+vc86lpKSwe/duQkJCmDZtGkqlEnd3d/bs2YObmxsRERHGtpmZmWzfvh1fX19mz56Ng4MD3t7ebN68GWdnZ6KiooyDtaCggO3bt+Ps7Mz8+fNxdXXF39+f9evXEx8fbzwWgEql4scff0Sr1fLoo4/i5eVF165dWbVqFb/88ovxWIDxGhUXFzN//nz8/f3p1asX0dHR7Nixw3gswHiNhDyEPFqrPC6eSJCUR1WFikcWLMDf35+CIfprnHzkd0l5FOVdZebMmYSEhKBSRRAdHc2pQ/sl5ZGZetFKHicO/SYpj0vJp6zkcTLhgKQ8khMTrORx9GgCwR39rOSxJ+GA5MNZDpsGtzS5KOfPnzfrqKurK/Pnz8fBwYHo6GgKCgqMF+Xo0aPGiwLg4ODA7Nmz8fHxYdWqVWRmZhovyp49e4wXBUCpVDJt2jSCg4NZv349KSkpxouyefNm40VRKBQoFAqioqLo378/mzdvJjEx0XhR1q9fT3BwsNnAiYiIIDIykj179hAXFwfoB+mqVavw8fExGzjh4eFMmjSJo0ePEhsbi06no6CggOjoaBwcHMwGTkhICNOnT+f8+fPExMSg1WpRqVRER0ejVqvNBo6/vz9z584lNzeXNWvWoFarjQMnNzfXbOB4eXkxf/581Go10dHRqFQqIQ8hDyGPViyP++67j4bS4KXeli9fjo+PDwUFBVZPGwMGgVRVVeHt7c3ly5fNLooppgIJDAzk3LlzZhfFFFOBhISEkJycbHZRTDEVSM+ePUlJSbEapKYYBNK9e3dSU1OtBqkpBoEEBQWRl5eHo6Oj2SA1xSAQPz8/ysvL0Wg0ZoPUFMMNYnjtLi4utnr6GzDcILa2tri4uJCdnS3kIeQh5PEHrUkeubm5+PlZm2ikaNSMPDc3l6ioKMmLAvon3bx581CpVFy+fJmhQ4dKXhSoe9Kp1WrOnTtH9+7dJS8K1D3ptFotycnJtGnTRvKiAMYnXZs2bUhOTkar1coOUtDPPLp37865c+dQq9WygxT0M4+hQ4dy+fJlVCoV8+bNkxykoJ95REVFkZGRQVFREXPmzJEcpKCfeUyfPp2cnBxycnKYPn265CAF/cxjzpw5FBUVkZGRIeQh5CHkYUJrl4ccjVLkAAcOHEClUkl+p9Pp2Ldvn3H7xIkTFBQUyO7r0KFDxr9TU1ONry1SnDhxwvi3SqXi/Pnzsm3Pnz9v1kfT31qSmZlJamqqZJ8sKSgoMNvXvn37ZOOlVSoVBw4cMG7v2bMH7R8x15ao1Wr27t1r3N67dy/qPxJrLNFqtezZs8e4LeQh5GHYlwEhj9YrDzkapcinT59uZoMyxdLGtHTpUjMblCWmNqbnn3/eygZliqmNadmyZYSEhJjZoEwxvLKFhISwbNkyKxuUKaY2v+eff97KJmiKqc1v6dKlVjZBU0xtfosXL2bWrFlmNkFTTF/ZFi5cyMKFC81sgqaYvrLNmjWLxYsXC3kIeQh53CHyqI9GKXJ3d3crhwJYX5Tw8HBJh4LURYmIiJB1KFhelKioKGxtbSUdCqYXxWBjsrW1lXQogLTjRsrBA0g6bqQcPGA+SA02PykHD5gPUoPNT8rBA9KOZikHj5CHkIeQR+uQx9mzZ2kojXJ2Llq0CD8/PzPBzZs3j3379ll5ew1YCu706dNW3l4DloLLzc218vYasBQcIOl9B2vBGQQg57gxFZwhzMzS+27AVHDDhw/n22+/tfK+GzAV3MSJE1m7dq2V992A6Y00c+ZMtmzZYuV9NyDkIeQh5NE65fHPf/6ThnBditxwcVauXGl8ysl5e00vTn5+PoCstxfqLk56ejqArLcX6i6O4cnVo0cPWUeB6cUB6NixY72OG8NgBWjXrp2s9x3qBivoHSgLFiyQddykpKTw/fffA2Bra8uCP+JgpcjMzGTlypVoNPqM2lmzZsk6boQ86hDy0CPkUUdLlMcPP/xgVPrXotHOTgOenp54e3sbt4ODg2Xburq6EhRUl73Uq1cv2bYODg5m34eFhcku/qtUKunbt69xu2/fvrLeXoVCQVhYmFkf5AapZR+DgoJkBymYn7u3tzeeEhlgBkyD/J2cnPD19ZVt6+vri5NTXZZafQkCQh51CHnoEfKooyXKQ+6hJMV1KXLD09sQsuPm5ibpUDAQFxdHQkICAwcOpF27drIOBdA/vXfs2EFoaCgBAQGsXr1a1juckpJCTEwMwcHBBAcHExMTI+lQAP3Te/Xq1QQEBBAaGsqOHTtkHQqGV7F27doxcOBAEhISJB08UPf0dnNzM4ZeSTl4oO7pbbA3VlRUSDp4oO7pXVFRYbTLSTl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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution_interfaceflow = diagrams.solution_interfaceflow()\n", "glue(\"fig_solution_interfaceflow\", solution_interfaceflow, display=False)" ] }, { "cell_type": "markdown", "id": "9f430ef3", "metadata": {}, "source": [ "```{glue:figure} fig_solution_interfaceflow\n", "---\n", "name: fig_steady_interface4.0\n", "---\n", "Steady interface in a coastal aquifer, where $h$ is the head in the freshwater zone above sea level and $z_i$ is the elevation of the interface with respect to sea level.\n", "```" ] }, { "cell_type": "markdown", "id": "eca9239d", "metadata": {}, "source": [ "      Steady interface flow means that the interface has reached a steady-state position, the saltwater is at rest, and only the freshwater is flowing. When the saltwater is at rest and an observation well is screened in the saltwater, the saltwater rises to exactly sea level; this is called the saltwater head. As the saltwater is not flowing, the saltwater head in the saltwater is the same everywhere. After all, Darcy’s law states that water moves from a high head to a low head. When the Dupuit approximation is adopted for flow in the freshwater zone, the depth of the interface may be computed from the head in the freshwater as explained in the following.\n", "
      Consider steady interface flow as depicted in {numref}`Figure %s `. The elevation of the interface $z_i$ is measured with respect to sea level (i.e., $z_i$ is negative). An observation well has its opening at the interface and is filled with freshwater. The freshwater rises to elevation $h$ above sea level so that the pressure $p_f$ at the bottom of the observation well is\n", "\n", "$$\n", "p_f=\\rho_f g(h - z_i)\n", "$$(eq_pf4.0)\n", "\n", "where $\\rho_f$ is the density of freshwater. Just to the right of the freshwater observation well is a second observation well, which also has its opening at the interface but is filled with saltwater. The saltwater in the second observation well rises up to sea level ($z = 0$) ({numref}`Figure %s `). The pressure $p_s$ at the bottom of the second observation well is\n", "\n", "$$\n", "p_s=\\rho_s g (0 - z_i)\n", "$$(eq_ps4.0)\n", "\n", "The pressures at the bottoms of both observation wells must be equal ($p_f=p_s$ since they are at the same elevation and the interface is not moving). Setting Eq. ({eq}`eq_pf4.0`) and Eq. ({eq}`eq_ps4.0`) equal and rearrangement of terms leads to an expression for the elevation of the interface $z_i$ as a function of the head $h$ above sea level in the freshwater\n", "\n", "$$\n", "z_i=-\\alpha h\n", "$$(eq_GH4.0)\n", "\n", "where\n", "\n", "$$\n", "\\alpha = \\frac{\\rho_f}{\\rho_s - \\rho_f}\n", "$$(eq_alpha4.0)\n", "\n", "Relation ({eq}`eq_GH4.0`) is known as the Ghyben-Herzberg equation (e.g., {cite:alp}`post2018ghijben`). \n", "Using the density values for freshwater and seawater provided above gives $\\alpha=40$. In words: If the head in the freshwater at a location is 1 m above sea level, the steady interface at that location is 40 m below sea level.\n", "
      Note that the Ghyben–Herzberg relation holds for the case that the freshwater flow is steady and the saltwater is at rest. The head $h$ in Eq. ({eq}`eq_GH4.0`) is the head in the freshwater at the interface. When the Dupuit approximation is adopted (i.e., the resistance to flow in the vertical direction is neglected and the vertical head distribution is approximated as hydrostatic), the elevation of the interface may be computed from the head at any elevation in the freshwater with the Ghyben–Herzberg equation ({eq}`eq_GH4.0`)." ] }, { "cell_type": "code", "execution_count": null, "id": "c7b30b4d-d198-4262-a9e2-74637f380841", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.13.3" } }, "nbformat": 4, "nbformat_minor": 5 }