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{
"cells": [
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"from pretty_plots import setdefaults\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.integrate import odeint"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"setdefaults()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Particle in Vortex\n",
"\n",
"Create ODE describing radius, and angle (R, $\\theta$) of a particle in a viscous vortex. Assuming the flow field of the fluid is\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"def dy(y,t):\n",
" c=0.01; # 0.01 kg/s\n",
" m=0.001; # 0.001 kg = 1 g\n",
" w=10; # fluid rotating at 10 rad/s\n",
" return [y[1],y[0]*y[3]**2,y[3],c/m*w-c/m*y[3]-2*y[1]*y[3]/y[0]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot solution for 1-g particle in vortex starting at 5, 10, 15, and 20 m from origin at rest."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f2f9d4f89b0>"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for R0 in np.arange(5,25,5):\n",
" y0=[R0,0,0,0]\n",
" t=np.linspace(0,1)\n",
" sol = odeint(dy, y0, t)\n",
" R=sol[:,0]\n",
" A=sol[:,2]\n",
" x=R*np.cos(A)\n",
" y=R*np.sin(A)\n",
" plt.plot(x,y,label='R(0)=%i m'%R0)\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f2f9ef0dba8>]"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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QAncVzcKLD9yAFfOmafMPtnThzsfewGOvHMUgO+QzBIOBiKLKzLQJ+O0/L8d/3pGP5ATlEDbgkvjxi4ewpvIfaDp70eQSRj8GAxFFHZtN4AvXzcG2+1ZiWU6aNn/viQ7c+rPX8Zs3j7FDvnFgMBBR1MqdPglVGz6Cfy27Egl2pU+N3gE3/uOFRvzTr/fgdEePySWMTgwGIopqDrsNX71pHp7/6gpcmTVZm7/76DmUPbwLf3J+yA75RonBQEQxIX/mFLzwtRW458Y8rUO+rt5BfLPqXWz4rRPnLvaZW8AowmAgopiR5LDj26sX4I8bPoLLp03U5u/YfwZlD+3Ci40tJpYuejAYiCjmFM9Jx7b7VmLdtTnavPOX+rHht05884/v4kIvO+QbCYOBiGJSSpID379zMX7zz9cgKzVJm/+nug+x6qFdeOPoORNLZ20MBiKKaTfOn44d99+IO5fO1Oad7uzF5375Nr73QiN6+tmlhj8GAxHFvCkTE/DwZ5bh8c8VYurEBG3+U28ew20/ex17T7SbWDrrYTAQUdy4dfEMvPjADbhlQaY2r+ncJdz1xJv4yYuH0D/ILjUABgMRxZnMycn45ReKsfmuqzDJq0O+R185ijsfewPvs0sNBgMRxR8hBD599WxUf30lls9N1+bvb76Af/rVHrRd6jexdOZjMBBR3JqdPhG//8q1+LePL0KSQzkcnurowX2/3wtXHPe1xGAgorhmswl86fq5ePxzhdq83UfP4X9rDplYKnMxGIiIANyyMAv33TxPm37slfexI05bSjMYiIhUXy+ZjxvmT9emv/nHd+NyfAcGAxGRym4T+NlnlmLW1AkAgK6+QdzztBOX+gZNLllkMRiIiLykTUzEL9YVaZXRh89cxKY/vRdXXXczGIiI/BRcNgXfv7NAm/7be8349RvHzCtQhDEYiIgCWFM8G3cvH+qd9QfbDmDPB20mlihyGAxEREH8x+2LsHS2Mqa0yy1x7zN1OHOh1+RShR+DgYgoiCSHHU+sK8S0lEQAwLmLfbj3mbqY71OJwUBENIIZUybg559dpg0X6jzejh9sO2BuocKMwUBEFMJ18zKwadUCbfqpN4/h+b2nTCxReDEYiIh0WH9DLlYXZGvT3/7zezjQfMHEEoUPg4GISAchBH68ZgnypqcAAHoH3LjnaSc6e2Jv/GgGAxGRTpOSHKj8fBFSEu0AgOPnu/GNZ/fBHWM9sTIYiIhGYV7mZPx4zRJt+qWDrXj0laMmlsh4DAYiolG6dfEMrL8hV5t+aOdhvHqo1cQSGYvBQEQ0BhvLrsS1ucrob1ICX//DPpxs6za5VMZgMBARjYHDbsOjdxciOzUZANDZM4B7nnaid8BlcsnGj8FARDRGGZOS8Pi6QiTYldZvjacv4LvPN0R9T6wMBiKicSjMmYp/vz1fm97q/BC/23PCxBKNH4OBiGic1i3PwV2Fs7Tp773QiL0n2k0s0fgwGIiIxkkIgf/5ZAEWzUgFAAy4lJ5Yz13sM7lkY8NgICIyQHKCHZWfL8KUCQkAgObOXnztd3sx6Iq+nlgZDEREBpmdPhEPf2YphNoT6z+azuPHOw6ZW6gx0B0MQohCIUSVEKJdfVUJIQpHszP1O3KE1/rR/xOIiKzjpiszcf8t87XpyteaUF3fbGKJRk9XMAghSgA4AZQDaFNf5QCcQojyUezPEyQdQV7xMW4eEcW0r908DzcvyNSmv1X1Lo62XjSxRKMTMhiEEGkAatTJUillnpQyD0CpOq9KXUePXABNUsqpQV5bR/9PICKyFptN4KFPL0VO+kQAwKV+Fzb8thYX+wZNLpk+eq4YPLd3Nkspd3pmqp+3+K0TlFd4NI2qhEREUWjKxAT8Yl0RkhOUw+z7Zy9h49Z3o6Lxm55g8FwZPBtgWaXfOiMpVt/rdKxLRBT1Fs1MxQ8/tVib3lbfgidft/65sZ5gyAUAKeWwA7rXvFz/ZcG2A2iV0O1qhbNTCLFRV2mJiKLMJ5fNwhc+crk2/aPqg3jz/XMmlig03cFgwDp56vtGKBXXTeqrEECFEMKpYxtERFHnO7ctQtHlUwEAbgl87Xd70dzZY3KpgtP7uGrHGJd58zyRtFVKKaSURWoldh6U20uFQoiKYF8WQqwXQtQKIWrPnj2rc5dEROZLdNjw+OcKkTEpCQBw/lI//uXpOvQNWrMnVhGqIkQIIQFASinGslxXIYTIBfC+3u0UFxfL2trase6OiMgUbzWdx+d++TZc6lCg667NwffvXBziW8YQQjillMWh19R3xaCnpmRctSlSSs9tJU9IEBHFnGtzp+HB1Qu06affOoGtzg9NLFFguoMhUCtnr3l6byfpwUZuRBSzvnT9XHz8qhna9Heeq8ehli4TSzScnmCoUt/XBljmmVcZYJlGCJGmPoEUsB9atY1DLoAOKaWRIUNEZClCCFTcdRWuyJwEAOgbdGPLLms9whoyGKSUnkZsG72vGtTPG/3W8SwrUbvR8GyjA8BOAGlCiEq/ddMAvKRObhrLP4KIKJqkJDlQUX6VNv1iY4ulhgTV+1TSBvXdKYSoEULUQOk7yXsZAJ8uNGr86gvWQLkttV5tw1CjPqLaDuWJpa3+AUNEFKuWzU7D3IwUAMDFvkG8dKDV5BIN0RUM6gG7FMpjpSXqqw5K30m6DuZSyg718dRNAGqhtITOhXIlsUZKuWb0xSciik5CCHxi6Uxt+vl9p0wsjS+H3hXVvpGKdKzXASDoI6dSys0ANuvdLxFRrPrE0svw8M4jAIBXD7Wio7sfaRMTTS4VB+ohIjLN3IwULJk1BYAyHGh1Q4vJJVIwGIiITHTH0su0z8/vtcbtJAYDEZGJbl8yAzb15vueY2043WF+H0oMBiIiE2VOTsaKeRkAACmBv7572uQSMRiIiEx3xxLvp5MYDEREcW9VQTaSHMrh+EDzBRw+Y24XGQwGIiKTTU5OQMnCLG36Lya3aWAwEBFZwB1ejd3+su+0qWNDMxiIiCzgo1dOR2qy0ub4w/Ye1J0I2OdoRDAYiIgsIMlhx62Lh7rjfn6veZXQDAYiIov4hFdjt7/XN2PA5TalHAwGIiKLWD43HdmpyQCAtkv92H3knCnlYDAQEVmEzSZ8KqHN6nGVwUBEZCHeXXHvaDyD7v7BiJeBwUBEZCGLZqRqw372DLhQs/9MxMvAYCAispBhA/iY0OMqg4GIyGK8n07adeQczl/si+j+GQxERBYzO30iCnPSAAAut8S2+uaI7p/BQERkQXcuG7pq+EuEe1xlMBARWdBti2fAro7gU3u8HSfbuiO2bwYDEZEFTZuUhJVXZGjTL0RwAB8GAxGRRd3pNx50pHpcZTAQEVlU6aIsTEiwAwCOtF7EgebIDODDYCAisqiUJAdKF0V+AB8GAxGRhd25bKix2wvvnobbHf7bSQwGIiILW3nFdEydmAAAaO7sxZ5jbWHfJ4OBiMjCEuw23HbV0AA+1RFo7MZgICKyuOVzp2mfz0agewwGAxGRxdmE0D5H4olVBgMRkcV55QKDgYiIAK9cgASfSiIiinu8YiAiIj8i9CoGYjAQEUWRSPSWxGAgIrI43koiIiIfvjeSWPlMRBT3BNsxEBGRN9/HVcOPwUBEZHEisg8lMRiIiKJJJEZxYzAQEVmcz1NJEdgfg4GIyOIEWPlMRETeeMVARETefJ5KYh0DERGJCD+WxGAgIiIfDAYiIovzvZUU/v0xGIiILM73cVXWMRARxT0+rkpERD7YJQYREflgHQMREfk4dKZL+5ySZA/7/hgMREQW98K7p7XPNy3IDPv+GAxERBZ2sq0be090AAAcNoFbC2aEfZ8MBiIiC/vre0NXCyuvyMDUlMSw75PBQERkYS/sGwqG25fMjMg+GQxERBZ15EwXDrYoFc9JDhs+lp8dkf0yGIiILMq70vmWhZmYlOSIyH4ZDEREFiSlxF+9guGOCN1GAhgMRESWVH+qE8fOdwMAJiU58NErw/+YqgeDgYjIgrwrnT+Wn4XkhPA3bPNgMBARWYzbLfG395q16UjeRgIYDERElvPOsTa0XOgFAKSnJGLFvIyI7p/BQERkMd5PI60uyEaCPbKHagYDEZGFDLjc2FZv3m0kgMFARGQpu4+eQ3v3AABgxpRkXD0nPeJlYDAQEVmId9uFj181AzZbhEfpAYOBiMgyOrsHsKPxjDZ9x5LLTCkHg4GIyALcbolv/HEfLvYNAgDmZqSg4LJUU8rCYCAisoAnXnsfLx1s1aY3rVoAEenBnlUMBiIik+0+cg4/3XFIm/7KyrlYVRCZnlQDYTAQEZmoubMH9/1hL9xSmb5mTjo2rlpgapkYDEREJukfdOPeZ+rQdqkfAJAxKQmP3r0s4g3a/OneuxCiUAhRJYRoV19VQojC0e7QqO0QEUW7H2w7oI3nbLcJPHb3MmSmJptcKp3BIIQoAeAEUA6gTX2VA3AKIcr17syo7RARRbu/7DuFp948pk1vWnUlludOM69AXkIGgxAiDUCNOlkqpcyTUuYBKFXnVanrRGQ7RETR7vCZLnz7T/Xa9Kr8bHxlZa6JJfKl54phvfq+WUq50zNT/bzFb51IbIeIKGpd7BvEPU870TPgAqC0V9i85irTHk0NRE8weM7onw2wrNJvnUhsh4ho3Nov9eOVg6042dYdsX1KKbFp63toOnsJAJCcYMMT6wqRmpwQsTLooWdk6VwAkFLW+S+QUtapKafnGsio7RARjcurh1rx5d/UYtAtYbcJPPXFq7Hyiulh3WfbpX5857l6VDe0aPN++KnFWJBtTuvmkei5YtB90I/QOkREY3apbxD3P7sPg2rDAZdb+nRzHQ6vHGpF2cO7fEJh3bU5+OSyWWHd71jpuWIAgI4Qy/RWGo95O0KI9VDrIHJycnTujojI154P2tChdmvtEa77+939g/ifvx/AM2+f8Jn/2Wty8O8fzw/LPo2gNxhGOvCP5kmiMW9HSrkFaiV1cXGxHMU+iYg0nk7qAODqOVPx9JeXIzEMDcrqTrTjG8/uw7HzQ3UYGZOSUHHXYtyyMMvw/RlJTzA0IfQtnqYIboeIaMzmZqRon+tPdaKze8DQRmUDLjd+/tIRPPrKUa2bCwAoy8/CDz65GNMmJRm2r3DRE5NNgNJi2X+B17yRbhEZvR0iojHLn5mK/JlKhW/vgBtffOodXOgdCPGt0KSUcB5vw6cefxM/e3koFCYlOfCTNUvwi3VFUREKgL5gqFLf1wZY5plXGWBZuLZDRDRmQgh8e/UCeAZGazx9Abc+8jqq65sh5ejuUrvdErXH2vBff92PFT96GXc98Q/Un+rUli+fm47qr69EedEsS7VTCEXo+SGEEJ6VijyPm6pn+U4AkFIKv/VL1Pk7x7OdYIqLi2Vtba2eVYmIAnr2nRPY5NX6GAAKc9JQsigLy+emY/FlaUh0DD93drkl3jnWhur6ZlQ3tKC1q2/YOol2G/617Ep86fq5pgzNGYgQwimlLNazrt7K5w1QzuadQgjPwb7Ea5n3zrWuL4QQeVJK73oD3dshIgqntVfnwGGz4b//vl97SqnuRAfq1E7tkhNsyJs+CQMuN3oGXOjpd6N3wIWeARdc7sAn1GkTE1C6MAtfuSEX87MmR+zfYjRdVwyAdhVQAcBTH1AHYFOAq4I0AO3qpH8w6N7OSHjFQERG6ejux8M7j+C3bx0PesAfSXpKIsrys3Hr4mxcmzvN9C6zgxnNFYPuYLASBgMRGa25swe7j5zDng/asOdYG46fD95VxvTJSSjLz8KtBTNwzdx0OCwaBt7CcSuJiCimzZgyAWuKZ2NN8WwAQEtnL5o7ezAh0Y4JCcorWf1s1asCozAYiIgCyJ6SjOwp5g+aY4bYjj0iIho1BgMREflgMBARkQ8GAxER+WAwEBGRDwYDERH5YDAQEZGPqGz5LIQ4C+C42eWIUhkAzpldCOLfwULi5W9xuZRS18DWURkMNHZCiFq9zeIpfPh3sA7+LYbjrSQiIvLBYCAiIh8MhvizxewCEAD+HayEfws/rGMgIiIfvGIgIiIfDAYiIvLBYCCimCKEKBRCVAkh2tVXlRCiMPQ3w7OdaMQ6hjghhFgPoGk0Y2sTRRt1TPkaddIz3nwmmOI0AAAFz0lEQVSu+r5GSrk1ktuJVrxiiANCiDQAlQDWjPH7cXvmZBQjfkP1O3KE1/pwlT8aqP+dew7mpVLKPCllHoBSdV6Vuk5EthPNGAzx4cmxflE9c3ICKAfQpr7KATiFEOXGFC+2GfgbeoKkI8irzagyRylPMG72vjJWP2/xWycS24laDIYYJYQoF0JUCiHaoRyExrKNuD9zGi+Df8NcKLcDpwZ5xfTtDR08v+mzAZZV+q0Tie1ELQZD7HoQylnNeA7ccX/mZABDfkOv8GgaccX4lgsAUso6/wVe83L9l4VxO1GLwRCjpJRFUkohpRQYY90CeOZkBKN+Q08nb8MOVqTRfdCP0DpRi8FAI4n7MycDGHoWC2iV0O1qhbNTCLHRmKLGhI4xLgvXdqKSw+wCkKXF/ZmTAYz6DfPUd08I1EG5TVgIoFAIsVZKWTSG8sWakW6djua2qlHbiUq8YqBQ4vrMySBG/IaeJ5K2qrcIi9RK7DwoIVEohKgYTyFjgJ76l0iuE7UYDBRKXJ85GWTcv6GUslQNhDV+85swVIcU77eUmgClzYj/Aq95eoLYqO1ELd5KsiAhxPuj/EpHmG4jNCH0bY6YPnMy4G8R9t9QStkkhGgCkCuEyFXDIh5VASgBsBbDK+nXqu+VCM2o7UQtdokRB9RGVFUAtkgpN4ziezVQ/gcp8q88Vc+cnADqeG87uEj9hmqA5QKYKqWM6bPZkQghPAc07ff2+p2hPqXnvX6JOn/neLYTa3griUZSpb6vDbAsLs6cDDDu31AIkaY+gdQebDmUUOiI51BQeU58nEKIGjWYnX7LAPg0PqwRQvhf1eneTkySUvIV4y8oLZ8lgMoR1ikBUBJgvlRfhV7zCj3zzf63RcNrtL9hoL8FlAPYsL8hlDoKp7psvdn/Viu81N/P6fW7O4P8t53mtU7uWLcTiy/eSooDoW4lqWdOnrPRPOl1j1rtmM1zRuu53C5R3zdIKTksYgij+Q2D/S3U+U6oVwYAagGkw/dppbE2ZCTywcpnGpGUcotasVmBoYNZHYBNkl1462LEbyiVW0R5amO2Ugy1hN4J5Soi3vtJIgPxioGIiHyw8pmIiHwwGIiIyAeDgYiIfDAYiIjIB4OBiChKCSFKRhoHfKzb5eOqRETRqxaBB+IaV+tsPq5KRBRhaqPHpnC0BVK793ACmCvH2EUKbyUREUWQ2oq9EiGG3BVCFHqN1teufh7WFXgAlVAaT4653ywGAxFRZD0ZagW111cnlH7O2tRXOZRO/cpDfC93vF3VMBiIiMJMCFEuhKhUe8gNemBX1/X0+goApVLKPKmM1leqzqtS1wmkEsCm8ZaXwUBEFH4PAlgPfSP2rVffN3vXQaift/ito1HrLWBEv1kMBiKiENSz/VBn+uVCiIBja0hljG4hlQF+QvWC67kyeDbAskq/dbxtgkHjo/BxVSKi0DZBub/fEehJIjU0KgAYMZphLgBIvxH/PPOEENo6XvsvVOcZ0ssurxiIiEJQn/ApAlDpGQ7UQ52ugDIMqBEj6IUaIzzQOiVQRvAzZLxvBgMRkQ7qQb8USjgUAlooVEKpJDZyWNWRthVo2VoMDQI1bryVRESkk5SySQhRCmWc6Aoot5hKjTpT9zJSJfWwZVJKI25haXjFQEQ0CmoIVGCoIZnRoaBne0bv0weDgYhoFNQuJzZB6Y+oQp02kmec72GtnL3mGXnbahgGAxGRTmoI1ABYo7Yu3gDltpKe9gl6VanvawMs88wz5LHUYBgMREQ6eLVI3uB5lFR9dHUDlEdZDQkHr+4sNnpfNaifN/qtExYMBiKiENSDvhNKKPg8/aNOe9o5GHXl4Ok22ymEqBFC1Kj7914WNnwqiYgotAooFc0BHwmVUm5VG55VwIADt5RyixDCU8ntaTdRN1IZjMTxGIiIyAdvJRERkQ8GAxER+WAwEBGRDwYDERH5YDAQEZEPBgMREflgMBARkQ8GAxER+fj/vbNFR6dCG1MAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": []
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 5, 10, 15, 20])"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.arange(5,25,5)"
]
},
{
"cell_type": "code",
"execution_count": null,
"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": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}