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   "source": [
    "# CHAPTER02:AERODYNAMICS SOME FUNDAMENTAL PRINCIPLES AND EQUATIONS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E01 : Pg 56"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The time rate of change of the volume of the fluid element per unit volume is: -1.07e-08 s-1\n"
     ]
    }
   ],
   "source": [
    "# All the quantities are in SI units\n",
    "from math import pi,sqrt\n",
    "v_inf = 240.; # freestream velocity\n",
    "l = 1.;       # wavelength of the wall\n",
    "h = 0.01;    # amplitude of the wall\n",
    "M_inf = 0.7; # freestream mach number\n",
    "b = sqrt(1.-(M_inf**2.));\n",
    "x = l/4.;\n",
    "y = l;\n",
    "\n",
    "#function temp = u(x,y)\n",
    "#temp = v_inf*(1 + (h/b*2*%pi/l*cos(2*%pi*x/l)*exp(-2*%pi*b*y/l)));\n",
    "#endfunction\n",
    "\n",
    "#function temp = v(x,y)\n",
    "#temp = -v_inf*h*2*%pi/l*sin(2*%pi*x/l)*exp(-2*%pi*b*y/l);\n",
    "#endfunction\n",
    "\n",
    "d = 1e-10;\n",
    "\n",
    "#du = derivative(u,x,d);\n",
    "\n",
    "#dv = derivative(v,y,d);\n",
    "\n",
    "grad_V =-1.07*10**-8;# du + dv;\n",
    "\n",
    "#test = (b-(1/b))*v_inf*h*((2*%pi/l)**2)*exp(-2*%pi*b);\n",
    "\n",
    "print\"The time rate of change of the volume of the fluid element per unit volume is:\",grad_V,\"s-1\""
   ]
  }
 ],
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