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   "source": [
    "## Chapter 6 : Dimensional Analysis and Dynamic Similitude"
   ]
  },
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   "metadata": {},
   "source": [
    "### Example 6.2 Page no 233"
   ]
  },
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     "text": [
      "Hence the model should be tested at a velocity of  2.7 m/s. This velocity in the model is called corresponding velocity\n"
     ]
    }
   ],
   "source": [
    "# Velocity of the flow\n",
    "\n",
    "# Given\n",
    "\n",
    "L = 10                          # length scale lp/l\n",
    "\n",
    "# crue oil at 20 deg C\n",
    "\n",
    "rhop = 0.86*998.2                 # density inn kg/m**3\n",
    "\n",
    "mup = 8*10**-3                    # viscosity in Ns/m**2\n",
    "\n",
    "Vp = 2.5                          # Velocity in m/s\n",
    "\n",
    "# water at 20 deg C\n",
    "\n",
    "rhom = 998.2                     # density in kg/m**3\n",
    "\n",
    "mum = 1.005*10**-3               # viscosity in Ns/m**2\n",
    "\n",
    "# Solution\n",
    "\n",
    "Vm = Vp*L*(rhop/rhom)*(mum/mup)  # velocity in m/s\n",
    "\n",
    "print \"Hence the model should be tested at a velocity of \",round(Vm,2),\"m/s. This velocity in the model is called corresponding velocity\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 6.3 Page no 233"
   ]
  },
  {
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   "execution_count": 1,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum discharge, Qm =  5.65685425 cfs\n",
      "Maximum head over crest =  4.74 ft\n"
     ]
    }
   ],
   "source": [
    "# Mximum head on the crest and corresponding discharge for dynamically similar conditions\n",
    "\n",
    "# Given\n",
    "\n",
    "from __future__ import division\n",
    "\n",
    "from math import *\n",
    "\n",
    "l = 300                               # length in ft\n",
    "\n",
    "Q = 100000                            # discharge in cfs\n",
    "\n",
    "Cd = 3.8                              # coefficient of discharge\n",
    "\n",
    "L = (1/50)                              # length scale\n",
    "\n",
    "# Solution\n",
    "\n",
    "Qm = 100000*(L)**(5/2)                     # model discharge in cfs\n",
    "\n",
    "print \"Maximum discharge, Qm = \",round(Qm,8),\"cfs\"\n",
    "\n",
    "H = (Q/(Cd*l))**(2/3)                 # height over spill way\n",
    "\n",
    "h = H*L*12                              # head over spill model\n",
    "\n",
    "print \"Maximum head over crest = \",round(h,2),\"ft\""
   ]
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