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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Chapter 7 : Fluid Resistance"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.1 Page no 245"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from math import *\n",
"\n",
"from __future__ import division\n",
"\n",
"\n",
"nu1 = 0.804*10**-6 # viscosity in m**2/s\n",
"\n",
"V = 0.3 # velocity in m/s\n",
"\n",
"D = 0.02 # diameter in m/s\n",
"\n",
"\n",
"rho = 995.7 # density in kg/m**3\n",
"\n",
"\n",
"mu = 8620*10**-4 # viscosity in Ns/m**2\n",
"\n",
"S = 1.26 # specific gravity\n",
"\n",
"nu2 = mu/(S*rho) # viscosity of glycerine in Ns/m**2\n",
"\n",
"\n",
"R1 = V*D/nu1\n",
"\n",
"print \"Reynolds number for water =\",round(R1,0)\n",
"\n",
"print \"R > 2000 the flow is turbulent for water\"\n",
"\n",
"print \"\\n\"\n",
"R2 = V*D/nu2\n",
"\n",
"print \"Reynolds number for glycerine =\",round(R2,1)\n",
"\n",
"print \"R < 2000 the flow is laminar for glycerine\"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Reynolds number for water = 7463.0\n",
"R > 2000 the flow is turbulent for water\n",
"\n",
"\n",
"Reynolds number for glycerine = 8.7\n",
"R < 2000 the flow is laminar for glycerine\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.2 Page no 248"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from math import *\n",
"\n",
"from __future__ import division\n",
"\n",
"from scipy import *\n",
"\n",
"import numpy as np\n",
"\n",
"from sympy import *\n",
"\n",
"y = Symbol('y')\n",
"\n",
"d = 0.0175 # diameter in m\n",
"\n",
"s = 0.3 # shear stress at a distance in m\n",
"\n",
"tau = 103 # shear stress in Pa\n",
"\n",
"rho = 1000 # density in kg/m**3\n",
"\n",
"\n",
"\n",
"Up = diff(8.5+0.7*log(y),y)\n",
"\n",
"print Up\n",
"\n",
"Up = (0.7/0.3) # for y = 0.3\n",
"\n",
"k = sqrt(tau/(rho*s**2*Up**2))\n",
"\n",
"print \"Turbulence constant = \",round(k,2)\n",
"\n",
"Ml = k*s*100 # mixing length\n",
"\n",
"print \"Mixing length = \",round(Ml,1),\"cm\"\n",
"\n",
"Eta = rho*(Ml/100)**2*Up\n",
"\n",
"print \"Eddy viscosity =\",round(Eta,1),\"Nm/s**2\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.7/y\n",
"Turbulence constant = 0.46\n",
"Mixing length = 13.8 cm\n",
"Eddy viscosity = 44.1 Nm/s**2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.3 Page no 256"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from math import *\n",
"\n",
"from __future__ import division\n",
"\n",
"from pylab import plt\n",
"\n",
"from numpy import *\n",
"\n",
"from scipy import *\n",
"\n",
"from sympy import *\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"\n",
"S = 1.26 # specific gravity \n",
"\n",
"mu = 0.862 # dynamic viscosity in Ns/m**2\n",
"\n",
"rho = S *1000 # density in kg/m**3\n",
"\n",
"K2 = 0.332\n",
"\n",
"V=1 # velocity in m/s\n",
"\n",
"\n",
"\n",
"x = [0,0.1,0.5,1.0,2.0];\n",
"\n",
"d = 0.1307*np.sqrt(x)*100\n",
"\n",
"tauo = K2*rho*V**2/(sqrt(1462)*np.sqrt(x))\n",
"\n",
"plt.plot(x, d, 'r')\n",
"plt.xlabel('x(m)')\n",
"plt.ylabel('delta(cm),tauo(N/m**2)')\n",
"\n",
"plt.plot(x, tauo, 'b')\n",
"plt.xlabel('x')\n",
"plt.legend('d''t')\n",
"plt.show()\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.4 page no 260"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import numpy as np\n",
"\n",
"from math import *\n",
"\n",
"from __future__ import division\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from numpy import sqrt\n",
"\n",
"\n",
"rho = 1.197 # air density in kg/m**3\n",
"\n",
"mu = 18.22*10**-6 # viscosity in Ns/m**2\n",
"\n",
"l = 5 # length of the plate\n",
"\n",
"V = 8 # velocity in m/s\n",
"\n",
"Rec = 5*10**5 # crictical reynolds number\n",
"\n",
"l1 = 0.951 # length from 0 to 0.951\n",
"\n",
"l2 = 5.0 # length from 0 to 5\n",
"\n",
"l3 = 0.951 # length from 0 to 0.951\n",
"\n",
"\n",
"X = Rec/525576\n",
"\n",
"x = [0,0.1,0.3,0.6,0.951];\n",
"\n",
"d = 0.0069*np.sqrt(x)*100\n",
"\n",
"plt.figure()\n",
"plt.plot(x, d, 'r')\n",
"plt.xlabel('x(m)')\n",
"plt.ylabel('delta(cm)')\n",
"plt.title('delta v/s x')\n",
"plt.legend('L')\n",
"plt.show()\n",
"\n",
"X1 = [0.951,1.5,2.0,2.5,3.0,4.0,5.0]\n",
"\n",
"Dt = 0.0265*np.power(X1,(4/5))*100\n",
"\n",
"plt.figure()\n",
"plt.plot(X1, Dt, 'g')\n",
"plt.xlabel('x(m)')\n",
"plt.ylabel('delta(cm)')\n",
"plt.title('delta v/s x')\n",
"plt.legend('T')\n",
"plt.show()\n",
"\n",
"Td = 0.664*sqrt(mu*rho*V**3*l1)+0.036*rho*V**2*l2*(mu/(rho*V*l2))**0.2-0.036*rho*V**2*l3*(mu/(rho*V*l3))**0.2\n",
"\n",
"print \"Total Drag = \",round(Td,3),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total Drag = 0.595 N\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.5 Page no 270"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from math import *\n",
"\n",
"from pylab import plt\n",
"\n",
"from __future__ import division\n",
"\n",
"\n",
"d = 0.01 # doameter of sphere in m\n",
"\n",
"v = 0.05 # velocity in m/s\n",
"\n",
"S = 1.26 # specific gravity\n",
"\n",
"mu = 0.826 # kinematic viscosity in Ns/m**2\n",
"\n",
"rho = S*1000 # density\n",
"\n",
"\n",
"R = rho*v*d/mu\n",
"\n",
"\n",
"Cd = 35\n",
"\n",
"Fd = 0.5*Cd*rho*v**2*pi*d**2/4\n",
"\n",
"print \"Drag on the sphere = \",round(Fd,4),\"N\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Drag on the sphere = 0.0043 N\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}