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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9 : Forces on bodies immersed in fluids"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 9.1 pageno : 166"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"rho = 1.2\n",
"mu = 1.85/100000\n",
"pi = 3.1428\n",
"d = 3.\n",
"v = 50.*1000/3600\n",
"\n",
"#calculation part 1\n",
"Re = d*rho*v/mu\n",
"\n",
"#from chart of drag coeff. vs Re\n",
"Cd = 0.2 #coeff. of drag\n",
"Ad = pi*d**2/4. #projected area\n",
"Fd = Ad*Cd*rho*v**2/2.\n",
"print \"The drag force on sphere in N\",Fd \n",
"\n",
"#part 2\n",
"v = 2.\n",
"l = 0.25\n",
"Re = l*v*rho/mu\n",
"zi = 4*pi*(l**3*3./4/pi)**(2/3.)/6./l**2 #sphericity\n",
"\n",
"#using graph\n",
"Cd = 2.\n",
"Ad = l**2\n",
"Fd = Ad*Cd*rho*v**2/2.\n",
"print \"The drag force on cube in N\",Fd \n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The drag force on sphere in N 163.6875\n",
"The drag force on cube in N 0.3\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 9.2 page no : 168"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"rho = 1.2\n",
"mu = 1.85/100000\n",
"pi = 3.1428\n",
"g = 9.81\n",
"d = 1.38\n",
"t = 0.1 #thickness\n",
"v = 30*1000/3600.\n",
"T = 26.2 #Tension\n",
"m = 0.51 #mass\n",
"theta = 60.*pi/180.\n",
"\n",
"#calculation\n",
"Fd = T*math.cos(theta)\n",
"print \"Drag force in N: %.4f\"% Fd\n",
"A = pi*d**2/4.\n",
"Ad = A*math.cos(theta) #area component to drag\n",
"Cd = 2*Fd/Ad/rho/v**2 #coeff of drag\n",
"print \"The drag coefficient: %.4f\"% Cd \n",
"Fg = m*g #force of gravity\n",
"Fb = rho*pi*d**2/4.*t*g #buoyant force\n",
"Fl = Fg-Fb+T*math.sin(theta)\n",
"print \"The lift force in N : %.4f\"%Fl\n",
"Al = A*math.sin(theta)\n",
"Cl = 2*Fl/Al/rho/v**2\n",
"print \"The coefficient of lift: %.4f\"%Cl \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Drag force in N: 13.0909\n",
"The drag coefficient: 0.4202\n",
"The lift force in N : 25.9368\n",
"The coefficient of lift: 0.4803\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 9.3 page no : 171"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"rhog = 1200. #density of glycerol\n",
"mu = 1.45\n",
"pi = 3.1428\n",
"g = 9.81\n",
"rhos = 2280. #density of sphere\n",
"v = 0.04 #terminal velocity\n",
"a = 2*mu*g*(rhos-rhog)/v**3./3./rhog**2 #a = Cd/2/Re\n",
"\n",
"#using graph of Cd/2/Re vs Re\n",
"Re = 0.32\n",
"d = Re*mu/v/rhog\n",
"print \"Diameter of sphere in (m): %.4f\"%d \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diameter of sphere in (m): 0.0097\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 9.4 page no : 173"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"rhoa = 1.218 #density of air\n",
"mu = 1.73/100000\n",
"pi = 3.1428\n",
"g = 9.81\n",
"rhog = 1200.\n",
"rhop = 2280. #density of polythene\n",
"d = 0.0034 #diameter\n",
"a = 4*d**3*(rhop-rhoa)*rhoa*g/3/mu**2 #a = Cd*Re**2\n",
"\n",
"#using graph of Cd*Re**2 vs Re\n",
"Re = 2200.\n",
"v = Re*mu/d/rhog\n",
"print \"The terminal velocity in (m/s) %f\"%v \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The terminal velocity in (m/s) 0.009328\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"example 9.6 page no : 177"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math \n",
"\n",
"# Initialization of Variable\n",
"pi = 3.1428\n",
"rho = 825\n",
"mu = 1.21\n",
"g = 9.81\n",
"l = 0.02\n",
"de = 0.02 #dia exterior\n",
"di = 0.012 #dia interior\n",
"\n",
"# Initialization of Variable\n",
"rho = 998. #density of water\n",
"mu = 1.25/1000 #viscosity of water\n",
"w = 100. #mass of water\n",
"pi = 3.1428\n",
"g = 9.81\n",
"rhog = 2280. #density of glass\n",
"wg = 60. #mass of glass\n",
"d = 45.*10**-6 #diameter of glass sphere\n",
"\n",
"#claculation\n",
"rhom = (w+wg)/(w/rho+wg/rhog) #density of mixure\n",
"e = w/rho/(w/rho+wg/rhog) #volume fraction of watter\n",
"\n",
"#using charts\n",
"zi = math.exp(-4.19*(1.-e))\n",
"\n",
"K = d*(g*rho*(rhog-rho)*zi**2/mu**2)**(1./3) #stoke's law coeff.\n",
"print K\n",
"if K<3.3:\n",
" print \"settling occurs in stoke-s law range\"\n",
" U = g*d**2*e*zi*(rhog-rhom)/18/mu\n",
" print \"settling velocity in m/s: %f\"%U\n",
"else:\n",
" print \"settling does not occurs in stoke-s law range\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.504080734813\n",
"settling occurs in stoke-s law range\n",
"settling velocity in m/s: 0.000297\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"\n",
"example 9.7 page no : 180"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"from numpy import linspace\n",
"\n",
"\n",
"# Initialization of Variable\n",
"rhog = 1200. #density of glycerol\n",
"mu = 1.45 #viscosity of glycerol\n",
"pi = 3.1428\n",
"g = 9.81\n",
"rhos = 2280. #density of sphere\n",
"d = 8/1000.\n",
"s = 0.\n",
"uf = 0.8*0.026\n",
"\n",
"#calculation\n",
"def intre():\n",
" s = 0.\n",
" u = linspace(0,uf,1000)\n",
" for i in range(0,1000):\n",
" y = ((pi/6*d**3*rhos*g-pi*d**3/6*rhog*g-0.5*pi*d**2/4*24*mu/d/rhog*rhog*u[i])/pi*6/d**3/rhos)**(-1)*uf/1000\n",
" s = s+y\n",
" a = s\n",
" return a\n",
"\n",
"t = intre()\n",
"print \"Time taken by particle to reach 80%% of its velocity in (s): %f\"%t\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Time taken by particle to reach 80% of its velocity in (s): 0.009020\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}