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{
"metadata": {
"name": "",
"signature": "sha256:d2599cf416e0a07710e4c3d128cbc7fa43fd432b07cfc1f586c709ffa82e3638"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 10 : Forces on Immersed Bodies"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.1 Page No : 301"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"nu = 0.001 \t#ft**2 /s\n",
"L = 1.5 \t#ft\n",
"U = 2. \t#ft/s\n",
"s = 0.925\n",
"ro = 1.94\n",
"b = 6.\n",
"\t\n",
"#calculations\n",
"R = L*U/nu\n",
"Cf = 1.328/math.sqrt(R)\n",
"Ff = Cf*s*ro*U*b/12 *L\n",
"delta = 4.91 *L/math.sqrt(R)\n",
"T0 = 0.332*nu*s*ro*U/L *math.sqrt(R)\n",
"print R\n",
"#Results\n",
"print \"Friction drag = %.3f lb\"%(Ff)\n",
"print \" Thickness of boundary layer = %.4f ft\"%(delta)\n",
"print \" Shear stress = %.4f lb/ft**2\"%(T0)\n",
"\n",
"#Similar calculations are done for SI units case"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"3000.0\n",
"Friction drag = 0.065 lb\n",
" Thickness of boundary layer = 0.1345 ft\n",
" Shear stress = 0.0435 lb/ft**2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.2 Page No : 305"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"nu = 0.00015 \t#ft**2/s\n",
"L = 35. \t#ft\n",
"U = 88. \t#fps\n",
"g = 32.2 \t#ft/s**2\n",
"b = 10. \t #ft\n",
"w = 8. \t#ft\n",
"rho = 0.0725\n",
"\t\n",
"#calculations\n",
"R = L*U/nu\n",
"Cf = 0.455 /(math.log10(R))**2.58\n",
"B = 2*b + w\n",
"Ff = Cf*rho/g *U**2 /2 *L*B\n",
"Rx = R/10**5\n",
"delta = L*0.377 /(b* Rx**(0.2))\n",
"T0 = 0.0587 *rho/g *U**2 /2 *(nu/(L*U))**(0.2)\n",
"\t\n",
"#Results\n",
"print \"Frictional drag = %.1f lb\"%(Ff)\n",
"print \" Thickness of boundary layer = %.3f ft\"%(delta)\n",
"print \" Shear stress = %.4f lb/ft**2\"%(T0)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Frictional drag = 22.9 lb\n",
" Thickness of boundary layer = 0.455 ft\n",
" Shear stress = 0.0176 lb/ft**2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.3 Page No : 308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"nu = 0.0000166 \t#ft**2 /s\n",
"U = 5.06 \t#fps\n",
"L = 50. \t#ft\n",
"g = 32.2\n",
"dia = 10. \t#ft\n",
"\t\n",
"#calculations\n",
"R = L*U/nu\n",
"Cf = 0.0028\n",
"Ff = Cf*64/g *U**2 /2 *math.pi*dia*L\n",
"Rx = R/L\n",
"ec = 26*nu/U *Rx**(0.25)\n",
"Rx2 = Rx*L/2\n",
"T02 = 0.0587*U**2 /2 /(Rx2)**(0.2)\n",
"delta2 = 60*nu/math.sqrt(T02)\n",
"\t\n",
"#Results\n",
"print \"Friction drag = %.f lb\"%(Ff)\n",
"print \" Critical roughness = %.4f ft\"%(ec)\n",
"print \" height of roughness = %.4f ft\"%(delta2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Friction drag = 112 lb\n",
" Critical roughness = 0.0020 ft\n",
" height of roughness = 0.0056 ft\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.4 Page No : 314"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"Cd = 0.45\n",
"rho = 0.0725/32.2\n",
"V = 88. \t#fps\n",
"A = 8*10.\n",
"\t\n",
"#calculations\n",
"Fd = Cd*rho*V**2 /2 *A\n",
"Drag2 = 23\n",
"D = Fd-Drag2\n",
"\t\n",
"#Results\n",
"print \"Pressure drag = %.f lb\"%(D)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure drag = 291 lb\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.5 Page No : 315"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sympy import Symbol,solve\n",
"import math\n",
"\n",
"#Initialization of variables\n",
"Cd = 0.2\n",
"D = 8.5/12 \t#in\n",
"v = 1.57*10**-4\n",
"rho = 0.00238\n",
"\t\n",
"#calculations\n",
"A = (math.pi*D**2)/4\n",
"#From trail and error method,\n",
"V = 412 \t#fps\n",
"R = (D*V)/v\n",
"\n",
"\t\n",
"#Results\n",
"print \"Free fall velocity = %.2e fps\"%(R)\n",
"print \"Since the values of R and Cd check with the figure, V = 412 fps\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Free fall velocity = 1.86e+06 fps\n",
"Since the values of R and Cd check with the figure, V = 412 fps\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.6 Page No : 319"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#Initialization of variables\n",
"nu = 1.15*10**-5 \t#m**2/s\n",
"D = 2.*10**-3 \t #m\n",
"V = 15. \t#m/s\n",
"T = -20. \t #C\n",
"\t\n",
"#calculations\n",
"R = D*V/nu\n",
"f = 0.2 *V/D *(1+T/R)\n",
"\t\n",
"#Results\n",
"print \"Frequency of oscillation = %d Hz\"%(round(f,-2))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Frequency of oscillation = 1500 Hz\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.7 Page No : 324"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"n = 90. \t#rpm\n",
"R = 2. \n",
"rho = 0.0765/32.2\n",
"B = 25.\n",
"U = 120. \t#fps\n",
"\t\n",
"#calculations\n",
"vt = 2*math.pi*R*n/60\n",
"T = 2*math.pi*R*vt\n",
"Fl = rho*B*U*T\n",
"theta = math.degrees(math.asin(-T/(4*math.pi*R*U)))\n",
"\n",
"#Results\n",
"print \"Peripheral velocity = %.2f fpx\"%vt\n",
"print \"Value of circulation = %.f ft62/s\"%(T)\n",
"print \" Transverse or lift force = %d lb\"%(round(Fl,-1))\n",
"print \" Position of stagnation points = %.1f degrees\"%(180-theta)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Peripheral velocity = 18.85 fpx\n",
"Value of circulation = 237 ft62/s\n",
" Transverse or lift force = 1690 lb\n",
" Position of stagnation points = 184.5 degrees\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.8 Page No : 331"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"B = 36. \t#ft\n",
"c = 6. \t#ft\n",
"Cl = 0.8\n",
"tau = 0.175 \n",
"rho = 0.001756\n",
"V = 300. \t#fps\n",
"\t\n",
"#calculations\n",
"alphai = Cl/(math.pi*B/c) *(1+tau) *180/math.pi\n",
"alpha = 5.4 \n",
"lift = -5.6 \t#degrees\n",
"alphao = alpha-alphai\n",
"alphaod = alphao-lift\n",
"alphaor = alphaod*math.pi/180\n",
"eta = Cl/(2*math.pi*alphaor)\n",
"Fl = Cl*rho*V**2 /2 *B*c\n",
"Fd = 0.047/Cl *13680\n",
"HP = Fd*V/550\n",
"\t\n",
"#Results\n",
"print \"Friction coefficient = %.3f \"%(eta)\n",
"print \" weight of the wing = %d lb\"%(round(Fl,-1))\n",
"print \" Horsepower required = %d hp\"%(HP)\n",
"\n",
"# rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Friction coefficient = 0.896 \n",
" weight of the wing = 13650 lb\n",
" Horsepower required = 438 hp\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.9 Page No : 334"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"k = 1.4\n",
"R = 287.\n",
"T = 249. \t#K\n",
"v = 600. \t#velocity - m/s\n",
"d = 0.2 \t#diameter - m\n",
"\t\n",
"#calculations\n",
"c = math.sqrt(k*R*T)\n",
"M = v/c\n",
"Cd = 0.62\n",
"rho = 47.22*10**3 /(R*T)\n",
"Fd = Cd*rho*v**2 /2 *math.pi*d**2 /4\n",
"\t\n",
"#Results\n",
"print \"Drag = %d N\"%(Fd)\n",
"\n",
"# note : answer is accurate"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Drag = 2316 N\n"
]
}
],
"prompt_number": 15
}
],
"metadata": {}
}
]
}
|
