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{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6 : Turbulent Flow"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.1 - Page No :200\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math \n",
"\n",
"\n",
"# Variables\n",
"# given\n",
"q = 50.; \t\t\t #[gal/min] - volumetric flow rate\n",
"d = 2.067/12; \t \t\t #[ft] - diameter\n",
"A = 0.02330; \t\t #[ft**2] - flow area\n",
"p = 0.99568*62.43; \t\t\t #[lb/ft**3] - density of water at 86degF\n",
"mu = 0.8007*6.72*10**-4; \t\t #[lb/ft*sec] - viscosity of water at 86degF\n",
"u = q/(60.*7.48*A);\n",
"\n",
"# Calculations\n",
"# using the formula Nre = d*u*p/mu;\n",
"Nre = round((d*u*p)/mu,-2);\n",
"\n",
"# Results\n",
"print \"Nre = \",Nre\n",
"print \"Hence the flow is turbulent. Note also that Nre is dimensionless\";\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Nre = 95100.0\n",
"Hence the flow is turbulent. Note also that Nre is dimensionless\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.2 - Page No :202\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"# given\n",
"p = 0.99568*62.43; \t\t\t #[lb/ft**3] - density of water at 86degF\n",
"mu = 0.8007*6.72*10**-4; \t\t #[lb/ft*sec] - viscosity of water at 86degF\n",
"u = 4.78; \t\t\t #[ft/sec] - free stream velocity \n",
"Nre = 5.*10**5; \t\t\t # the lower limit for the transition reynolds number range is substituted\n",
"\n",
"# Calculations\n",
"x = (Nre*mu)/(p*u);\n",
"\n",
"# Results\n",
"print \"x = %.1f\"%x\n",
"print \"Thus the transition could star at about %.2f ft. \\\n",
"\\nThe reynolds number at the upper end of the transition range is %.0e .\\\n",
"\\nThe value of x at this location is ten times then the value obtained above i.e %.1f ft\"%(x,Nre*10,x*10)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"x = 0.9\n",
"Thus the transition could star at about 0.91 ft. \n",
"The reynolds number at the upper end of the transition range is 5e+06 .\n",
"The value of x at this location is ten times then the value obtained above i.e 9.1 ft\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.3 - Page No :212\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"# given\n",
"t = [0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.11, 0.12];\n",
"Ux = [3.84, 3.50, 3.80, 3.60, 4.20, 4.00, 3.00, 3.20, 3.40, 3.00, 3.50, 4.30, 3.80];\n",
"Uy = [0.43, 0.21, 0.18, 0.30, 0.36, 0.28, 0.35, 0.27, 0.21, 0.22, 0.23, 0.36, 0.35];\n",
"Uz = [0.19, 0.16, 0.17, 0.13, 0.09, 0.10, 0.16, 0.15, 0.13, 0.18, 0.17, 0.18, 0.17];\n",
"# using the formula AREA = [deltat/2]*[U1+U13+2*[U2+U3+U4+U5+U6+U7+U8+U9+U10+U11+U12]]\n",
"# for Uxmean\n",
"deltat = 0.01;\n",
"T = t[12]-t[0];\n",
"\n",
"# Calculation and Results\n",
"AREA = (deltat/2)*(Ux[0]+Ux[12]+2*(Ux[1]+Ux[2]+Ux[3]+Ux[4]+Ux[5]+Ux[6]+Ux[7]+Ux[8]+Ux[9]+Ux[10]+Ux[11]));\n",
"Uxmean = AREA/T;\n",
"print \"Uxmean = %.2f m s**-1\"%Uxmean\n",
"\n",
"# for Uymean\n",
"deltat = 0.01;\n",
"AREA = (deltat/2)*(Uy[0]+Uy[12]+2*(Uy[1]+Uy[2]+Uy[3]+Uy[4]+Uy[5]+Uy[6]+Uy[7]+Uy[8]+Uy[9]+Uy[10]+Uy[11]));\n",
"Uymean = AREA/T;\n",
"print \"Uymean = %.2f m s**-1\"%Uymean\n",
"\n",
"# for Uzmean\n",
"AREA = (deltat/2)*(Uz[0]+Uz[12]+2*(Uz[1]+Uz[2]+Uz[3]+Uz[4]+Uz[5]+Uz[6]+Uz[7]+Uz[8]+Uz[9]+Uz[10]+Uz[11]));\n",
"Uzmean = AREA/T;\n",
"print \"Uzmean = %.2f m s**-1\"%Uzmean\n",
"U = (Uxmean**2+Uymean**2+Uzmean**2)**(1./2);\n",
"print \"U = %.3f m s**-1\"%U\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Uxmean = 3.61 m s**-1\n",
"Uymean = 0.28 m s**-1\n",
"Uzmean = 0.15 m s**-1\n",
"U = 3.624 m s**-1\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.4 Page no : 218"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"# Variables\n",
"#Following values are taken from example 6.3\n",
"U_dash_z2 = 8.917*10**-4 #m**2s**-2 square velocity\n",
"Uz2 = .02340 #m**2s**-2\n",
"U_dash_x2 = 8.947 * 10**-4 #m**2s**-2\n",
"Ux22 = .02409 #m**2s**-2\n",
"U = 3.634\n",
"U2x = 3.63 #m**2s**-2\n",
"U2x2 = .41 #m**2s**-2\n",
"Ix = 11.37 #percent\n",
"U2y = .0288 #m**2s**-2\n",
"U2y2 = .069 #m**2s**-2\n",
"Iy = 1.92 #percent\n",
"dt = .01108\n",
"\n",
"# Calculation\n",
"rmsUz = math.sqrt(U_dash_z2)\n",
"rmsUx = math.sqrt(Uz2)\n",
"rmsUx2 = math.sqrt(U_dash_x2)\n",
"rmsUx2 = math.sqrt(Ux22)\n",
"I = 100*rmsUz/U\n",
"Ux = 3.84 - 3.61\n",
"Uy = .43 - .28\n",
"UxUy = Ux*Uy\n",
"ratio = dt/(U2x2*U2y2)\n",
"\n",
"\n",
"# Results\n",
"print \"I = %.2f percent\"%I\n",
"print \"U'xU'y = %.4f m**2s**-2\"%UxUy\n",
"print \"The ratio = %.2f \"%ratio"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"I = 0.82 percent\n",
"U'xU'y = 0.0345 m**2s**-2\n",
"The ratio = 0.39 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.5 - Page No :232\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"%matplotlib inline\n",
"\n",
"from numpy import *\n",
"from matplotlib.pyplot import *\n",
"import math \n",
"\n",
"\n",
"# Variables\n",
"# given\n",
"UzmaxbyU = 24.83;\n",
"roUbyv = 2312.;\n",
"Re = 100000.;\n",
"\n",
"# using the formula Et/v = 95.5*((r/ro)/slope)-1\n",
"# from fig 6.6 at Re = 100000\n",
"rbyro = [0, 0.040, 0.100, 0.200, 0.300, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.960, 1]\n",
"slope = [0, 0.105, 0.112, 0.126, 0.144, 0.168, 0.201, 0.252, 0.336, 0.503, 1.007, 2.517, 94.59]\n",
"\n",
"# Calculations\n",
"Etbyv = zeros(13)\n",
"for i in range(1,13):\n",
" Etbyv[i] = 95.5*((rbyro[i])/slope[i])-1;\n",
"\n",
"# Results\n",
"plot(rbyro,Etbyv);\n",
"suptitle(\"Eddy viscosity ratio (E,/v) versus dimensionless radius.\")\n",
"xlabel(\"r/ro\")\n",
"ylabel(\"Er/v\")\n",
"\n",
"show()\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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zhYWHs9O6LHgGQY+4c0d2Ss+fz+JApm35cuDqVTlNOBkGzyDMmBByGo0GDeTK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\nRK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1cfb950>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.7 page no : 246"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"# variables\n",
"do = .0508\n",
"Uz = .8467 # cyclohexane\n",
"aveP = 774.9 # the density of cyclohexane\n",
"u = 8.892*10**-4 # the viscosity\n",
"aveF = .00570\n",
"\n",
"# Calculation\n",
"Nre = do*Uz*aveP/u\n",
"rw = (1./2)*aveP*(Uz**2)*aveF\n",
"U = math.sqrt(rw/aveP)\n",
"\n",
"# for y = .001\n",
"y001 = (2.54*10**-5)*U*aveP/u\n",
"\n",
"\n",
"# Results\n",
"print \"Nre = %.2e \"%Nre\n",
"print \"The wall shear stress rw = %.3f N m**-2\"%rw\n",
"print \"The friction velocity U* = %.5f m s*-1\"%U\n",
"print \"Universal velocity Distribution :\" \n",
"print \"for y = 0.001 = %d \"%y001\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Nre = 3.75e+04 \n",
"The wall shear stress rw = 1.583 N m**-2\n",
"The friction velocity U* = 0.04520 m s*-1\n",
"Universal velocity Distribution :\n",
"for y = 0.001 = 1 \n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.8 Pageno :250"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"# variables\n",
"Cp = 4184. # lg-K-=4184Jkg-K-*\n",
"P = 1000. # g cm**-3\n",
"k = 0.628 # wm**-1\n",
"Nre = 1.2*10**5\n",
"v = 1*10**-6\n",
"do = 2*0.05\n",
"\n",
"# calculation\n",
"alpha = k/(P*Cp)\n",
"qa = (1.7*10**4)/(P*Cp)\n",
"Uz = Nre*v/(do)\n",
"U = Uz*math.sqrt(.0045/2)\n",
"y = (5*v)/U\n",
"\n",
"# Results\n",
"print \"A = %.3e m**2s**-2\"%alpha\n",
"print \"The average velocity = %.2f m s**-1\"%Uz\n",
"print \"U* = %.5f m s**-1\"%U\n",
"print \"the value of y = %.3e cm\"%y\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A = 1.501e-07 m**2s**-2\n",
"The average velocity = 1.20 m s**-1\n",
"U* = 0.05692 m s**-1\n",
"the value of y = 8.784e-05 cm\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.9 - Page No :258\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"p = 0.84*62.4; \t\t\t #[lbf/ft**3] - density\n",
"dP = 80.*144; \t\t\t #[lbf/ft**2] - pressure\n",
"dz = 2000.; \t\t\t #[ft] - length of pipe\n",
"gc = 32.174; \t\t\t #[(lbm*ft)/(lbf*sec**2)] - gravitational conversion consmath.tant\n",
"dpbydz = -dP/dz;\n",
"do = 2.067/12; \t\t\t #[ft]\n",
"\n",
"# Calculations\n",
"U = 2000*(1./24)*(1./3600)*(42)*(1./7.48)*(1./0.02330);\n",
"# using the formula f = ((do/2)*(-dp/dz)*gc)/(p*(U)**2)\n",
"f = ((do/2)*(-dpbydz)*gc)/(p*(U)**2)\n",
"\n",
"# Results\n",
"print \"f = %.5f (dimensionless)\"%f\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"f = 0.00979 (dimensionless)\n"
]
}
],
"prompt_number": 19
}
],
"metadata": {}
}
]
}
|
