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{
"metadata": {
"name": "",
"signature": "sha256:03b40b6d5c44ff714aac13480905f296c46afa917e2740a687e8aa66bb21b428"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 10: Laminar and Turbulent Flows in Bounded System"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.1, Page 329"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"import sympy\n",
"from sympy import symbols,diff,solve\n",
"\n",
" #Initializing the variables\n",
"mu = 0.9;\n",
"rho = 1260;\n",
"g = 9.81;\n",
"x = 45; #theta in degrees\n",
"P1 = 250 * 10**3;\n",
"P2 = 80* 10**3;\n",
"Z1 = 1;\n",
"Z2 = 0; # datum\n",
"U = -1.5;\n",
"Y = 0.01;\n",
"\n",
" #Calculations\n",
"gradP1 = P1+ rho*g*Z1;\n",
"gradP2 = P2+ rho*g*Z2;\n",
"DPstar = (gradP1-gradP2)*math.sin(math.radians(x))/(Z1-Z2);\n",
"A = U/Y; # Coefficient U/Y for equation 10.6\n",
"B = DPstar/(2*mu) # Coefficient dp*/dx X(1/2mu) for equation 10.6\n",
"y = symbols('y')\n",
"v = round((A + B*Y),1)*y -round(B)*y**2\n",
"duBYdy = diff(v,y);\n",
"tau = 0.9*duBYdy;\n",
"stagPnts = solve(duBYdy,y)\n",
"ymax=stagPnts[0] #value of y where derivative vanishes.;\n",
"umax = (A + B*Y)*ymax + B*ymax**2; # Check the value there is slight mistake in books answer\n",
"def u(y):\n",
" z = (A + B*Y)*y -B*y**2;\n",
" return diff(z,y)\n",
"def dif(y):\n",
" return round((A + B*Y)) -2*round(B)*y\n",
"\n",
"taumax=abs(mu*dif(Y))\n",
"\n",
"print \"velocity distribution :\",v\n",
"print \"shear stress distribution :\",mu*dif(y)\n",
"print \"maximum flow velocity (m/s) :\",round(umax,2)\n",
"print \"Maximum Shear Stress (kN/m^2):\",(round(taumax)/1000)\n",
" \n",
"\n",
"print "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"velocity distribution : -71638.0*y**2 + 566.4*y\n",
"shear stress distribution : -128948.4*y + 509.4\n",
"maximum flow velocity (m/s) : 3.36\n",
"Maximum Shear Stress (kN/m^2): 0.78\n",
"\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.2, Page 335"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
" #Initializing the variables\n",
"mu = 0.9;\n",
"rho = 1260;\n",
"d = 0.01;\n",
"Q = 1.8/60*10**-3; #Flow in m**3 per second\n",
"l = 6.5;\n",
"ReCrit = 2000;\n",
" #Calculations\n",
"A = (math.pi*d**2)/4;\n",
"MeanVel = Q/A;\n",
"Re = rho*MeanVel*d/mu/10; # Check properly the answer in book there is something wrong\n",
"Dp = 128*mu*l*Q/(math.pi*d**4)\n",
"Qcrit = Q*ReCrit/Re*10**3;\n",
"\n",
"print \"Pressure Loss (kN/m2) :\",round(Dp/1000,0)\n",
"print \"Maximum Flow rate (litres/s) :\",round(Qcrit,0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure Loss (kN/m2) : 715.0\n",
"Maximum Flow rate (litres/s) : 112.0\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.3, Page 341"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
" #Initializing the variables\n",
"mu = 1.14*10**-3;\n",
"rho = 1000;\n",
"d = 0.04;\n",
"Q = 4*10**-3/60; #Flow in m**3 per second\n",
"l = 750;\n",
"ReCrit = 2000;\n",
"g = 9.81;\n",
"k = 0.00008; # Absolute Roughness\n",
"\n",
" #Calculations\n",
"A = (math.pi*d**2)/4;\n",
"MeanVel = Q/A;\n",
"Re = rho*MeanVel*d/mu;\n",
"Dp = 128*mu*l*Q/(math.pi*d**4);\n",
"hL = Dp/(rho*g);\n",
"f = 16/Re;\n",
"hlDa = 4*f*l*MeanVel**2/(2*d*g); # By Darcy Equation\n",
"Pa = rho*g*hlDa*Q;\n",
"\n",
" #Part(b)\n",
"Q = 30*10**-3/60; #Flow in m**3 per second\n",
"MeanVel = Q/A;\n",
"Re = rho*MeanVel*d/mu;\n",
"RR = k/d; # relative roughness\n",
"f = 0.008 #by Moody diagram for Re = 1.4 x 10**4 and relative roughness = 0.002\n",
"hlDb = 4*f*l*MeanVel**2/(2*d*g); # By Darcy Equation\n",
"Pb = rho*g*hlDb*Q;\n",
"\n",
"\n",
"print \"!---- Case (a) ----!\\n\",\"Head Loss(mm) :\",round(hlDa*1000,1)\n",
"print \"Power Required (W) :\",round(Pa,4)\n",
"print \"\\n!---- Case (b) ----!\\n\",\"Head Loss(m) :\",round(hlDb,2)\n",
"print \"Power Required (W) :\",round(Pb,0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"!---- Case (a) ----!\n",
"Head Loss(mm) : 92.5\n",
"Power Required (W) : 0.0605\n",
"\n",
"!---- Case (b) ----!\n",
"Head Loss(m) : 4.84\n",
"Power Required (W) : 24.0\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.4, Page 343"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
" #Initializing the variables\n",
"w = 4.5;\n",
"d = 1.2 ;\n",
"C = 49;\n",
"i = 1/800;\n",
"\n",
" #Calculations\n",
"A = d*w;\n",
"P = 2*d + w;\n",
"m = A/P;\n",
"v = C*(m*i)**0.5;\n",
"Q = v*A;\n",
"\n",
"print \"Mean Velocity (m/s):\",round(v,2)\n",
"print \"Discharge (m3/s) :\",round(Q,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mean Velocity (m/s): 1.53\n",
"Discharge (m3/s) : 8.28\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.5, Page 348"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import sympy\n",
"from sympy import symbols\n",
"\n",
" #Initializing the variables\n",
"r,R = symbols('r R')\n",
"\n",
"#Calculations\n",
"rbyR=round((1-(49/60)**7),3)\n",
"r = (rbyR)*R \n",
"\n",
"#Result\n",
"print \"radius at which actual velocity is equal to mean velocity is\",r"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"radius at which actual velocity is equal to mean velocity is 0.758*R\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10.7, Page 355"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
" #Initializing the variables\n",
"d1 = 0.140;\n",
"d2 = 0.250;\n",
"DpF_DpR = 0.6; #Difference in head loss when in forward and in reverse direction\n",
"K = 0.33 #From table\n",
"g = 9.81;\n",
" #Calculations\n",
"ratA = (d1/d2)**2;\n",
"v =(DpF_DpR*2*g/((1-ratA)**2-K))**0.5;\n",
"\n",
"print \"Velocity (m/s):\",round(v,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity (m/s): 9.13\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}
|
