{
"metadata": {
"name": "",
"signature": "sha256:b340580fbd227dce130b380a32e6ef916d9ee3613549fbd41c895ab6ef6ec7e3"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8 : Steady Incompressible Flow in Pressure Conduits"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.1 Page No : 205"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"s = 0.85\n",
"v = 1.8*10**-5 \t#m**2 /s\n",
"d = 10. \t#cm\n",
"flow = 0.5 \t #L/s\n",
"\t\n",
"#calculations\n",
"Q = flow*10**3\n",
"A = math.pi*d**2 /4\n",
"V = Q/A\n",
"V = V/10**2\n",
"R = d*10**-2 *V/v\n",
"\t\n",
"#Results\n",
"print \"reynolds number = %.f. Hence the flow is laminar\"%(R)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"reynolds number = 354. Hence the flow is laminar\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.2 Page No : 212"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#Initialization of variables\n",
"Vc = 12.7 \t#cm/s\n",
"r = 2. \t#cm\n",
"r2 = 5. \t#cm\n",
"R = 354.\n",
"rho = 0.85\n",
"V = 6.37 \t#cm/s\n",
"D = 0.1 \t#m\n",
"\t\n",
"#calculations\n",
"k = Vc/r2**2\n",
"f = 64/R\n",
"T0 = f/4 *rho*V**2 /2\n",
"T02 = T0/10\n",
"hr = f*(V*10**-2)**2 /(2*9.81*D)\n",
"\t\n",
"#Results\n",
"print \"Friction factor = %.2f\"%(f)\n",
"print \" Shear stress at the pipe wall = %.3f N/m**2\"%(T02)\n",
"print \" Head loss per pipe length = %.5f m/m\"%(hr)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Friction factor = 0.18\n",
" Shear stress at the pipe wall = 0.078 N/m**2\n",
" Head loss per pipe length = 0.00037 m/m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.3 Page No : 222"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"Q = 2. \n",
"A = 0.196 \t#cm**2\n",
"D = 0.5 \t #ft\n",
"rho = 0.9*1.94\n",
"mu = 0.0008 \t#viscosity - lb s/ft**2\n",
"hl = 25.\n",
"g = 32.2 \t #ft/sec**2\n",
"L = 200. \t #ft\n",
"r = 2. \t #in\n",
"\t\n",
"#calculations\n",
"V = Q/A\n",
"R = D*V*rho/mu\n",
"f = hl*D*2*g/(L*V**2)\n",
"umax = V*(1+1.33*math.sqrt(f))\n",
"T0 = f*rho*V**2 /8\n",
"u2 = umax - 5.75* math.sqrt(T0/rho) *math.log10(D*12/r)\n",
"\t\n",
"#Results\n",
"print \"Center line velocity = %.1f fps\"%(umax)\n",
"print \" Shear stress = %.2f lb/ft**2\"%(T0)\n",
"print \" Velcoity at 2 in from center line = %.2f fps\"%(u2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Center line velocity = 12.9 fps\n",
" Shear stress = 0.88 lb/ft**2\n",
" Velcoity at 2 in from center line = 10.93 fps\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4 Page No : 228"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"f = 0.0131\n",
"d = 0.5 \t#m\n",
"\t\n",
"#calculations\n",
"V = 2.12 \t#m/s\n",
"R = 10**6\n",
"Q = math.pi*d**2 /4 *V \n",
"d1 = 32.8*10**-6 /(V* math.sqrt(f))\n",
"\n",
"#Results\n",
"print \"flow rate = %.3f m**3/s\"%(Q)\n",
"print \" nominal thickness = %.3e m\"%(d1)\n",
"\n",
"# note : rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"flow rate = 0.416 m**3/s\n",
" nominal thickness = 1.352e-04 m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.5 Page No : 241"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"dz = 260. \t#ft\n",
"ke = 0.5\n",
"f = 0.02\n",
"l = 5000. \t#length of pipe - ft\n",
"D = 10. \t#in\n",
"A2 = 0.545\n",
"\t\n",
"#calculations\n",
"V2by2g = dz/(1 + ke + f*l/(D/12))\n",
"V2 = V2by2g*2*32.2\n",
"V = math.sqrt(V2)\n",
"DV = D*V\n",
"Q = math.pi/4 *(D/12)**2 *V\n",
"\t\n",
"#Results\n",
"print \"Flow rate = %.2f cfs\"%(Q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flow rate = 6.40 cfs\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.6 Page No : 242"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"z = 260. \t#ft\n",
"f = 0.02\n",
"\t\n",
"#calculations\n",
"V2by2g = z/(1.11*256 + 6000*f)\n",
"V2 = V2by2g*2*32.2\n",
"V = math.sqrt(V2)\n",
"Q = 0.545*V\n",
"V3 = 16*V\n",
"H = z-f*6000*V2by2g\n",
"V3 = 16*V\n",
"\n",
"#Results\n",
"print \"rate of discharge = %.2f cfs\"%(Q)\n",
"print \"V3 = %.1f fps\"%V3\n",
"\n",
"# rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"rate of discharge = 3.51 cfs\n",
"V3 = 103.0 fps\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.7 Page No : 246"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\t\n",
"#Initialization of variables\n",
"g = 52.\n",
"Hp = 2.\n",
"\t\n",
"#calculations\n",
"Q = 3.48 \t#cfs\n",
"V6 = 3.48/0.196\n",
"P = -20.9 \t#ft\n",
"P2 = P*(g/144)\n",
"\t\n",
"#Results\n",
"print \"Flow rate = %.2f cfs\"%(Q)\n",
"print \" Pressure in the pipe = %.2f psi\"%(P2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flow rate = 3.48 cfs\n",
" Pressure in the pipe = -7.55 psi\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8 Page No : 250"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Initialization of variables\n",
"h = 10. \t#m\n",
"g = 9.81 \t#m/s**2\n",
"f1 = 0.019\n",
"f2 = 0.021\n",
"f3 = 0.020\n",
"z1 = 300. \t#m\n",
"z2 = 150. \t#m\n",
"z3 = 250. \t#m\n",
"d1 = 0.3 \t#m\n",
"d2 = 0.2 \t#m\n",
"d3 = 0.25 \t#m\n",
"\t\n",
"#calculations\n",
"print (\"part(a)\")\n",
"Vbyg = h/(f1*z1/d1 +f2*z2/d2 *(d1/d2)**4 + f3*z3/d3 *(d1/d3)**4)\n",
"V1 = math.sqrt(2*g*Vbyg)\n",
"Q = math.pi/4 *d1**2 *V1\n",
"print \" Flow rate = %.3f m**3/s\"%(Q)\n",
"print ('Part(b)')\n",
"Le2 = z2*f2/f1 *(d1/d2)**5\n",
"Le3 = z3*f3/f1 *(d1/d3)**5\n",
"Le1 = z1\n",
"Le = Le1+Le2+Le3\n",
"V1byg = h*d1/Le/f1\n",
"V2 = math.sqrt(2*g*V1byg)\n",
"Q1 = math.pi/4 *d1**2 *V2\n",
"print \" Flow rate = %.3f m**3/s\"%(Q1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"part(a)\n",
" Flow rate = 0.084 m**3/s\n",
"Part(b)\n",
" Flow rate = 0.084 m**3/s\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.9 Page No : 252"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"d1 = 6./12 \t#ft\n",
"d2 = 4./12 \t#ft\n",
"d3 = 8./12 \t#ft\n",
"l1 = 2000. \t#ft\n",
"l2 = 1600. \t#ft\n",
"l3 = 4000. \t#ft\n",
"f1 = 0.020\n",
"f2 = 0.032\n",
"f3 = 0.024\n",
"El1 = 200.\n",
"El2 = 50.\n",
"El3 = 120.\n",
"g = 32.2\n",
"\t\n",
"#calculations\n",
"Vc = math.sqrt(2*g*(El1-El2)/288.9)\n",
"Qc = math.pi/4 *d3**2 *Vc\n",
"Va = 1.346*Vc\n",
"Qa = math.pi/4 *d1**2 *Va\n",
"Vb = (d3**2 *Vc - d1**2 *Va)/d2**2\n",
"Qb = math.pi/4 *d2**2 *Vb\n",
"P = 62.4/144 *(El1 - El3 - f1*l1/d1 *Va**2 /(2*g))\n",
"\t\n",
"#Results\n",
"print \"Flowrate at A = %.3f cfs\"%(Qa)\n",
"print \"Flowrate at B = %.3f cfs\"%(Qb)\n",
"print \"Flowrate at C = %.3f cfs\"%(Qc)\n",
"print \"Pressure at P = %.2f psi\"%(P)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flowrate at A = 1.528 cfs\n",
"Flowrate at B = 0.490 cfs\n",
"Flowrate at C = 2.018 cfs\n",
"Pressure at P = 2.06 psi\n"
]
}
],
"prompt_number": 9
}
],
"metadata": {}
}
]
}