{
"metadata": {
"name": "",
"signature": "sha256:994ba4703f91ead0a5ff4da6459451af8490fc9d0d26864c4973279092fd8132"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8 : Uniform Open Channel Flow"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.1 Page No : 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"b = 4. \t\t\t #m\n",
"y = 1.2 \t\t\t#m\n",
"sf = 0.001\n",
"n = 0.012\n",
"gam = 9.81*1000\n",
"\t\t\t\n",
"#calculations\n",
"A = b*y\n",
"R = A/(b+ 2*y)\n",
"Q = 1/n *A*R**(2./3) *sf**(1./2)\n",
"T = gam*R*sf\n",
"\t\t\t\n",
"#results\n",
"print \"Discharge = %.3f m**3/s\"%(Q)\n",
"print \" bed shear = %.2f N/m**2\"%(T)\n",
"#The answer in textbook is wrong for discharge. Please use a calculator."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Discharge = 10.442 m**3/s\n",
" bed shear = 7.36 N/m**2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.2 Page No : 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"b = 6. \t\t \t#m\n",
"y = 2. \t\t\t #m\n",
"sf = 0.005\n",
"slope = 2.\n",
"gam = 9.81*1000\n",
"Q = 65. \t\t\t#m**3/s\n",
"\t\t\t\n",
"#calculations\n",
"A = (b+ 2*y)*slope\n",
"P = b+ 2*y*math.sqrt(slope**2 +1)\n",
"R = A/P\n",
"V = Q/A\n",
"n = R**(2./3) *sf**(1./2) /V\n",
"\t\t\t\n",
"#results\n",
"print \"Value of mannings coefficient = %.3f\"%(n)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of mannings coefficient = 0.026\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.3 Page No : 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"b = 3. \t\t\t#m\n",
"y = 1. \t\t\t#m\n",
"sf = 0.005 #slope\n",
"n = 0.028 \n",
"gam = 9.81*1000\n",
"Q = 0.25 \t\t\t#discharge - m**3/s\n",
"slope = 1.5\n",
"\t\t\t\n",
"#calculations\n",
"A = 0.5 *b*y\n",
"P = 2*math.sqrt(1 + (slope)**2)\n",
"R = A/P\n",
"yx = Q*n/(slope * R**(2./3) *sf**(1./2))\n",
"y = yx**(3./8)\n",
"\t\t\t\n",
"#results\n",
"print \"depth = %.2f m\"%(y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth = 0.45 m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.4 Page No : 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"sf = 0.0064 #slope\n",
"n = 0.015\n",
"Q = 6. \t\t\t#discharge - m**3/s\n",
"gam = 9.81*1000\n",
"\t\t\t\n",
"#calculations\n",
"AR = n*Q/math.sqrt(sf)\n",
"print (\"On trial and error, \")\n",
"y = 0.385 \t\t\t#m\n",
"print \"normal depth = %.3f m\"%(y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"On trial and error, \n",
"normal depth = 0.385 m\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.5 Page No : 308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy import *\n",
"\t\t\t\n",
"#Initialization of variables\\\n",
"sf = 0.00007\n",
"n = 0.013\n",
"gam = 9.81*1000\n",
"V = 0.45 \t\t\t#velocity - m/s\n",
"Q = 1.4 \t\t\t#m**3/s\n",
"\t\t\t\n",
"#calculations\n",
"by = Q/V\n",
"#x = poly(0,\"x\")\n",
"#y = roots(x**2 -2.66*x +1.55)\n",
"y = roots([1,-2.66,1.55])\n",
"b = by/y\n",
"\t\t\t\n",
"#results\n",
"print \"y = \", y \n",
"print \"corresponding b = \" ,b"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"y = [ 1.7978675 0.8621325]"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"corresponding b = [ 1.73044516 3.60862294]\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.6 Page No : 310"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"sf = 0.0016 #slope\n",
"n = 0.02\n",
"Q = 0.84 \t\t\t#m**3/s\n",
"gam = 9.81*1000\n",
"\t\t\t\n",
"#calculations\n",
"y53 = Q*n/math.sqrt(sf)\n",
"y = y53**(3./5)\n",
"\t\t\t\n",
"#results\n",
"print \"depth of flow = %.2f m\"%(y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth of flow = 0.59 m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.7 Page No : 313"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"n = 0.015\n",
"Q = 1.3 \t\t\t#m**3/s\n",
"V = 0.6 \t\t\t#m/s\n",
"gam = 9.81*1000\n",
"\t\t\t\n",
"#calculations\n",
"alpha = 60. \t\t\t#degrees\n",
"A = 0.5 *(1./2)**2 *(180-alpha)/180 *math.pi -(1./4)**2 *math.radians(math.tan(alpha))\n",
"A = 0.206\n",
"P = 0.5*(180-alpha)/180 *math.pi\n",
"R = A/P\n",
"d2 = V*n/(R**(2./3))\n",
"d8 = Q*n*4*4**(2./3) /math.pi\n",
"d = math.sqrt(d8/d2)\n",
"sf = (d2**2/d**(4./3))\n",
"\t\n",
"#results\n",
"print \"Diameter = %.2f m\"%(d)\n",
"print \" slope = %.5f \"%(sf)\n",
"#The answer given in textbook is wrong. please check"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diameter = 1.53 m\n",
" slope = 0.00040 \n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.8 Page No : 315"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"b = 0.5 \t\t\t#m\n",
"y = 0.35 \t\t\t#m\n",
"sf = 0.001 #slope\n",
"nc = 0.016\n",
"gam = 9.81*1000\n",
"Q = 0.15 \t\t\t#m**3/s\n",
"\t\t\t\n",
"#calculations\n",
"A = b*y\n",
"P = b+ 2*y\n",
"R = A/P\n",
"ng = 1/Q *A*R**(2./3) *sf**(1./2)\n",
"n = (b*nc**(3./2) + 2*y*ng**(3./2))**(2./3) /(P**(2./3))\n",
"Q2 = 1/n *A*R**(2./3) *sf**(1./2)\n",
"\t\t\t\n",
"#results\n",
"print \"flow in case 2 = %.3f m**3/s\"%(Q2)\n",
"\n",
"# note : rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"flow in case 2 = 0.120 m**3/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.9 Page No : 316"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"b1 = 8. \t\t\t#m\n",
"b2 = 5. \t\t\t#m\n",
"y = 5. \t\t\t#m\n",
"b5 = 15. \t\t\t#m\n",
"b3 = 3. \t\t\t#m\n",
"b4 = 3. \t\t\t#m\n",
"y2 = 2. \t\t\t#m\n",
"y3 = 3. \t\t\t#m\n",
"n1 = 0.025\n",
"n2 = 0.035\n",
"sf = 0.0008\n",
"\t\t\t#calcuations\n",
"A = (b1+b2)*y\n",
"P = b1+ math.sqrt(b2**2 +y**2) + math.sqrt(b3**2 +b4**2)\n",
"R = A/P\n",
"Q1 = 1/n1 *A*R**(2./3) *sf**(1./2)\n",
"A2 = b5*y2 - 0.5*y2*y2 + 0.5*y3*y2\n",
"P2 = b5 + math.sqrt(b4**2 + y3**2)\n",
"R2 = A2/P2\n",
"Q2 = 1/n2 *A2*R2**(2./3) *sf**(1./2)\n",
"Q = Q1+Q2\n",
"\t\t\t\n",
"#results\n",
"print \"Total discharge = %.f m**3/s\"%(Q)\n",
"\n",
"# rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total discharge = 200 m**3/s\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.10 Page No : 320"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"Q = 12. \t\t\t#m**3/s\n",
"n = 0.023\n",
"A = 2.472\n",
"b = 0.472\n",
"sf = 1./8000\n",
"\t\t\t\n",
"#calculations\n",
"y8 = Q*n/A *2**(2./3) /sf**(1./2)\n",
"y = y8**(3./8)\n",
"b2 = b*y\n",
"\t\t\t\n",
"#results\n",
"print \"depth = %.3f m\"%(y)\n",
"print \" width = %.2f m\"%(b2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"depth = 2.819 m\n",
" width = 1.33 m\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8.11 Page No : 320"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"Q = 30. \n",
"V = 1.\n",
"\t\t\t\n",
"#calculations\n",
"A = Q/V\n",
"y = math.sqrt(A/(math.sqrt(2) + 0.5))\n",
"b = (A- 0.5*y**2)/y\n",
"\t\t\t\n",
"#results\n",
"print \"width = %.2f m\"%(b)\n",
"print \" depth = %.2f m\"%(y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"width = 5.60 m\n",
" depth = 3.96 m\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}