{
"metadata": {
"name": "",
"signature": "sha256:3ba83c4a558b39f0e29ab129afe92e29743f0b738fbd3a8e9c39956304967803"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 5 : Notches and weirs"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.1 Page No : 98"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"q = 0.2\n",
"Cd = 0.62\n",
"g = 9.81\n",
"\n",
"# Calculations \n",
"# using the relation\n",
"z = (3*q*(2**1.5))/(2*Cd*((2*g)**0.5))\n",
"b = z**0.4\n",
"\n",
"# Results \n",
"print \"the lenght of the notch in cm \",round((b*100),1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the lenght of the notch in cm 62.5\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.2 Page No : 98"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"b = 1.\n",
"H = 0.15\n",
"Cd1 = 0.62\n",
"x = 90.\n",
"g = 9.81\n",
"Cd2 = 0.58\n",
"\n",
"# Calculations \n",
"Q1 = 2*Cd1*b*((2*g*H*H*H)**0.5)/3\n",
"z = (15*Q1)/(8*Cd2*((2*g)**0.5)*(math.tan(math.radians(x/2))))\n",
"H1 = z**0.4\n",
"\n",
"# Results \n",
"print \"the depth over the traingular veir in cm\",round((H1*100),2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the depth over the traingular veir in cm 35.98\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.3 Page No : 99"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"x = 90.\n",
"Cd = 0.62 # co-efficient\n",
"H = 0.36\n",
"g = 9.81\n",
"\n",
"# Calculations \n",
"Q = (8*Cd*math.tan(math.radians(x/2))*((2*g)**0.5)*(H**2.5))/15\n",
"q = Q*1000\n",
"\n",
"# Results \n",
"print \"the actual discharge in litres/sec\",round(q,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the actual discharge in litres/sec 113.89\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.4 Page No : 100"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"x = 90.\n",
"H = 0.2\n",
"b = 0.3\n",
"Cd = 0.62\n",
"g = 9.81\n",
"\n",
"# Calculations \n",
"q1 = (8*Cd*math.tan(math.radians(x/2))*((2*g)**0.5)*(H**2.5))/15\n",
"q2 = 2*Cd*b*((2*g*H*H*H)**0.5)/3\n",
"q = q1+q2\n",
"\n",
"# Results \n",
"print \"discharge over the trapezoidal notch in m3/sec\",round(q,6)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"discharge over the trapezoidal notch in m3/sec 0.075327\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.5 Page No : 100"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"a = 20*(10**6)\n",
"x = 0.03\n",
"q = a*x\n",
"qf = q*0.4/3600\n",
"n = 2.\n",
"H = 0.6\n",
"\n",
"# Calculations \n",
"# using Francis formula \n",
"L = (qf/(1.84*(H**1.5)))+(0.1*n*H)\n",
"\n",
"# Results \n",
"print \"the lenght of the weir in m\",round(L,4)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the lenght of the weir in m 78.0786\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.6 Page No : 101"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"L = 36\n",
"v1 = 2\n",
"g = 9.81\n",
"H = 1.2\n",
"H1 = (v1*v1)/(2*g)\n",
"n = 2*12\n",
"w = 0.6\n",
"Nv = 11\n",
"\n",
"# Calculations \n",
"Lf = L-(Nv*w)\n",
"Q = 1.84*(Lf-(0.1*n*(H+H1)))*((H+H1)**1.5-(H1**1.5))\n",
"\n",
"# Results \n",
"print \"dischsrge over the weir in m3/sec\",round(Q,3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"dischsrge over the weir in m3/sec 75.261\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.7 Page No : 102"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"l = 0.77\n",
"H = 0.39\n",
"H1 = 0.6\n",
"Dp = H+H1\n",
"Cd = 0.623\n",
"g = 9.81\n",
"\n",
"# Calculations \n",
"Q = (2*Cd*l*((2*g*H*H*H)**0.5))/3\n",
"v = Q/(l*Dp)\n",
"Ha = (v*v)/(2*g)\n",
"q = (2*Cd*l*((2*g)**0.5)*(((H+Ha)**1.5)-(Ha**1.5)))/3\n",
"\n",
"# Results \n",
"print \"discharge in m3/sec\",round(q,6)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"discharge in m3/sec 0.357447\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.8 Page No : 103"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"Q1 = 0.005\n",
"Cd = 0.62\n",
"g = 9.81\n",
"Q2 = 0.75\n",
"h = 0.07\n",
"\n",
"# Calculations \n",
"z = (Q1*15)/(8*Cd*((2*g)**0.5)*(h**2.5))\n",
"H = h*((Q2/Q1)**0.4)\n",
"W = 2*H*z\n",
"\n",
"\n",
"print \"width of the water surface in m\",round(W,3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"width of the water surface in m 2.736\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.9 Page No : 104"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"b = 4.\n",
"H = 0.2\n",
"Cd = 0.62\n",
"g = 9.81\n",
"\n",
"# Calculations \n",
"Q1 = 2*Cd*b*((2*g*H*H*H)**0.5)/3\n",
"Q2 = (2*Cd*((2*g)**0.5)*(H**1.5)*(b-(0.2*H)))/3\n",
"m = 0.405+(0.003/H)\n",
"Q3 = m*b*((2*g)**0.5)*(H**1.5)\n",
"\n",
"# Results \n",
"print \"discharge when end contraction are supressed in m3/sec\",round(Q1,3)\n",
"print \"discharge when end contraction are taken into account by francis formula in m3/sec\",round(Q2,4)\n",
"print \"discharge when end contraction are taken into account by bazin formula in m3/sec\",round(Q3,5)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"discharge when end contraction are supressed in m3/sec 0.655\n",
"discharge when end contraction are taken into account by francis formula in m3/sec 0.6485\n",
"discharge when end contraction are taken into account by bazin formula in m3/sec 0.66559\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.10 Page No : 104"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"Cd = 0.6\n",
"x = 45.\n",
"H = 0.5\n",
"g = 9.81\n",
"\n",
"# Calculations and Results\n",
"q1 = (8*Cd*math.tan(math.radians(x/2))*((2*g)**0.5)*(H**2.5))/15\n",
"\n",
"print \"rate of flow over the rectangular notch in m3/sec\",round(q1,5)\n",
"\n",
"dq1 = 0.025\n",
"dh = dq1*H/2.5\n",
"h1 = H+dh\n",
"h2 = H-dh\n",
"print \"limiting values of head in centimeters\",h2*100,h1*100\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"rate of flow over the rectangular notch in m3/sec 0.10379\n",
"limiting values of head in centimeters 49.5 50.5\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5.11 Page No : 105"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Variables\n",
"Cd = 0.6\n",
"x = 90.\n",
"q = 0.05\n",
"g = 9.81\n",
"\n",
"# Calculations \n",
"dh = 0.00025\n",
"z = (15*q)/(8*Cd*((2*g)**0.5)*(math.tan(math.radians(x/2))))\n",
"H = z**0.4\n",
"error = 2.5*(dh/H)\n",
"\n",
"# Results \n",
"print \"the percentage error in the discharge\",round((error),5)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the percentage error in the discharge 0.00238\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}