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"cells": [
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"cell_type": "heading",
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"metadata": {},
"source": [
"Chapter 6 : Dimensional Analysis and Dynamic Similitude"
]
},
{
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"level": 3,
"metadata": {},
"source": [
"Example 6.2 Page no 233"
]
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"input": [
"# Velocity of the flow\n",
"\n",
"# Given\n",
"\n",
"L = 10 # length scale lp/l\n",
"\n",
"# crue oil at 20 deg C\n",
"\n",
"rhop = 0.86*998.2 # density inn kg/m**3\n",
"\n",
"mup = 8*10**-3 # viscosity in Ns/m**2\n",
"\n",
"Vp = 2.5 # Velocity in m/s\n",
"\n",
"# water at 20 deg C\n",
"\n",
"rhom = 998.2 # density in kg/m**3\n",
"\n",
"mum = 1.005*10**-3 # viscosity in Ns/m**2\n",
"\n",
"# Solution\n",
"\n",
"Vm = Vp*L*(rhop/rhom)*(mum/mup) # velocity in m/s\n",
"\n",
"print \"Hence the model should be tested at a velocity of \",round(Vm,2),\"m/s. This velocity in the model is called corresponding velocity\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hence the model should be tested at a velocity of 2.7 m/s. This velocity in the model is called corresponding velocity\n"
]
}
],
"prompt_number": 3
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"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.3 Page no 233"
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"input": [
"# Mximum head on the crest and corresponding discharge for dynamically similar conditions\n",
"\n",
"# Given\n",
"\n",
"from __future__ import division\n",
"\n",
"from math import *\n",
"\n",
"l = 300 # length in ft\n",
"\n",
"Q = 100000 # discharge in cfs\n",
"\n",
"Cd = 3.8 # coefficient of discharge\n",
"\n",
"L = (1/50) # length scale\n",
"\n",
"# Solution\n",
"\n",
"Qm = 100000*(L)**(5/2) # model discharge in cfs\n",
"\n",
"print \"Maximum discharge, Qm = \",round(Qm,8),\"cfs\"\n",
"\n",
"H = (Q/(Cd*l))**(2/3) # height over spill way\n",
"\n",
"h = H*L*12 # head over spill model\n",
"\n",
"print \"Maximum head over crest = \",round(h,2),\"ft\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum discharge, Qm = 5.65685425 cfs\n",
"Maximum head over crest = 4.74 ft\n"
]
}
],
"prompt_number": 1
},
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"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
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