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authorThomas Stephen Lee2015-09-04 22:04:10 +0530
committerThomas Stephen Lee2015-09-04 22:04:10 +0530
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Chapter 6 : Dimensional Analysis and Dynamic Similitude"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Example 6.2 Page no 233"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "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"
+ ]
+ }
+ ],
+ "source": [
+ "# 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\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Example 6.3 Page no 233"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Maximum discharge, Qm = 5.65685425 cfs\n",
+ "Maximum head over crest = 4.74 ft\n"
+ ]
+ }
+ ],
+ "source": [
+ "# 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\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
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+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
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+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}