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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:cd2be77f3b9478c6cae134ea907a28e897f525fa56fe0f236e6cf640bce7cb59"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Chapter 5 : Fluid Momentum"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.1 Page no 192"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Resultant force on the elbow\n",
+ "\n",
+ "from math import *\n",
+ "\n",
+ "# Given\n",
+ "\n",
+ "Q = 0.3 # Water flow rate in m**3/s\n",
+ "\n",
+ "d1 = 0.3 # diameter at inlet in meters\n",
+ "\n",
+ "A1 = pi*d1**2/4 # inlet area in m**2\n",
+ "\n",
+ "d2 = 0.15 # diameter at outlet in m\n",
+ "\n",
+ "A2 = pi*d2**2/4 # area at outlet in m**2\n",
+ "\n",
+ "P1 = 175*10**3 # inlet pressure in kN/m**2\n",
+ "\n",
+ "P2 = 160*10**3 # Pressure at outlet in kN/m**2\n",
+ "\n",
+ "F1 = P1*A1 # Force at inlet\n",
+ "\n",
+ "F2 = P2*A2 # Force at outlet\n",
+ "\n",
+ "rho = 1000 # density of water in kg/m**3\n",
+ "\n",
+ "V1 = Q/A1 # inlet velocity in m/s\n",
+ "\n",
+ "V2 = Q/A2 # Velocity at outlet in m/s\n",
+ "\n",
+ "theta = 45*pi/180 # angle in deg\n",
+ "\n",
+ "# Soultion\n",
+ "\n",
+ "# Applying the X momentum equation we get\n",
+ "\n",
+ "Rx = F1 - F2*cos(theta)-rho*Q*(V2*cos(theta)-V1)\n",
+ "\n",
+ "# Applying the Y momentum equation\n",
+ "\n",
+ "Ry = F2*sin(theta)+rho*Q*(V2*sin(theta)-0)\n",
+ "\n",
+ "R = sqrt(Rx**2+Ry**2)\n",
+ "\n",
+ "print \"Resultant force on the elbow = \",round(R,2),\"N\"\n",
+ "\n",
+ "a = atan(Ry/Rx)*180/pi\n",
+ "\n",
+ "print \"Angle of resultant force = \",round(a,4),\"deg\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant force on the elbow = 9800.58 N\n",
+ "Angle of resultant force = 34.8516 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.2 Page no 194"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Force exerted by the jet on the vane\n",
+ "\n",
+ "from math import *\n",
+ "\n",
+ "# Given\n",
+ "\n",
+ "V1 = 80 # Velocity in ft/s\n",
+ "\n",
+ "A1 = 0.1 # area in ft**2\n",
+ "\n",
+ "g = 32.2 # Acceleration due to gravity in ft/s**2\n",
+ "\n",
+ "rho = 1.94 # density in lb/ft**3\n",
+ "\n",
+ "a = pi/3 # angle of pipe bend\n",
+ "\n",
+ "# Solution\n",
+ "\n",
+ "Q = A1*V1 # Total discharge in m**3\n",
+ "\n",
+ "# Applying bernoullis at point 1 and 2\n",
+ "\n",
+ "V2 = sqrt((2*g*V1**2/(2*32.2))-3*2*g)\n",
+ "\n",
+ "# Pressure at the end of the section are atmospheric and hence 0\n",
+ "\n",
+ "# momentum equation in X direction\n",
+ "\n",
+ "Rx = -(rho*Q*(V2*cos(a)-80))\n",
+ "\n",
+ "# momentum equation in Y direction\n",
+ "\n",
+ "Ry = (rho*Q*(V2*sin(a)-0))\n",
+ "\n",
+ "R = sqrt(Rx**2+Ry**2)\n",
+ "\n",
+ "print \"Resultant force = \",round(R,0),\"lbs\"\n",
+ "\n",
+ "ang = atan(Ry/Rx)*180/pi\n",
+ "\n",
+ "print \"Angle of resultant force = \",round(ang,4),\"deg\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant force = 1232.0 lbs\n",
+ "Angle of resultant force = 59.2396 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example no 5.3 Page no 195 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Force needed to hold the Y position \n",
+ "\n",
+ "# Given\n",
+ "\n",
+ "from __future__ import division\n",
+ "\n",
+ "from math import *\n",
+ "\n",
+ "Q1 = 0.5 # discharge from pipe 1 in m**3/s\n",
+ "\n",
+ "Q2 = 0.3 # discharge from pipe 2 in m**3/s\n",
+ "\n",
+ "Q3 = 0.2 # discharge from pipe 3 in m**3/s\n",
+ "\n",
+ "d1 = 0.45 # diameter of pipe 1 in m\n",
+ "\n",
+ "d2 = 0.3 # diameter of pipe 2 in m\n",
+ "\n",
+ "d3 = 0.15 # diameter of pipe 3 in m\n",
+ "\n",
+ "A1 = pi*d1**2/4 # area in m**2\n",
+ "\n",
+ "A2 = pi*d2**2/4 # area in m**2\n",
+ "\n",
+ "A3 = pi*d3**2/4 # area in m**2\n",
+ "\n",
+ "P1 = 60*10**3 # Pressure at point 1 in kPa\n",
+ "\n",
+ "gma = 9810\n",
+ "\n",
+ "g = 9.81 # acceleration due to gravity in m/s**2\n",
+ "\n",
+ "rho = 1000 # density in kg/m**3\n",
+ "\n",
+ "# Solution\n",
+ "\n",
+ "V1 = Q1/A1\n",
+ "\n",
+ "V2 = Q2/A2\n",
+ "\n",
+ "V3 = Q3/A3\n",
+ "\n",
+ "P2 = gma*((P1/gma) + V1**2/(2*g) - V2**2/(2*g))\n",
+ "\n",
+ "P3 = gma*((P1/gma) + V1**2/(2*g) - V3**2/(2*g))\n",
+ "\n",
+ "F1 = P1*A1\n",
+ "\n",
+ "F2 = P2*A2\n",
+ "\n",
+ "F3 = P3*A3\n",
+ "\n",
+ "Rx = rho*(Q2*V2*cos(pi/6)-Q3*V3*cos(pi/9)-0)+F3*cos(pi/9)-F2*cos(pi/6)\n",
+ "\n",
+ "Ry = rho*((Q2*V2*sin(pi/6)+Q3*V3*sin(pi/9)-Q1*V1))+F3*sin(pi/9)-F2*sin(pi/6)-F1\n",
+ "\n",
+ "R = sqrt(Rx**2+Ry**2)\n",
+ "\n",
+ "a = atan(Ry/Rx)*180/pi\n",
+ "\n",
+ "print \"Resultant Force = \",round(R,0),\"N\"\n",
+ "\n",
+ "print \"Angle with horizontal = \",round(a,1),\"deg with horizontal\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resultant Force = 12489.0 N\n",
+ "Angle with horizontal = 69.2 deg with horizontal\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.4 Page no 199"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Normal force on the plate\n",
+ "\n",
+ "# Given\n",
+ "from math import *\n",
+ "\n",
+ "d = 2 # diameter in inches\n",
+ "\n",
+ "A = pi*d**2/(4*144) # Area of jet\n",
+ "\n",
+ "V = 100 # velocity of jet in ft/s\n",
+ "\n",
+ "Q = A*V # dischargge in ft**3/s\n",
+ "\n",
+ "gma = 62.4 # mass\n",
+ "\n",
+ "g = 32.2 # acceleration due to gravity in ft/s**2\n",
+ "\n",
+ "# Solution\n",
+ "\n",
+ "Rx = (gma*Q*V)/g # horizontal force required to keep plate in position\n",
+ "\n",
+ "print \"Normal force on the plate = \",round(Rx,0),\"lbs\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Normal force on the plate = 423.0 lbs\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.5 Page no 202"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Force on the plate ; work doen per second; efficiency\n",
+ "\n",
+ "# Given\n",
+ "\n",
+ "from math import *\n",
+ "\n",
+ "D = 0.075 # diameter in m\n",
+ "\n",
+ "A =pi*D**2/4 # area of jet\n",
+ "\n",
+ "V =15 # velocity of jet in m/s\n",
+ "\n",
+ "w = 9810 # specific weight\n",
+ "\n",
+ "g = 9.81 # acceleration due to gravity in m/s^2\n",
+ "\n",
+ "# Solution\n",
+ "\n",
+ "Q =A*V # Discharge in m**3/s\n",
+ "\n",
+ "Vp = 10 # velocity of plate in m/s\n",
+ "\n",
+ "Rx = w*Q*(V-Vp)/g # force in X direction\n",
+ "\n",
+ "print \"Force on the plate = \",round(Rx,2),\"N\"\n",
+ "\n",
+ "W = Rx*Vp\n",
+ "\n",
+ "print \"Work done per second = \",round(W,1),\"N.m/s\"\n",
+ "\n",
+ "Eff = 2*(V-Vp)*Vp/V**2\n",
+ "\n",
+ "E = 100*Eff\n",
+ "\n",
+ "print \"Efficiency = \",round(E,1),\"%\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force on the plate = 331.34 N\n",
+ "Work done per second = 3313.4 N.m/s\n",
+ "Efficiency = 44.4 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.6 Page no 204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Force exerted on the plate\n",
+ "\n",
+ "# Given\n",
+ "from math import *\n",
+ "\n",
+ "d = 3 # diameter in inches\n",
+ "\n",
+ "A = pi*d**2/(4*144) # Area of jet\n",
+ "\n",
+ "Q = 2 # discharge in ft**3/s\n",
+ "\n",
+ "rho = 1.94 # density in lbs/ft**3\n",
+ "\n",
+ "# Solution\n",
+ "\n",
+ "V = Q/A # velocity in ft/s\n",
+ "\n",
+ "alpha = pi/6 # inlet vane angle\n",
+ "\n",
+ "bta = pi/6 # outlet vane angle\n",
+ "\n",
+ "Rx = rho*Q*(V*cos(bta)+V*cos(alpha)) # force in X direction\n",
+ "\n",
+ "Ry = rho*Q*(V*sin(bta)-V*sin(alpha)) # force in Y direction\n",
+ "\n",
+ "print \"Force exerted in X direction = \",round(Rx,1),\"lbs\"\n",
+ "\n",
+ "print \"Force exerted in Y direction = \",round(Ry,1),\"lbs\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Force exerted in X direction = 273.8 lbs\n",
+ "Force exerted in Y direction = 0.0 lbs\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.7 Page no 207"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Angle of blade tips at inlet and exit ; work done on the vane; efficiency of the vane\n",
+ "\n",
+ "# Given\n",
+ "\n",
+ "from math import *\n",
+ "\n",
+ "V1 =40 # velocity in m/s\n",
+ "\n",
+ "Vp = 20 # velocity of the plate in m/s\n",
+ "\n",
+ "alpha = pi/6 # inlet vane angle\n",
+ "\n",
+ "bta = pi/9 # outlet vane angle\n",
+ "\n",
+ "g = 9.81\n",
+ "\n",
+ "# Solution\n",
+ "\n",
+ "V1x = V1*cos(alpha)\n",
+ "\n",
+ "Vw1 = V1x;\n",
+ "\n",
+ "V1y = V1*sin(alpha)\n",
+ "\n",
+ "dV = V1x - Vp\n",
+ "\n",
+ "theta = atan(V1y/dV)*180/pi\n",
+ "\n",
+ "Vr1 = V1y/sin(theta*pi/180)\n",
+ "\n",
+ "Vr2 = Vr1\n",
+ "\n",
+ "# from trial and error we get the blade tip angle at inlet and outlet\n",
+ "\n",
+ "print \"a ) Angle of blade top at inlet and Outlet, Phi = 4 deg\"\n",
+ "\n",
+ "phi = 4*pi/180 \n",
+ "\n",
+ "V2 = Vr2*sin(phi)/sin(bta)\n",
+ "\n",
+ "V2w = V2*cos(bta)\n",
+ "\n",
+ "W = (V2w+V1x)*Vp/g\n",
+ "\n",
+ "print \"b ) Work done per N of fluid per second = \",round(W,2),\"N.m\"\n",
+ "\n",
+ "Eff = (1 - (V2/V1)**2)*100\n",
+ "\n",
+ "print \"c ) Efficiency = \",round(Eff,2),\"%\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "a ) Angle of blade top at inlet and Outlet, Phi = 4 deg\n",
+ "b ) Work done per N of fluid per second = 80.31 N.m\n",
+ "c ) Efficiency = 98.4 %\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.8 Page no 211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Thrust on the plane; propeller efficiency ; theoretical horsepower ; pressure difference acros the blades\n",
+ "\n",
+ "# Given\n",
+ "\n",
+ "from math import *\n",
+ "\n",
+ "v = 220 # velocity in ft/s\n",
+ "\n",
+ "d = 6 # diameter of the propeller\n",
+ "\n",
+ "Q = 12000 # discharge in ft**3/s\n",
+ "\n",
+ "mf = 0.0022 # mass flow rate in slugs/ft**3\n",
+ "\n",
+ "# Solution\n",
+ "\n",
+ "V1 = v*5280/3600 # velocity in ft/s\n",
+ "\n",
+ "V = Q/(pi*d**2/4) # velocity in ft/s\n",
+ "\n",
+ "V4 = 2*V-V1\n",
+ "\n",
+ "F = mf*Q*(V4-V1) # thrust on the plane\n",
+ "\n",
+ "print \"a - Thrust on the plane = \",round(F,1),\"lbs\"\n",
+ "\n",
+ "Eff = V1/V # efficiency \n",
+ "\n",
+ "E = Eff*100\n",
+ "\n",
+ "print \"b - Theoretical efficiency = \",round(E,0),\"%\"\n",
+ "\n",
+ "Thp = F*V1/(500*Eff)\n",
+ "\n",
+ "print \"c - Theoretical horsepower required = \",round(Thp,0),\"hp\"\n",
+ "\n",
+ "dP = mf*(V4**2-V1**2)/2\n",
+ "\n",
+ "print \"d - Pressure difference across blades = \",round(dP,2),\"lbs/ft**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "a - Thrust on the plane = 5372.2 lbs\n",
+ "b - Theoretical efficiency = 76.0 %\n",
+ "c - Theoretical horsepower required = 4560.0 hp\n",
+ "d - Pressure difference across blades = 190.0 lbs/ft**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 11:23:19 +0000