{
"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": [
"\n",
"from math import *\n",
"\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",
"\n",
"\n",
"Rx = F1 - F2*cos(theta)-rho*Q*(V2*cos(theta)-V1)\n",
"\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": [
"\n",
"from math import *\n",
"\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",
"\n",
"Q = A1*V1 # Total discharge in m**3\n",
"\n",
"\n",
"V2 = sqrt((2*g*V1**2/(2*32.2))-3*2*g)\n",
"\n",
"\n",
"\n",
"Rx = -(rho*Q*(V2*cos(a)-80))\n",
"\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": [
"\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",
"\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": [
"\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",
"\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": [
"\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",
"\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": [
"\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",
"\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": [
"\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",
"\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",
"\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": [
"\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",
"\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": {}
}
]
}