{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2 : Fluid Statics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1 Page No : 44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"h1 = 1.5 \t\t\t#m\n",
"h2 = 2. \t\t\t#m\n",
"g1 = 800. \t\t\t#kg/m**3\n",
"g2 = 1000. \t\t\t#kg/m**3\n",
"g = 9.81\n",
"\t\t\t\n",
"#calculations\n",
"P = h1*g*g1 + h2*g*g2\n",
"\t\t\t\n",
"#results\n",
"print \"Pressure at the bottom of the vessel = %.2f kN/m**2\"%(P/1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure at the bottom of the vessel = 31.39 kN/m**2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2 Page No : 44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"depth = 8000. \t\t\t#m\n",
"sw = 10.06 \t\t\t#kN/m**3\n",
"BM = 2.05*10**9 \t\t\t#N/m**2\n",
"\t\t\t\n",
"#calculations\n",
"g = sw*10**3 /(1- sw*10**3 *depth/BM)\n",
"Ph = 2.3*BM*math.log10(BM/(BM-depth*9.81*1025))\n",
"\t\t\t\n",
"#results\n",
"print \"Specific weight = %.2f kN/m**2\"%(g/1000)\n",
"print \" Pressure at depth h = %.2f MN/m**2\"%(Ph/10**6)\n",
"\n",
"# note : rounding off error."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Specific weight = 10.47 kN/m**2\n",
" Pressure at depth h = 81.97 MN/m**2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.3 Page No : 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"Patm = 101.3/9.81 \t\t\t#m of water\n",
"x1 = 0.45 \t\t\t#m\n",
"x2 = 0.3 \t\t\t#m\n",
"s1 = 920. \t\t\t#Kg/m**3\n",
"s2 = 13.6 \t\t\t#Kg/m**3\n",
"g = 9.81 \t\t\t#m/s**2\n",
"\t\t\t\n",
"#calculations\n",
"Pa = (s1*x1*g + s2*x2*g)/1000\n",
"Pa2 = Pa*10**3/(1000*g)\n",
"Pa3 = Pa/(s2)\n",
"\t\t\t\n",
"#results\n",
"print \"Pressure at A = %.1f kPa\"%Pa\n",
"print \" Pressure at A = %.3f m of water\"%(Pa2)\n",
"print \" Pressure at A = %.3f m of mercury\"%(Pa3)\n",
"print \" Pressure at A = %.1f m of water absolute\"%(Pa/1000 +101.3)\n",
"print \" Pressure at A = %.3f m of mercury\"%(Pa2+10.3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure at A = 4.1 kPa\n",
" Pressure at A = 0.418 m of water\n",
" Pressure at A = 0.302 m of mercury\n",
" Pressure at A = 101.3 m of water absolute\n",
" Pressure at A = 10.718 m of mercury\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.4 Page No : 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"sg = 1.25 # gravity\n",
"d = 0.5 \t\t\t#m\n",
"d2 = 13.5*10**-2\t#m\n",
"sw = 9.81 \t\t\t#specific weight of water - kN/m**2\n",
"\t\t\t\n",
"#calculations\n",
"sl = sg*sw #specific weight of liquid\n",
"sm = 13.6*sw #specfic weight of mercury\n",
"Pa = sl*d - sm*d2\n",
"\t\t\t\n",
"#results\n",
"print \"Pressure at A = %.2f kN/m**2 vacuum \"%(-Pa)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure at A = 11.88 kN/m**2 vacuum \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.5 Page No : 56"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"#Following values are ontained from the figure 2.17\n",
"s1 = 0.85\n",
"s2 = 13.6\n",
"z1 = 30\n",
"z2 = 15\n",
"z3 = 20\n",
"z4 = 35\n",
"z5 = 60\n",
"\t\t\t\n",
"#calculations\n",
"dHa = s1*(z1+z5+z3-z4) +s2*z4 -z3+s2*z2-s1*(z1+z2) #Ha-Hb\n",
"Pd = 1000*9.81*dHa/100 #Pa-Pb\n",
"\t\t\t\n",
"#results\n",
"print \"Pressure difference = %.2f kN/m**2\"%(Pd/1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure difference = 67.25 kN/m**2\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.6 Page No : 57"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"P = 450 \t\t\t#pressure - kN/m**2\n",
"alt = 2000 \t\t\t#altitude - m\n",
"r = 610 \t\t\t#atmospheric pressure - mm of mercury\n",
"\t\t\t\n",
"#calculations\n",
"Pat = 760-r\n",
"Pat2 = Pat*13.6*9.81*10**-3\n",
"Pg = Pat2+P\n",
"\t\t\t\n",
"#results\n",
"print \"Gauge reading = %.2f kN/m**2\"%(Pg)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Gauge reading = 470.01 kN/m**2\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.7 Page No : 62"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"g = 9.81 \t\t\t#kN/m**2\n",
"hc = 16.25 \t\t\t#m\n",
"w = 1.5 \t\t\t#width - m\n",
"b = 2.5 \t\t\t#depth - m\n",
"f = 0.3 #coefficient of friction\n",
"Pi = 50. \t\t\t#weight of gate - kN\n",
"\t\t\t\n",
"#calculations\n",
"P = g*hc*w*b\n",
"Preq = Pi+f*P\n",
"\t\t\t\n",
"#results\n",
"print \"Force required to lift the gate = %.2f kN\"%(Preq)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Force required to lift the gate = 229.34 kN\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.8 Page No : 62"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"a = 6. \t\t\t#m\n",
"b = 8. \t\t\t#m\n",
"\t\t\t\n",
"#calculations\n",
"Ixy = 9./32 *b**4 /4\n",
"xp = Ixy/(2./3 *b *1./2 *a*b)\n",
"ICG = 1./36 *a*b**3\n",
"yp = 2./3*b + ICG/(2./3 *b* 1./2 *a*b )\n",
"\t\t\t\n",
"#results\n",
"print \"The coordinates of centre of pressure are %.2f,%d\"%(xp,yp)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The coordinates of centre of pressure are 2.25,6\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.9 Page No : 63"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"z = 1.2 \t\t\t#m\n",
"y = 1. \t\t\t#m\n",
"\t\t\t\n",
"#calculations\n",
"hp = 0.6 + 1./12 *y*z**3 /(0.6*y*z)\n",
"\t\t\t\n",
"#results\n",
"print \"Position of hinge = %.1f m\"%(hp)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Position of hinge = 0.8 m\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.10 Page No : 64"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from sympy import *\n",
"\t\t\t\n",
"#Initialization of variables\n",
"r = 0.75 \t\t\t#radius of plane - m\n",
"gam = 8. \t\t\t#specific weight of fluid - kN/m**3\n",
"\t\t\t\n",
"#calculations\n",
"P = gam*2./3 *r**3\n",
"hp = Symbol('hp')\n",
"hp = 4*r/(3*math.pi) + (math.pi/gam - gam/(9*math.pi)) * r**4/(4*r/(3*math.pi) * 1./2*math.pi*r**3)\n",
"\n",
"\t\t\t\n",
"#results\n",
"print \" Total pressure = %.2f kN\"%(P)\n",
"print \"Total pressure location = %.3f m\"%(hp)\n",
"\n",
"# note : answer is slightly different because of rounding off error. please check."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Total pressure = 2.25 kN\n",
"Total pressure location = 0.483 m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.11 Page No : 65"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"B = 3. \t\t\t#m\n",
"b = 2. \t\t\t#m\n",
"h1 = 0.75 \t\t\t#m\n",
"h2 = 1. \t\t\t#m\n",
"sg = 0.9 #specific gravity\n",
"\t\t\t\n",
"#calculations\n",
"IP = sg*9.81*h2\n",
"F1 = 0.5*IP*h2\n",
"F2 = IP*h1\n",
"F3 = 0.5*(9.81*h1)*h1\n",
"F = B*(F1+F2+F3)\n",
"ybar = (F1*(h1+ 1./3) + F2* h1/2 + F3* h1/3)/(F1+F2+F3)\n",
"\t\t\t\n",
"#results\n",
"print \"Total force = %.2f kN\"%(F)\n",
"print \"Location = %.3f m from the base\"%(ybar)\n",
"\n",
"# note : rounding off error."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total force = 41.39 kN\n",
" Location = 0.577 m from the base\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.12 Page No : 67"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from scipy.integrate import quad\n",
"\t\t\t\n",
"#Initialization of variables\n",
"g = 1000*9.81 \t\t\t#kg/m**3\n",
"hc = 20. \t\t\t#m\n",
"Ax = 40.*1 \t\t\t#m**2\n",
"y1 = 0. \t\t\t#m\n",
"y2 = 40. \t\t\t#m\n",
"\t\t\t\n",
"#calculations\n",
"Fx = g*hc*Ax\n",
"def fy(y):\n",
" return (12*y)**(1./3)\n",
"\n",
"Fy = quad(fy,y1,y2)\n",
"Fy = g*Fy[0]\n",
"F = math.sqrt(Fx**2 +Fy**2)\n",
"\t\t\t\n",
"#results\n",
"print \"Net force = %d kN\"%(F/1000)\n",
"#The answer is a bit different due to rounding off error in the textbook"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Net force = 8179 kN\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.13 Page No : 68"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"g = 9.81 \t\t\t#kN/m**2\n",
"hc = 1. \t\t\t#m\n",
"l = 3. \t\t\t#m\n",
"b = 0.5 \t\t\t#m\n",
"\t\t\t\n",
"#calculations\n",
"Ax = l*b \t\t\t#m**2\n",
"Fx = g*hc*Ax\n",
"Fz = g*(0.5* math.pi/4 *b**2)*l\n",
"F = math.sqrt(Fx**2 + Fz**2)\n",
"theta = math.degrees(math.atan(Fz/Fx))\n",
"\t\t\t\n",
"#results\n",
"print \"Magintude of resultant force = %.3f kN\"%(F)\n",
"print \" Direction of the resultant force = %.1f deg\"%(theta)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magintude of resultant force = 14.996 kN\n",
" Direction of the resultant force = 11.1 deg\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.14 Page No : 71"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"r1 = 920. \t\t\t#density of ice - kg/m**3\n",
"r2 = 1030. \t\t\t#density of sea water - kg/m**3\n",
"\t\t\t\n",
"#calculations\n",
"VtbyV2 = r2/r1\n",
"V1byV2 = VtbyV2-1\n",
"V1byVt = 1./(1+1/V1byV2)\n",
"\t\t\t\n",
"#results\n",
"print \"fraction = %.3f \"%(V1byVt)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fraction = 0.107 \n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.15 Page No : 72"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"d = 3. \t\t\t #diameter of balloon - m\n",
"rh1 = 1.19 \t\t\t#density of air - kg/m**3\n",
"rh2 = 0.17 \t\t\t#density of helium - kg/m**3 \n",
"g = 9.81 \t\t\t#m/s**2\n",
"\t\t\t\n",
"#calculations\n",
"pay = (rh1-rh2)*g*math.pi/6 *d**3\n",
"\t\t\t\n",
"#results\n",
"print \" Pay load = %.2f N\"%(pay)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Pay load = 141.46 N\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.16 Page No : 76"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy import roots\t\t\t\n",
"#calculations\n",
"y = [6,-6,1]\n",
"z = roots(y)\n",
"\t\t\t\n",
"#results\n",
"print \"For stability, s must be greater than %.2f and less than %.2f and must be less than 1\"%(z[0],z[1])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"For stability, s must be greater than 0.79 and less than 0.21 and must be less than 1\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.17 Page No : 81"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"ax = 1.5 \t\t\t#m/s**2\n",
"g = 9.81 \t\t\t#m/s**2\n",
"\t\t\t\n",
"#calculations\n",
"alpha = math.degrees(math.atan(ax/g))\n",
"\t\t\t\n",
"#results\n",
"print \"The interface is inclined at %.f degrees with the horizontal\"%(alpha)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The interface is inclined at 9 degrees with the horizontal\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.18 Page No : 81"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\t\t\n",
"#Initialization of variables\n",
"d = 10. \t\t\t#diameter - cm\n",
"h = 25. \t\t\t#height - cm\n",
"hw = 15. \t\t\t#cm\n",
"g = 9.81 \t\t\t#m/s**2\n",
"\t\t\t\n",
"#calculations\n",
"z = d**2 *d*2/d**2\n",
"w = math.sqrt(z*2*g/(d/2)**2 *100)\n",
"N = w/(2*math.pi) *60\n",
"\t\t\t\n",
"#results\n",
"print \"Speed of rotation = %d rpm\"%(N)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Speed of rotation = 378 rpm\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.19 Page No : 82"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from scipy.integrate import quad\n",
"\t\t\t\n",
"#Initialization of variables\n",
"dia = 1. \t\t\t#diameter - m\n",
"h = 3. \t\t\t #height - m\n",
"rho = 1000. \t\t#kg/m**3\n",
"N = 80. \t\t\t#rpm\n",
"g = 9.81 \t\t\t#m/s**2\n",
"\n",
"#calculation\n",
"w = 2*math.pi*N/60\n",
"def fun(r):\n",
" return 0.5*rho*w**2 *r**3 *2*math.pi\n",
"\n",
"vec = quad(fun,0,dia/2)\n",
"Pt = vec[0] + math.pi/4 *dia**2 *(h-dia)*rho*g\n",
"\t\t\t\n",
"#results\n",
"print \"Total pressure on base = %.2f kN\"%(Pt/1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total pressure on base = 18.85 kN\n"
]
}
],
"prompt_number": 15
}
],
"metadata": {}
}
]
}