{
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Chapter 5: Flow <h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.1, Page Number: 310<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"#(i)\n",
"\n",
"#variable declaration\n",
"d=75.0*10**-3 # diameter of pipe\n",
"a=math.pi*d**2/4 # area of cross section of pipe\n",
"v=760.0*10**-3 # flow velocity\n",
"\n",
"#calculation\n",
"Q=v*a\n",
"Q=Q*10**3\n",
"print('(i)\\nVolume Flow Rate Q=%.3f *10^-3 m^3/sec' %Q)\n",
"rho=1000.0\n",
"W=rho*Q*10**-3\n",
"\n",
"#result\n",
"print('\\n(ii)\\nMass Flow rate W=%.3f kg/sec' %W)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i)\n",
"Volume Flow Rate Q=3.358 *10^-3 m^3/sec\n",
"\n",
"(ii)\n",
"Mass Flow rate W=3.358 kg/sec"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.2, page Number:310<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"D=40.0 # Diameter of pipe\n",
"d=20.0 # Diameter of Orifice\n",
"mr=15.0 # Manometer reading\n",
"\n",
"#calculation\n",
"h=(13.6-1)*15.0*10.0\n",
"B=d/D\n",
"M=1/math.sqrt(1-(B**4))\n",
"Cd=0.5999\n",
"x=math.sqrt(2*9.8*h*(10**-3))\n",
"Q=x*Cd*M*(math.pi*((20*(10**-3))**2))/4\n",
"Q=Q*3600.0\n",
"\n",
"#result\n",
"print('Volumetric flow rate Q= %.4f m^3/hr' %Q)\n",
"#Answer slightly deviates from answer given in the book because of pi value.\n",
"#if pi=3.14, then answer is same as in textbook "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Volumetric flow rate Q= 4.2649 m^3/hr"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.3, Page Number: 310<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"#variable declaration\n",
"Re=10.0**5 # Reynolds number\n",
"D=40.0*10**-3 # Diameter of pipe \n",
"v=10**-6 # Kinematic viscosity in m^2/sec\n",
"\n",
"#calculation\n",
"V1=Re*v/D\n",
"A1=(math.pi*(40.0*10**-3)**2)/4\n",
"A2=(math.pi*(20.0*10**-3)**2)/4\n",
"V2=V1*A1/A2\n",
"\n",
"#result\n",
"print('V2=%.1f m/sec' %V2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"V2=10.0 m/sec"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.4, Page Number: 311<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"Cd=0.61 # discharge coefficient\n",
"D=40.0*10**-3 # Diameter of pipe\n",
"d=20.0*10**-3 # Diameter of Orifice \n",
"\n",
"#calculation\n",
"M=1/math.sqrt(1-(d/D)**4)\n",
"V2=10.0\n",
"rho=1000.0\n",
"g=9.8\n",
"X=V2*math.sqrt(rho/(2*g))/(Cd*M)\n",
"p_diff=X**2\n",
"p_diff=math.floor(p_diff/100)\n",
"p_diff=p_diff/100.0\n",
"\n",
"\n",
"#result\n",
"print('P1-P2 = %.2f kg/cm^2'%p_diff)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P1-P2 = 1.28 kg/cm^2"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.5, Page Number: 312<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"Cd=0.6 # discharge coefficient\n",
"D=150.0*10**-3 # Diameter of pipe\n",
"d=75.0*10**-3 # Diameter of Orifice \n",
"p=250.0 # pressure recorded\n",
"g=9.8 # acceleration due to gravity\n",
"rho=1000.0 # Water density \n",
"s=75.0*10**-3 # venturi tube size\n",
"\n",
"#(a)\n",
"\n",
"#calculation\n",
"Q=Cd*math.pi*s**2*math.sqrt(2*g*p/rho)/(4*math.sqrt(1-(d/D)**4)) \n",
"\n",
"#result\n",
"print('(a) For orifice plate\\nQ=%f m^3/sec = %.3f litres/sec'%(Q,Q*1000))\n",
"\n",
"#calculation\n",
"Cd1=0.99\n",
"Q2=Cd1*math.pi*s**2*math.sqrt(2*g*p/rho)/(4*math.sqrt(1-(d/D)**4))\n",
"\n",
"#result\n",
"print('\\n\\n(b)For venturi tube\\nQ=%f m^3/sec = %.2f litres/sec'%(Q2,Q2*1000))\n",
"#Answer slightly deviates from answer given in the book because of pi value.\n",
"#if pi=3.14, then answer is same as in textbook "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) For orifice plate\n",
"Q=0.006060 m^3/sec = 6.060 litres/sec\n",
"\n",
"\n",
"(b)For venturi tube\n",
"Q=0.009999 m^3/sec = 10.00 litres/sec"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.6, Page Number: 312<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#(i)\n",
"\n",
"#variable declaration\n",
"V=0.02 # volumetric flow rate\n",
"d=10*10**-2 # Diameter of pipe\n",
"\n",
"#calculation\n",
"A=math.pi*d**2/4\n",
"v=V/A\n",
"rho=1000.0\n",
"Re=rho*v*d/10**-3\n",
"Re=Re/100000.0\n",
"\n",
"#result\n",
"print('(i)\\nReynolds number(Re) = %.3f * 10^5'%Re)\n",
"\n",
"#(ii)\n",
"\n",
"#variable declaration\n",
"Cd=0.98 # discharge coefficient \n",
"D=20*10**-2 # Diameter of pipe \n",
"d=10*10**-2 # Diameter of orifice\n",
"\n",
"#calculation\n",
"M=1/math.sqrt(1-(d/D)**4)\n",
"a2=math.pi*d**2/4\n",
"Q=0.02\n",
"g=9.8\n",
"X=Q*math.sqrt(rho)/(M*Cd*a2*math.sqrt(2*g))\n",
"p_diff=math.ceil(X**2)\n",
"\n",
"#result\n",
"print('\\n(ii)\\nPressur_difference = %d kg/m^2 = %.4f kg/cm^2'%(p_diff,p_diff/10000))\n",
"#Answer slightly deviates from answer given in the book because of pi value.\n",
"#if pi=3.14, then answer is same as in textbook "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i)\n",
"Reynolds number(Re) = 2.546 * 10^5\n",
"\n",
"(ii)\n",
"Pressur_difference = 323 kg/m^2 = 0.0323 kg/cm^2"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.7, Page Number: 313<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"\n",
"\n",
"#variable declaration\n",
"g=9.81 #acceleration due to gravity\n",
"h=20.0 #height\n",
"\n",
"#calculation\n",
"v=math.sqrt(2*g*h)\n",
"d=300.0*10**-3\n",
"A=(math.pi*d**2)/4\n",
"A=math.floor(A*1000)\n",
"A=A/1000.0\n",
"Q=A*v\n",
"\n",
"#result\n",
"print('Q = %.3f m^3/sec'%Q)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Q = 1.387 m^3/sec"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.8, Page Number:313<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"Cd=0.6 # coefficient of discharge \n",
"g=9.8 #acceleration due to gravity\n",
"h=400*10**-3 #height\n",
"\n",
"#calculation\n",
"V=Cd*math.sqrt(2*g*h)\n",
"\n",
"#result\n",
"print('V = %.2f m/sec' %V)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"V = 1.68 m/sec"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.9, Page Number: 314<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"Cd=0.98 # coefficient of discharge\n",
"g=9.8 #acceleration due to gravity\n",
"h=900.0*10**-3 #height\n",
"\n",
"#calculation\n",
"V=Cd*math.sqrt(2*g*h)\n",
"V=math.floor(V*100)\n",
"V=(V/100.0)\n",
"\n",
"#result\n",
"print('V = %.2f m/sec' %V)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"V = 4.11 m/sec"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.10, Page Number:314<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"del_p=20*10**3 #Pa\n",
"dens_water=1000 #kg/m^3\n",
"dens_air=1.29 #kg/m^3\n",
"\n",
"#calculations\n",
"\n",
"#(i)When flowing fluid is water\n",
"v=math.sqrt(2*del_p/dens_water)\n",
"\n",
"#(ii)When flowing fluid is air\n",
"v1=math.sqrt(2*del_p/dens_air)\n",
"\n",
"#result\n",
"print('\\n(i)When flowing fluid is water\\n\\tV=%.3f m/sec'%v)\n",
"print('\\n(ii)When flowing fluid is air\\n\\tV=%.0f m/sec'%v1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"(i)When flowing fluid is water\n",
"\tV=6.325 m/sec\n",
"\n",
"(ii)When flowing fluid is air\n",
"\tV=176 m/sec"
]
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.11, Page Number: 314<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"# variable declaration\n",
"dens=1026.0 # density of see water\n",
"p=25.0*10**3 # pressure difference in manometer \n",
"\n",
"#calculation\n",
"V=math.sqrt(2*p/dens)\n",
"\n",
"#result\n",
"print('V=%.2f m/sec =%.3f km/hr'%(V,V*18/5))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"V=6.98 m/sec =25.131 km/hr"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.12, Page Number: 314<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"# variable declaration\n",
"dens=1.29 # air density at height \n",
"\n",
"#calculation\n",
"p=12.5*1000\n",
"V=math.sqrt(2*p/dens)\n",
"\n",
"\n",
"#result\n",
"print('V=%.2f m/sec =%.2f km/hr'%(V,V*18/5))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"V=139.21 m/sec =501.16 km/hr"
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.13, Page Number: 315<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"Cd=0.6 # discharge coefficient\n",
"Dp=0.05 # inside diameter of metering tube \n",
"Df=0.035 # diameter of rotameter \n",
"g=9.8 # acceleration due to gravity\n",
"rho_f=3.9*10**3 # density of cylindrical float\n",
"rho=1000.0 # water density \n",
"Vf=3.36*10**-5 # volume of the float\n",
"\n",
"#calculation\n",
"Q=Cd*((Dp**2-Df**2)/Df)*math.sqrt(math.pi*g*Vf*(rho_f-rho)/(2*rho))\n",
"Q=Q*10000.0\n",
"\n",
"#result\n",
"print('Volumetric flow Q=%.4f *10^-4 m^3/sec' %Q)\n",
"#Answer slightly deviates from answer given in the book because of pi value.\n",
"#if pi=3.14, then answer is same as in textbook "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Volumetric flow Q=8.4652 *10^-4 m^3/sec"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.14, Page number: 315<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"# variable declaration\n",
"Cd=1 # discharge coefficient\n",
"Dp=0.018 # inside diameter of metering tube \n",
"Df=0.015 # diameter of rotameter \n",
"g=9.81 # acceleration due to gravity\n",
"rho_f=2.7 # density of cylindrical float\n",
"rho=0.8 # water density \n",
"Vf=520.0*10**-9 # volume of the float\n",
"\n",
"#case 1\n",
"\n",
"#caculation\n",
"Qmin=Cd*((Dp**2-Df**2)/Df)*math.sqrt(math.pi*g*Vf*(rho_f-rho)/(2*rho))\n",
"Qmin=Qmin*100000.0\n",
"\n",
"#result\n",
"print('Case 1: When float is at the bottom\\n Volumetric flow Qmin=%.3f *10^-5 m^3/sec'%Qmin)\n",
"\n",
"#case 2\n",
"\n",
"#calculation\n",
"Dp2=0.0617\n",
"Qmax=Cd*((Dp2**2-Df**2)/Df)*math.sqrt(math.pi*g*Vf*(rho_f-rho)/(2*rho))\n",
"Qmax=Qmax*100000\n",
"\n",
"#result\n",
"print('\\n\\nCase 2: When float is at the bottom\\n Volumetric flow Qmax=%.2f *10^-5 m^3/sec'%Qmax)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case 1: When float is at the bottom\n",
" Volumetric flow Qmin=2.879 *10^-5 m^3/sec\n",
"\n",
"\n",
"Case 2: When float is at the bottom\n",
" Volumetric flow Qmax=104.17 *10^-5 m^3/sec"
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.15, Page Number:316<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"# variable declaration\n",
"W=165.0 # weight of material on section of length\n",
"R=328.0 # Conveyor speed m/min\n",
"L=16.0 # Length of weighting platform in m\n",
"\n",
"#calculation\n",
"Q=W*R/L\n",
"\n",
"#result\n",
"print('Flow Rate Q=%.2f kg/min =%.1f kg/hour'%(Q,Q/60))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flow Rate Q=3382.50 kg/min =56.4 kg/hour"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.16, Page Number:316<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#variable declaration\n",
"f=100.0 # beat frequency\n",
"d=300.0*10**-3 # Sound path\n",
"a=45.0 #angle between transmeter and receiver in degrees\n",
"\n",
"#calculation\n",
"a_rad=45.0*math.pi/180.0\n",
"v=f*d/(2*math.cos(a_rad))\n",
"\n",
"#Result\n",
"print('Fluid Velocity V=%.1f m/sec'%v)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Fluid Velocity V=21.2 m/sec"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.17, Page Number: 316<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"# variable declaration\n",
"r=150.0 # speed of rotation\n",
"v=120.0 # volume trapped between gears and casting\n",
"\n",
"#clculation\n",
"Q=4.0*v*r\n",
"\n",
"#result\n",
"print('Volume flow rate Q=%d cm^3/min = %d litres/min'%(Q,Q/1000))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Volume flow rate Q=72000 cm^3/min = 72 litres/min"
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.18, Page Number: 317<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"# variable declaration\n",
"Q=2500.0 # Quantitty flow rate\n",
"d=2.75 # inner diameter\n",
"\n",
"#calculation\n",
"a=(math.pi*d**2)/4\n",
"v=Q/(60*a)\n",
"B=60.0\n",
"e=B*d*10**-2*v*10**-2\n",
"\n",
"#result\n",
"print('Induced emf e =%.4f V=%.1f mV'%(e,e*1000))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Induced emf e =0.1157 V=115.7 mV"
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.19, Pae Number:317<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"# variable declaration\n",
"e=0.2*10**-3 # voltage of electromagnetic flow meter\n",
"B=0.08 # Flux density\n",
"l=10.0*10**-2 # Diameter of pipe\n",
"\n",
"#calculation\n",
"v=e/(B*l)\n",
"\n",
"#result\n",
"print('V = %.3f m/sec = %.2f cm/sec'%(v,v*100))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"V = 0.025 m/sec = 2.50 cm/sec"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5.20, Page Number: 317<h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"# variable declaration\n",
"ei=0.15*10**-3 # peak value\n",
"em=2*ei # p-p amplifier output \n",
"B=0.1 # flux density\n",
"l=60.0*10**-3 # diameter of the pipe\n",
"\n",
"#calculation\n",
"v=em/(B*l)\n",
"\n",
"#result\n",
"print('Velocity of flow V = %.2f m/sec = %.1f cm/sec'%(v,v*100))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity of flow V = 0.05 m/sec = 5.0 cm/sec"
]
}
],
"prompt_number": 20
}
],
"metadata": {}
}
]
}