{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6: The Ideal Gas"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.1, page no. 101"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import scipy.integrate\n",
"\n",
"#intialization of variables\n",
"T1 = 40+460.0 #temperature(R)\n",
"T2 = 340+460.0 #temperature(R)\n",
"\n",
"#calculation\n",
"def Cv(T):\n",
"\tcv = 0.162+0.00046*T\n",
"\treturn cv\n",
"\t\n",
"du = scipy.integrate.quadrature(Cv, T1, T2)[0]\n",
"\n",
"#result\n",
"print \"Change in specific internal energy = %.1f B/lbm\" %du"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Change in specific internal energy = 138.3 B/lbm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2, page no. 103"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#initialization\n",
"\n",
"cp = 0.24 #B/lbm F\n",
"R = 53.3 #ft-lb/lbm F\n",
"\n",
"#calculation\n",
"cv = cp-R/778.0\n",
"\n",
"#result\n",
"print \"Specific heat at constant volume = %.3f B/lbm F\" %cv"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Specific heat at constant volume = 0.171 B/lbm F\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3, page no. 104"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import scipy.integrate\n",
"\n",
"#initialization\n",
"T1 = 1400+460.0 #temperature(R)\n",
"T2 = 1200+460.0 #temperature(R)\n",
"\n",
"#calculation\n",
"def Cp(T):\n",
"\tcp = 0.317- 1.2*100/T + 4*10**4/T**2\n",
"\treturn cp\n",
"\n",
"dh = scipy.integrate.quadrature(Cp, T1, T2)[0]\n",
"\n",
"#result\n",
"print \"Change in stagnation enthalpy = %.1f B/lbm\" %dh"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Change in stagnation enthalpy = -52.3 B/lbm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4, page no. 106"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import scipy.integrate\n",
"\n",
"#initialization\n",
"T1 = 100+460.0 #temperature(R)\n",
"T2 = 300+460.0 #temperature(R)\n",
"P1 = 15.0 #pressure(lb/in^2)\n",
"P2 = 30.0 #pressure(lb/in^2)\n",
"Cp = 0.3 #constant pressure(B/lbm F)\n",
"R = 40.0 #gas constant(ft-lb/lbm R)\n",
"\n",
"#calculation\n",
"def fun(f):\n",
"\ts=Cp/f\n",
"\treturn s\n",
"def fun1(f):\n",
"\ts2=R/(f*778)\n",
"\treturn s2\n",
"\n",
"ds1 = scipy.integrate.quadrature(fun, T1, T2)[0]\n",
"ds2 = scipy.integrate.quadrature(fun1, P1, P2)[0]\n",
"ds = ds1 - ds2\n",
"\n",
"#result\n",
"print \"Change in entropy = %.4f B/lbm R\" %ds"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Change in entropy = 0.0560 B/lbm R\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5, page no. 108"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#initialization\n",
"\n",
"T1 = 40+460.0 #temperature(R)\n",
"T2 = 340+460.0 #temperature(R)\n",
"P1 = 15.0 #pressure(lb/in^2)\n",
"cp = 0.24\n",
"cv = 0.171\n",
"\n",
"#calculation\n",
"gamma=cp/cv\n",
"P2=P1 *((T2/T1)**(gamma/(gamma-1)))\n",
"\n",
"#result\n",
"print \"Final pressure = %.1f lb/in^2\" %P2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Final pressure = 76.9 lb/in^2\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6, page no. 110"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#initialization\n",
"P1 = 16.0 #lb/in^2\n",
"P2 = 14.0 #lb/in^2\n",
"Tt = 83+460.0 #R\n",
"gamma = 1.4\n",
"cp = 0.24 #B/lbm F\n",
"\n",
"#calculation\n",
"T = Tt *(P2/P1)**((gamma-1)/gamma)\n",
"dh = cp*(Tt-T)\n",
"V = math.sqrt(2*32.2*778*dh)\n",
"\n",
"#result\n",
"print \"Actual temperature in the flow = %d R\" %T\n",
"print \"Flow velocity = %d ft/sec\" %V\n",
"\n",
"#difference in answeres is due to internal rounding off in Python"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Actual temperature in the flow = 522 R\n",
"Flow velocity = 494 ft/sec\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7, page no. 111"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"import scipy.integrate\n",
"\n",
"#initialization\n",
"T1 = 400.0+460.0 #R\n",
"P1 = 100.0 #lb/in^2\n",
"P2 = 20.0 #lb/in^2\n",
"T2 = 140.0+460.0 #R\n",
"Cp = 50.0\n",
"\n",
"#calculation\n",
"Pratio = P1/P2\n",
"Tratio = T1/T2\n",
"C = math.log(Tratio)/math.log(Pratio)\n",
"n=1/(1-C)\n",
"v1=Cp*T1/(144*P1)\n",
"v2=Cp*T2/(144*P2)\n",
"w=144*P1*v1**n\n",
"def fun(v):\n",
"\tp=w/v**n\n",
"\treturn p\n",
"\n",
"Work = scipy.integrate.quadrature(fun, v1, v2)[0]\n",
"\n",
"#result\n",
"print \"Work done = %f ft-lb/lbm\" %Work"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Work done = 45118.149895 ft-lb/lbm\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.8, page no. 113"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#initialization\n",
"P1 = 15.0 #lb/in^2\n",
"P2 = 20.0 #lb/in^2\n",
"T1 = 40+460 #R\n",
"T2 = 540+460 #R\n",
"\n",
"#calculation\n",
"#From table 6 at the two temperatures\"\n",
"phi1 = 0.58233\n",
"phi2 = 0.75042\n",
"ds = phi2-phi1-53.3*math.log(P2/P1)/778.0\n",
"\n",
"#result\n",
"print \"Entropy change = %.5f B/lbm R\" %ds"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Entropy change = 0.14838 B/lbm R\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.9, page no. 115"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#part a\n",
"\n",
"P2 = 1460.0 #pressure 2\n",
"P1 = 1900.0 #pressure 1\n",
"V2 = 1900.0 #volume 1\n",
"V1 = 1460.0 #volume 2\n",
"\n",
"pratio = (P2/P1)**3.5\n",
"vratio = (V2/V1)**2.5\n",
"\n",
"print \"Pressure ratio is \", round(pratio,2)\n",
"print \"Volume ratio is \", round(vratio,2)\n",
"\n",
"#part b\n",
"#from table 6\n",
"Pr2 = 50.34 #pressure 2\n",
"Pr1 = 141.51 #pressure 1\n",
"Vr2 = 10.743 #volume 1\n",
"Vr1 = 4.974 #volume 2\n",
"\n",
"pratio = (Pr2/Pr1)\n",
"vratio = (Vr2/Vr1)\n",
"\n",
"print \"Pressure ratio is \", round(pratio,2)\n",
"print \"Volume ratio is \", round(vratio,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure ratio is 0.4\n",
"Volume ratio is 1.93\n",
"Pressure ratio is 0.36\n",
"Volume ratio is 2.16\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}