{
"metadata": {
"name": "",
"signature": "sha256:e6f28e03dfd837b5aed00ee85654c1040a3b0c8129a67f41e8f2e4ba487b8f35"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9 : Steady Flow of Compressible Fluids"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.1 Page No : 268"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#Initialization of variables\n",
"T2 = 30. \t#C\n",
"T1 = 20. \t#C\n",
"cv = 716.\n",
"m = 15. \t#kg\n",
"cp = 1003.\n",
"\t\n",
"#calculations\n",
"di = cv*(T2-T1)\n",
"dU = di*m\n",
"dh = cp*(T2-T1)\n",
"dH = dh*m\n",
"\t\n",
"#Results\n",
"print \"Change in Internal energy = %d N m\"%(dU)\n",
"print \" Change in Enthalpy = %d Nm\"%(round(dH,-3))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Change in Internal energy = 107400 N m\n",
" Change in Enthalpy = 150000 Nm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.2 Page No : 268"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#Initialization of variables\n",
"cv = 716.\n",
"m = 15. \t#kg\n",
"cp = 1003.\n",
"T1 = 20.+273 \t#K\n",
"k = 1.4\n",
"ratio = 0.4\n",
"\t\n",
"#calculations\n",
"T2 = int((T1)*(1/ratio)**(k-1))\n",
"P1 = 95. \t#kN/m**2\n",
"P2 = int(P1*T2/(T1)/ratio)\n",
"di = round(cv*(T2-T1),-2)\n",
"dU = di*m\n",
"dh = round(cp*(T2-T1),-2)\n",
"dH = dh*m\n",
"\n",
"\n",
"#Results\n",
"print \"Final temperature = %d K\"%(T2)\n",
"print \" Final pressure = %d kN/m**2\"%(P2)\n",
"print \" Change in Internal energy = %d N m\"%(dU)\n",
"print \" Change in Enthalpy = %d Nm\"%(dH)\n",
"\n",
"#The answers are a bit different due to rounding off error.please check.\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Final temperature = 422 K\n",
" Final pressure = 342 kN/m**2\n",
" Change in Internal energy = 1386000 N m\n",
" Change in Enthalpy = 1941000 Nm\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.3 Page No : 271"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"k = 1.4\n",
"R = 1773.\n",
"v = 600. \t#fps\n",
"T = 660. \t#K\n",
"P = 100. \t#psia\n",
"cp = 6210.\n",
"g = 32.2\n",
"\t\n",
"#calculations\n",
"c = math.sqrt(k*R*T)\n",
"M = v/c\n",
"rho = k*P*144/c**2\n",
"Ps = P*144 + 0.5*(rho)*v**2 *(1+ 0.25*M**2)\n",
"Ts = (cp/g *T + v**2 /(2*g))*g/cp\n",
"\t\n",
"#Results\n",
"print \"Stagnation pressure = %d lb/ft**2\"%(Ps)\n",
"print \" Stagnation temperature = %.f R\"%(Ts)\n",
"\n",
"\n",
"# note :Please check the units of the answer.\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Stagnation pressure = 16736 lb/ft**2\n",
" Stagnation temperature = 689 R\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4 Page No : 275"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"g = 32.2\n",
"A = 0.0218 \t#ft**2\n",
"P1 = 25.6 \t#psia\n",
"T1 = 540. \t#K\n",
"k = 1.4\n",
"R = 1715.\n",
"\t\n",
"#calculations\n",
"G = g*A*P1*144/math.sqrt(T1) *math.sqrt(k/R *(2/(k+1))**((k+1)/(k-1)))\n",
"\t\n",
"#Results\n",
"print \"Flow rate = %.2f lb/s\"%(G)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flow rate = 1.84 lb/s\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.5 Page No : 278"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"P1 = 50. \t#psia\n",
"T1 = 540. \t#K\n",
"g = 32.2\n",
"R = 1715.\n",
"k = 1.4\n",
"P3 = 13.5 \t #psia\n",
"A2 = 0.0218 \t#ft**2\n",
"cp = 6000.\n",
"\t\n",
"#calculations\n",
"Pc = 0.528*P1\n",
"V32 = round(R*T1/g *k/(k-1) *(1- (P3/P1)**((k-1)/k)),-2)\n",
"V3 = round(math.sqrt(V32*2*g),-1)\n",
"G3 = g*A2*P1*144/math.sqrt(T1) *math.sqrt(k/R *(2/(k+1))**((k+1)/(k-1)))\n",
"T3 = T1 - V3**2 /(2*cp) \n",
"gam3 = g*P3*144/(R*T3)\n",
"gam2 = (Pc/P3 *gam3**k )**(1/k)\n",
"V2 = G3/gam2/A2\n",
"T2 = (V3**2 -V2**2)/(2*cp) + T3\n",
"A3 = G3/gam3/V3\n",
"D3 = math.sqrt(4/math.pi *A3)\n",
"G2 = G3\n",
"\n",
"#Results\n",
"print \" velocity at section 3 = %d fps\"%(V3)\n",
"print \" Flow rate at section 3 = %.3f lb/s\"%(G3)\n",
"print \" temperature at section 3 = %d R\"%(T3)\n",
"print \" velocity at section 2 = %d fps\"%(V2)\n",
"print \" Flow rate at section 2 = %.3f lb/s\"%(G2)\n",
"print \" temperature at section 2 = %d R\"%(T2)\n",
"print \" Required Diameter = %.2f in\"%(D3*12)\n",
"\n",
"# book anwers are wrong. please check."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" velocity at section 3 = 1420 fps\n",
" Flow rate at section 3 = 3.596 lb/s\n",
" temperature at section 3 = 371 R\n",
" velocity at section 2 = 1041 fps\n",
" Flow rate at section 2 = 3.596 lb/s\n",
" temperature at section 2 = 449 R\n",
" Required Diameter = 2.18 in\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.6 Page No : 281"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#Initialization of variables\n",
"P1 = 10. \t#psia\n",
"T1 = 460+40. \t#R\n",
"R = 1715.\n",
"k = 1.4\n",
"V1 = 1400. \t#fps\n",
"\t\n",
"#calculations\n",
"rho1 = P1/(R*T1)\n",
"c1 = math.sqrt(k*R*T1)\n",
"M1 = V1/c1\n",
"P2 = P1 * (2*k*M1**2 - (k-1))/(k+1)\n",
"V2 = V1*((k-1)*M1**2 +2)/((k+1)*M1**2) \n",
"rho2 = rho1*V1/V2\n",
"T2 = P2/rho2/R\n",
"P22 = 122.5\n",
"V22 = 286\n",
"T22 = 328\n",
"\t\n",
"#Results\n",
"print \"Pressure at point 2 = %.1f psia and %.1f N/m**2\"%(P2,P22)\n",
"print \" Velocity at point 2 = %d fps and %d m/s\"%(V2,V22)\n",
"print \" Temperature at point 2 = %d R and %d K\"%(T2,T22)\n",
"print (\"Similarly it can be done for SI units\")\n",
"\n",
"# note : ronding off error. please check."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pressure at point 2 = 17.4 psia and 122.5 N/m**2\n",
" Velocity at point 2 = 947 fps and 286 m/s\n",
" Temperature at point 2 = 588 R and 328 K\n",
"Similarly it can be done for SI units\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.7 Page No : 286"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"A = 140. \t#in**2\n",
"P = 48. \t#lb/in**2\n",
"mu = 3.78*10**-7\n",
"g = 32.2\n",
"G = 100. \t#lb/s\n",
"p = 80. \t#lb/in**2\n",
"T = 65.+460 \t#R\n",
"k = 1.4\n",
"R = 1715.\n",
"\t\n",
"#calculations\n",
"Rh = A/P /12\n",
"R1 = G*4*Rh/ (mu*g*A/144)\n",
"R2 = R1\n",
"f = 0.0083\n",
"gam1 = p*g*144/(R*T)\n",
"V1 = G*144/gam1/A\n",
"c = math.sqrt(k*R*T)\n",
"M1 = V1/c\n",
"M2 = 1/math.sqrt(k)\n",
"D = 4*Rh\n",
"L = ((1-M1**2 /M2**2)/(k*M1**2) - 2*math.log(M2/M1) )*D/f\n",
"Ln = 500 \t#ft\n",
"P2 = math.sqrt((p*144)**2 - G**2 *R*T/(g**2 *(A/144)**2 *f*Ln/D))\n",
"Pa = 12.2\n",
"\t\n",
"#Results\n",
"print \"Max. length = %d ft\"%(round(L,-1))\n",
"print \" Pressure required = %.1f psia\"%(P2/144 -Pa)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Max. length = 1260 ft\n",
" Pressure required = 67.1 psia\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.8 Page No : 287"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"G = 100. \t#lb/s\n",
"g = 32.2\n",
"V2 = 300. \t#fps\n",
"V1 = 250. \t#fps\n",
"\t\n",
"#calculations\n",
"Qh = (V2**2 -V1**2)/(2*g)\n",
"Q = Qh*G\n",
"\t\n",
"#Results\n",
"print \"Thermal energy added = %.2f ft lb/s\"%(Q)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Thermal energy added = 42701.86 ft lb/s\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.9 Page No : 290"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\n",
"#Initialization of variables\n",
"gam1 = 0.41\n",
"g = 32.2\n",
"V1 = 250. \t#fps\n",
"R1 = 8.2*10**6\n",
"f = 0.0083\n",
"A = 0.97 \t#ft**2\n",
"G = 100. \t#lb/s\n",
"k = 1.4\n",
"P = 80. \t#pressure - psia\n",
"ratio = 0.8\n",
"R = 1715\n",
"\t\n",
"#calculations\n",
"rho1 = gam1/g\n",
"X = G**2 /(gam1*A)**2 + 2*k/(k-1) *(P*144/rho1)\n",
"P2 = (k-1)/2/k *(X*ratio*rho1 - G**2 /(g**2 *A**2 *ratio*rho1))\n",
"L = 563 \t#ft\n",
"rho2 = ratio*rho1\n",
"V2 = G/(rho2*g*A)\n",
"T2 = P2/(rho2*R)\n",
"\t\n",
"#Results\n",
"print \"Length = %d ft\"%(L)\n",
"print \" velocity = %.f fps\"%(V2)\n",
"print \" Temperature = %d R\"%(T2)\n",
"\n",
"# note : rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Length = 563 ft\n",
" velocity = 314 fps\n",
" Temperature = 524 R\n"
]
}
],
"prompt_number": 19
}
],
"metadata": {}
}
]
}