{
"metadata": {
"name": "",
"signature": "sha256:5a87247e3e7d335ec3f93a6763434ef47db612054d0c0f12922c9d7638e3f184"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 15 : Impulse Turbines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.1 Page No : 486"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy import *\n",
"\t\n",
"#Initialization of variables\n",
"z2 = 500.\t#ft\n",
"z1 = 300.\t#ft\n",
"D = array([1, 1.5, 2 ,2.5, 3, 4, 6])\n",
"g = 32.2\n",
"gam = 62.4\n",
"\t\n",
"#calculations\n",
"Dj = D/12\n",
"Vj = sqrt((z2-z1)*2*g/(1.04 + 640.*Dj**4))\n",
"Aj = math.pi/4 *Dj**2\n",
"Q = Aj*Vj\n",
"Pjet = gam*Q*Vj**2 /(2*g) /550\n",
"Pj = max(Pjet)\n",
"for i in range(0,len(Pjet)):\n",
" if(Pjet[i] == Pj):\n",
" break\n",
" \n",
"diameter = D[i]\n",
"\t\n",
"#Results\n",
"print \"Dj,in Dj,ft Vj,fps Aj,ft**2 Q=AjVj,cfs Pjet,hp\"\n",
"for i in range(len(D)):\n",
" print \"%5.1f %5.3f %5.f %7.4f %5.2f %5.1f\"%(D[i],Dj[i],Vj[i],Aj[i],Q[i],Pjet[i])\n",
"print \"Thus a pipe of %d in will be the optimum\"%(diameter)\n",
"\n",
"# answer are slightly different because of rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dj,in Dj,ft Vj,fps Aj,ft**2 Q=AjVj,cfs Pjet,hp\n",
" 1.0 0.083 110 0.0055 0.60 12.7\n",
" 1.5 0.125 104 0.0123 1.27 24.2\n",
" 2.0 0.167 92 0.0218 2.00 29.6\n",
" 2.5 0.208 76 0.0341 2.58 26.1\n",
" 3.0 0.250 60 0.0491 2.96 19.0\n",
" 4.0 0.333 38 0.0873 3.31 8.4\n",
" 6.0 0.500 18 0.1963 3.48 1.9\n",
"Thus a pipe of 2 in will be the optimum\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.2 Page No : 498"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from sympy.functions.elementary.trigonometric import acot\n",
"\t\n",
"#Initialization of variables\n",
"phi = 0.46\n",
"g = 32.2\n",
"k = 0.44\n",
"cv = 0.98\n",
"d = 10. \t#in\n",
"A = 0.545 \t #ft**2\n",
"beta = 160. \t#degrees\n",
"\t\n",
"#calculations\n",
"u = phi*math.sqrt(2*g)\n",
"V1 = cv*math.sqrt(2*g)\n",
"gQ = 62.4*A*V1\n",
"T = d/2 *gQ/g *(1 - math.cos(math.radians(beta)) /math.sqrt(1+k) )*math.sqrt(2*g)*(cv-phi)\n",
"Power = T*2*u/d\n",
"\t\n",
"#Results\n",
"print \"Torque required = %d ft lb\"%(T)\n",
"print \" Power transferred = %d ft lb/s\"%(Power)\n",
"Pi = gQ\n",
"He = Power/Pi\n",
"print \" Hydraulic efficiency = %.2f\"%(He)\n",
"v1 = V1-u\n",
"v2 = v1/(math.sqrt(1+k))\n",
"hl = k*v2**2 /(2*g)\n",
"print \"Head loss in bucket friction = %.1f %%\"%(hl*100)\n",
"Hn = (1/cv**2 -1)*V1**2 /(2*g)\n",
"print \" Head loss in nozzle = %.4f\"%(Hn*100)\n",
"V2cos = u+v2*math.cos(math.radians(beta))\n",
"V2sin = v2*math.sin(math.radians(beta))\n",
"#alpha = math.degrees(1/math.atan(V2cos/V2sin))\n",
"alpha = math.degrees(acot(V2cos/V2sin))\n",
"V2 = V2sin/math.sin(math.radians(alpha))\n",
"Hd = V2**2/(2*g)\n",
"print \" Head loss at discharge = %.1f %%\"%(Hd*100)\n",
"Htotal = Hd+Hn+hl\n",
"print \" Total head loss = %.2f %%\"%(Htotal*100)\n",
"\n",
"# rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Torque required = 309 ft lb\n",
" Power transferred = 228 ft lb/s\n",
" Hydraulic efficiency = 0.85\n",
"Head loss in bucket friction = 8.3 %\n",
" Head loss in nozzle = 3.9600\n",
" Head loss at discharge = 2.5 %\n",
" Total head loss = 14.70 %\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.3 Page No : 501"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\t\n",
"#Initialization of variables\n",
"cv = 0.98\n",
"g = 32.2\n",
"h = 1320. \t#ft\n",
"A = 0.196 \t#ft**2\n",
"eta = 0.85\n",
"ne = 400.\n",
"phi = 0.45\n",
"\t\n",
"#calculations\n",
"V = cv*math.sqrt(2*g*h)\n",
"Q = A*V\n",
"bhp = eta*62.4*Q*h/550\n",
"ns = ne*math.sqrt(bhp) /h**(5./4)\n",
"u = phi*math.sqrt(2*g*h)\n",
"D = u*60/math.pi/ne\n",
"\t\n",
"#Results\n",
"print \"Pitch diameter = %.2f ft\"%(D)\n",
"\n",
"\n",
"# part b\n",
"#Initialization of variables\n",
"cv = 0.98\n",
"g = 32.2\n",
"h = 1320. \t#ft\n",
"A = 0.196 \t#ft**2\n",
"eta = 0.85\n",
"ne = 400.\n",
"phi = 0.45\n",
"\t\n",
"#calculations\n",
"V = cv*math.sqrt(2*g*h)\n",
"Q = A*V/3\n",
"bhp = eta*62.4*Q*h/550\n",
"ne2 = 600.\n",
"ns1 = ne2*math.sqrt(bhp) /h**(5./4)\n",
"D = 2500./ne2\n",
"Dj = math.sqrt(Q*4/V/math.pi)\n",
"\t\n",
"#Results\n",
"print \" Jet diameter = %.3f ft\"%(Dj)\n",
"print \" Specific speed = %.2f \"%(ns1)\n",
"print \" Pitch Diameter = %.2f ft\"%(D)\n",
"print \" Operating speed = %d rpm\"%(ne2)\n",
"\n",
"# rounding off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pitch diameter = 6.26 ft\n",
" Jet diameter = 0.288 ft\n",
" Specific speed = 3.68 \n",
" Pitch Diameter = 4.17 ft\n",
" Operating speed = 600 rpm\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}