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diff --git a/Problems_In_Hydraulics_by_R._S._Paradise/ch10.ipynb b/Problems_In_Hydraulics_by_R._S._Paradise/ch10.ipynb new file mode 100755 index 00000000..9cf18748 --- /dev/null +++ b/Problems_In_Hydraulics_by_R._S._Paradise/ch10.ipynb @@ -0,0 +1,589 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:54b93ceee4137049e1ed8024ecd6ba8e7f6645f46f71063561c8d2f8b4589ff2" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 10 : Hydraulic Prime Movers" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.1 Page No : 188" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#initialisation of variables\n", + "v= 231. \t#ft/sec\n", + "g= 32.2 \t#ft/sec**2\n", + "vc= 0.97\n", + "r= 0.47\n", + "p= 85. \t#per cent\n", + "A= 170. \t#degrees\n", + "p1= 88. \t#per cent\n", + "l= 950. \t#ft\n", + "\n", + "#CALCULATIONS\n", + "H= v**2/(vc**2*2*g)\n", + "u= r*v\n", + "vr= v-u\n", + "vr1= p*vr/100\n", + "w1= u-vr1*math.cos(math.radians(180-A))\n", + "W= u*(v-w1)/g\n", + "he= W*100/H\n", + "W1= p1*W/100\n", + "oe= W1*100/l\n", + "\n", + "#RESULTS\n", + "print 'hydraulic efficiency = %.f percent'%(he)\n", + "print ' overall efficiency = %.1f percent'%(oe)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "hydraulic efficiency = 86 percent\n", + " overall efficiency = 70.2 percent\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.2 Page No : 189" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#initialisation of variables\n", + "d= 1. \t#in\n", + "v= 95. \t#ft/sec\n", + "F= 173.2 \t#lb\n", + "A= 163. \t#degrees\n", + "H= 500. \t#ft\n", + "Cv= 0.97\n", + "d1= 1.33 \t#ft\n", + "r= 0.47\n", + "w= 62.4 \t#lb/ft**3\n", + "g= 32.2 \t#ft/sec**2\n", + "\n", + "#CALCULATIONS\n", + "Q= w*math.pi*v/(144*4)\n", + "k= (F-v)/(v*math.cos(math.radians(180-A)))\n", + "v1= Cv*math.sqrt(2*g*H)\n", + "W= v1*w*d**2*math.pi/(4*144)\n", + "N= 60*r*v1/(math.pi*d1)\n", + "whp= (v1-v)*(1+k*math.cos(math.radians(180-A)))*v1*2/550\n", + "Ns= N*whp**0.5/H**1.25\n", + "\n", + "#RESULTS\n", + "print 'specific speed = %.2f r.p.m'%(Ns)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "specific speed = 4.75 r.p.m\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.4 Page No : 192" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#initialisation of variables\n", + "D= 2. \t#ft\n", + "f= 0.005\n", + "l= 10000. \t#ft\n", + "g= 32.2 \t#ft/sec**2\n", + "H= 1000. \t#ft\n", + "w= 62.4 \t#lb/ft**3\n", + "\n", + "#CALCULATIONS\n", + "d= (2*D**5/(f*l))**0.25\n", + "v= math.sqrt(8*g*H*D**5/(f*l*d**4+4*D**5))\n", + "HP= w*math.pi*d**2*v**3/(2*g*550*4)\n", + "Q= math.pi*d**2*(HP/67)/4\n", + "\n", + "#RESULTS\n", + "print 'Quantity flowing = %.f cusecs'%(Q)\n", + "\n", + "# rounding off error\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Quantity flowing = 185 cusecs\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.5 Page No : 193" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#initialisation of variables\n", + "pl= 122.5 \t# ft\n", + "Hw= 1225 \t#ft\n", + "g= 32.2 \t#ft/sec**2\n", + "Cd= 0.98\n", + "Cd1= 0.45\n", + "N= 500. \t#r.p.m\n", + "P= 6800. \t#h.p\n", + "n= 0.86\n", + "w= 62.4 \t#lb/ft**2\n", + "l= 5450. \t#ft\n", + "f= 0.005\n", + "A= 18. \t#ft**2\n", + "\n", + "#CALCULATIONS\n", + "Ah= Hw-pl\n", + "js= Cd*math.sqrt(2*g*Ah)\n", + "bs= Cd1*js\n", + "D= bs*60*2/(N*2*math.pi)\n", + "a= P*2*g*550*144/(n*w*js**3*2)\n", + "vp= math.sqrt(pl*2*g/(4*f*l))\n", + "dp= (js*2*4*A/(math.pi*144*vp))**(2./3)\n", + "dp=2.495 \t#ft\n", + "\n", + "#RESULTS\n", + "print 'diameter of bucket circle D = %.1f ft'%(D)\n", + "print ' area of jet = %.f in**2'%(a)\n", + "print ' diameter of pipe = %.1f ft'%(dp)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "diameter of bucket circle D = 4.5 ft\n", + " area of jet = 18 in**2\n", + " diameter of pipe = 2.5 ft\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.6 Page No : 194" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#initialisation of variables\n", + "u= 10.*math.pi \t#ft/sec\n", + "u1= 5.*math.pi \t#ft/sec\n", + "a= 20. \t#degrees\n", + "A= 300. \t#r.p.m\n", + "v= 10. \t#ft/sec\n", + "g= 32.2 \t#ft/sec**2\n", + "wi= 2. \t#ft\n", + "d= 6. \t#in\n", + "w1= 62.4 \t#lb/ft**3\n", + "\n", + "#CALCULATIONS\n", + "w= v/math.tan(math.radians(a))\n", + "a1= math.degrees(math.atan((v/(u-w))))\n", + "b= math.degrees(math.atan((v/u1)))\n", + "W= u*w/g\n", + "A1= math.pi*wi*d/12\n", + "Q= A1*v\n", + "WHP= W*Q*w1/550\n", + "\n", + "#RESULTS\n", + "print 'Blade angle at inlet is given by = %.2f degrees'%(a1)\n", + "print ' Blade angle at inlet is given by = %.2f degrees'%(b)\n", + "print ' Water horse power = %.1f h.p'%(WHP)\n", + "\n", + "# rounding off error" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Blade angle at inlet is given by = 68.49 degrees\n", + " Blade angle at inlet is given by = 32.48 degrees\n", + " Water horse power = 95.5 h.p\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.7 Page No : 196" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#initialisation of variables\n", + "g= 32.2 \t#ft/sec**2\n", + "H= 100. \t#ft\n", + "a= 25. \t#degrees\n", + "a1= 20. \t#degrees\n", + "r1= 9./8\n", + "r2= 0.2\n", + "u= 6.63 \t#ft/sec\n", + "w= 62.4 \t#lb/ft**3\n", + "h1= 34. \t#ft\n", + "h2= 100. \t#ft\n", + "r= 0.1\n", + "\n", + "#CALCULATIONS\n", + "f= math.sqrt(H*g/((r1*1/math.tan(math.radians(a))*1/math.tan(math.radians(a1)))+r1*0.5+(r1*0.5**2*0.2/(math.sin(math.radians(a)))**2)+0.1/(math.sin(math.radians(a1+10)))**2))\n", + "W= u*f**2/g\n", + "q= a*H*550/(10*W*w)\n", + "q1= q/w\n", + "A= q/f\n", + "dh= h1+h2-((1+r)*f**2/((math.sin(math.radians(a1)))**2*2*g))\n", + "\n", + "#RESULTS\n", + "print 'f = %.1f ft/sec'%(f)\n", + "print ' Work Done = %.1f ft-lb/lb'%(W)\n", + "print ' Quantity flow = %.1f cusecs'%(q)\n", + "print ' Area form guides = %.3f ft**2'%(A)\n", + "print ' Pressure at entry of level = %.1f ft of water'%(dh)\n", + "\n", + "#The answer is a bit different due to rounding off error in textbook\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "f = 20.2 ft/sec\n", + " Work Done = 83.9 ft-lb/lb\n", + " Quantity flow = 26.3 cusecs\n", + " Area form guides = 1.302 ft**2\n", + " Pressure at entry of level = 74.5 ft of water\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.8 Page No : 199" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "#initialisation of variables\n", + "d= 8. \t#in\n", + "w= 2. \t#in\n", + "di= 12. \t#in\n", + "wi= 3. \t#in\n", + "a= 24. \t#degrees\n", + "p= 88. \t#per cent\n", + "a1= 85. \t#degrees\n", + "a2= 30. \t#degrees\n", + "p1= 94. \t#per cent\n", + "h= 180. \t#ft\n", + "d1= 18. \t#in\n", + "Cd= 0.92\n", + "g=32.2\n", + "n1= 111. \t#rpm\n", + "\n", + "#calculations\n", + "r1= 1./math.tan(math.radians(a))\n", + "r2= (1./math.tan(math.radians(a1)))+r1\n", + "r3= 2*r2/3\n", + "r4= (1/math.tan(math.radians(a2)))-r3\n", + "a3= math.tan(math.radians(1/r4))\n", + "r5= math.sin(math.radians(a3))\n", + "f= math.sqrt(g*h*(p/100.)/(r1*r2+r3*r4+(r5**2/2)))\n", + "A= r2*f/(d/12)\n", + "N= (A*60/(2*math.pi))-n1\n", + "W= (r1*r2+r3*r4)*f**2/g\n", + "Q= math.pi*(d1/12)*(w/12)*Cd*f*62.08\n", + "whp= W*Q/550\n", + "bhp= p1*whp/100\n", + "\n", + "#RESULTS\n", + "print 'Speed = %.f rpm'%(N)\n", + "print ' output horsepower = %.f hp'%(bhp)\n", + "\n", + "# slightly change in r1,r2,r3 and that leads to some error in answer. Please check manually." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed = 905 rpm\n", + " output horsepower = 369 hp\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.9 Page No : 201" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#initialisation of variables\n", + "N= 428.6 \t#r.p.m\n", + "D= 5. \t#ft\n", + "w= 62.4 \t#lb/ft**3\n", + "hp= 16800. \t#hp\n", + "Qw= 435. \t#cuses\n", + "g= 32.2 \t#ft/sec**2\n", + "v= 32. \t#ft/sec\n", + "v1= 24. \t#f/sec\n", + "H= 200. \t#ft\n", + "lh1= 0.32 \t#ft lb/lb\n", + "\n", + "#CALCULATIONS\n", + "u= math.pi*D*N/60\n", + "W= hp*550/(Qw*w)\n", + "w= W*g/u\n", + "a= math.radians(math.tan(v/w))\n", + "va= math.sqrt(w**2+v**2)\n", + "b= math.radians(math.tan(v/(u-w)))\n", + "B= 180-b\n", + "vew= va**2/(2*g)\n", + "ve1w= v1**2/(2*g)\n", + "LH= H+vew-ve1w-W+lh1\n", + "\n", + "#RESULTS\n", + "print ' Absolute velocity at entry to runner = %.1f ft/sec'%(va)\n", + "print ' Loss of head in runner = %.2f ft lb/lb'%(LH)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Absolute velocity at entry to runner = 102.8 ft/sec\n", + " Loss of head in runner = 15.05 ft lb/lb\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.10 Page No : 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "\n", + "#initialisation of variables\n", + "A1= 25. \t#degrees\n", + "A2= 80. \t#degrees\n", + "H1= 100. \t#ft\n", + "H2= 13. \t#ft\n", + "g= 32.2 \t#ft/sec**2\n", + "v= 8. \t#ft/sec\n", + "d= 3.5 \t#in\n", + "de= 15.4 \t#in\n", + "b= 1.5 \t#in\n", + "w= 62.4 \t#lb/ft**3\n", + "\n", + "#CALCULATIONS\n", + "W= H1-H2-(v**2/(2*g))\n", + "f= math.sqrt(W*g/(1/math.tan(math.radians(A1))*(1/math.tan(math.radians(A1))-1/math.tan(math.radians(A2)))))\n", + "u= f*(1/math.tan(math.radians(A1))-1/math.tan(math.radians(A2)))\n", + "V= d*u/7.7\n", + "r= math.degrees(math.atan(f/V))\n", + "N= 60*u*12/(math.pi*de)\n", + "Q= math.pi*de*f*b/144\n", + "HP= Q*w*W/550\n", + "Ns= N*math.sqrt(HP)/H1**1.25\n", + "di= math.sqrt(Q*4*144/(math.pi*f))\n", + "\n", + "#RESULTS\n", + "print 'angle = %.f degrees'%(r)\n", + "print \" Angular speed = %.1f rpm\"%(Ns)\n", + "print ' inlet diameter to draft tube = %.2f in'%(di)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angle = 48 degrees\n", + " Angular speed = 26.6 rpm\n", + " inlet diameter to draft tube = 9.61 in\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.12 Page No : 207" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#initialisation of variables\n", + "H= 82.1 \t#ft\n", + "h= 90. \t#ft\n", + "k= 0.00646\n", + "k1= 0.00454\n", + "vd= 11. \t#ft/sec\n", + "P= 0.53 \t#hp\n", + "\n", + "#CALCULATIONS\n", + "Q= math.sqrt((1/k))*math.sqrt(h-H)\n", + "Qu= Q/math.sqrt(H)\n", + "Q1= math.sqrt(vd/k1)\n", + "hf= Q1**2*k\n", + "Qu1= Q1/math.sqrt(h-hf)\n", + "Pu= P*(h-hf)**1.5\n", + "\n", + "#RESULTS\n", + "print 'Qu = %.2f cuses'%(Qu)\n", + "print ' Q = %.1f cuses'%(Q1)\n", + "print ' power Developed = %.f hp'%(Pu)\n", + "\n", + "\n", + "# rounding off error" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Qu = 3.86 cuses\n", + " Q = 49.2 cuses\n", + " power Developed = 340 hp\n" + ] + } + ], + "prompt_number": 7 + } + ], + "metadata": {} + } + ] +}
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