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"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 19 : CROSS DRAINAGE WORKS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.1 pg : 857"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy import linspace,zeros\n",
"\n",
"#design an expansion transition for canal by Mitra's method\n",
"\t\t\t\t\n",
"#Given\n",
"Lf = 16.; \t\t\t\t#length of flume\n",
"Bf = 9.; \t\t\t\t#width of throat\n",
"Bo = 15.; \t\t\t\t#width of canal\n",
"\n",
"#width at any dismath.tance x from flumed section is given by\n",
"#Bx = Bo*Bf*Lf/(Lf*Bo-(Bo-Bf)x)\n",
"#on solving we get\n",
"#Bx = 2160/(240-6x)\n",
"\n",
"x = linspace(2,16,8) \t\t\t\t#dismath.tance\n",
"print \"width at any dismath.tance x from flumed section:\";\n",
"Bx = zeros(8)\n",
"for i in range(8):\n",
" Bx[i] = 2160./(240-6*x[i]);\n",
" Bx[i] = round(Bx[i]*100)/100;\n",
" print '%.2f'%(Bx[i]);\n"
],
"language": "python",
"metadata": {},
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{
"output_type": "stream",
"stream": "stdout",
"text": [
"width at any dismath.tance x from flumed section:\n",
"9.47\n",
"10.00\n",
"10.59\n",
"11.25\n",
"12.00\n",
"12.86\n",
"13.85\n",
"15.00\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.2 pg : 857"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy import linspace,zeros\n",
"\n",
"#design an expansion transition for canal by Chaturvedi's method\n",
"\t\t\t\t\n",
"#Given;\n",
"Lf = 16.; \t\t\t\t#length of flume\n",
"Bf = 9.; \t\t\t\t#width of throat\n",
"Bo = 15.; \t\t\t\t#width of canal\n",
"\n",
"x = linspace(2,16,8); \t\t\t\t#dismath.tance\n",
"\n",
"#dismath.tance x is related as x = Lf*Bo**(2/3)(1-(Bf/Bx)**1.5)/(Bo**1.5-Bf**1.5)\n",
"#on solving we get\n",
"#(Bf/Bx)**1.5 = 1-(x/29.893) (relation is misprinted in book)\n",
"#let (Bf/Bx)**1.5 = r\n",
"r = zeros(8)\n",
"R = zeros(8)\n",
"Bx = zeros(8)\n",
"\n",
"print \"width at any dismath.tance x from flumed section:\";\n",
"for i in range(8):\n",
" r[i] = 1-(x[i]/29.893); \t\t\t\t#Bf/Bx**(1.5)\n",
" R[i] = r[i]**(2./3); \t\t\t\t#Bf/Bx\n",
" Bx[i] = Bf/R[i]; \n",
" Bx[i] = round(Bx[i]*100)/100; \n",
" print \"%.2f.\"%(Bx[i]);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"width at any dismath.tance x from flumed section:\n",
"9.43.\n",
"9.90.\n",
"10.45.\n",
"11.08.\n",
"11.81.\n",
"12.67.\n",
"13.71.\n",
"15.00.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.3 pg : 860"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy import linspace,zeros,zeros_like\n",
"\n",
"#design a syphon aqueduct\n",
"\n",
"#Given\n",
"Q = 25.; \t\t\t\t#design discharge of canal\n",
"B = 20.; \t\t\t\t#bed width of canal\n",
"D = 1.5; \t\t\t\t#depth of water in canal\n",
"bl = 160.; \t\t\t\t#bed level of canal\n",
"hfq = 400.; \t\t\t\t#high flood discharge of drainage\n",
"hfl = 160.5; \t\t\t\t#high flood level of drainage\n",
"bl_drain = 158.; \t\t\t\t#bed level of drainage\n",
"gl = 160.; \t\t\t\t#general ground level\n",
"\n",
"#demath.sing of drainage water-way\n",
"P = 4.75*(hfq)**0.5; \t\t\t\t#laecey P-Q formula\n",
"print \"design of drainage water-way:wetted perimeter of river = %i m.provide 13 spans \\\n",
"of 6 m each,separated by 12 piers each of 1.25 m thick.\"%(P);\n",
"t = 78.+15;\n",
"print \"total length of water-way = %i m.\"%(t);\n",
"v = 2; \t\t\t\t#velocity through syphon\n",
"hb = hfq/(78*v);\n",
"ac = hfq/(6*2.5*1.3); \t\t\t\t#calculation is wrong in book\n",
"hb = round(hb*100)/100;\n",
"ac = round(ac*100)/100;\n",
"print \"height of barrels = %.2f m.provide recmath.tangular barrels 6 m wide and 2.5 m high.actual \\\n",
"velocity through barrels = %.2f m/sec.\"%(hb,ac);\n",
"\n",
"#design of canal waterway\n",
"print \"design of canal waterway:Type 3 aqueduct is adopted.\";\n",
"l1 = B-10;\n",
"l2 = (20-10)*3/2;\n",
"print \"providing a splay 2:1 in expansion,length of contraction transition = %i m.providing\\\n",
" a splay of 3:1 in expansion,length of expansion transition = %i m.\"%(l1,l2);\n",
"print 'In transition side slopes are warped from original slope of 1.5:1 to vertical.';\n",
"\n",
"#design of levels of different sectionn\n",
"print \"design of levels of different sectionn:at section 4-4:\";\n",
"A = (B+1.5*D); \t\t\t\t#area\n",
"V = Q/A; \t\t\t\t#velocity of flow\n",
"vh = V**2/(2*9.81); \t\t\t\t#velocity head\n",
"ws = gl+D; \t\t\t\t#R.L of water surface\n",
"tel = ws+vh;\n",
"tel = round(tel*1000)/1000;\n",
"print \"R.L of T.E.L = %.2f m. at section 3-3:\"%(tel);\n",
"A = 10*D; \t\t\t\t#area of trough\n",
"V = Q/A; \t\t\t\t#velocity\n",
"vh1 = V**2/(2*9.81); \t\t\t\t#velocity head\n",
"le = 0.3*(vh1-vh); \t\t\t\t#loss of head in expansion from section 3-3 to 4-4\n",
"tel = tel+le;\n",
"rlw = tel-vh1;\n",
"rlb = rlw-D;\n",
"tel = round(tel*1000)/1000;\n",
"rlb = round(rlb*1000)/1000;\n",
"print \"elevation of T.E.L = %.2f m.R.L of bed to maintain consmath.tant water depth = %.2f m.\"%(tel,rlb);\n",
"\n",
"#at section 2-2\n",
"R = A/P;\n",
"N = 0.016;\n",
"S = V**2*N**2/R**(4./3); \t\t\t\t#from manning's formula\n",
"L = 93; \t\t\t\t#length of trough\n",
"hl = L*S; \t\t\t\t#head loss\n",
"tel = tel+hl;\n",
"rlw = tel-vh1;\n",
"rlb = rlw-D;\n",
"tel = round(tel*1000)/1000;\n",
"rlb = round(rlb*1000)/1000;\n",
"print \"at section 2-2:R.L of T.E.L = %.2f m.R.L of bed to maintain consmath.tant water depth = %.2f m.\"%(tel,rlb);\n",
"\n",
"#at section 1-1\n",
"hl = 0.2*(vh1-vh); \t\t\t\t#loss of hed in contraction transition\n",
"tel = tel+hl;\n",
"rlw = tel-vh;\n",
"rlb = tel-D;\n",
"tel = round(tel*1000)/1000;\n",
"rlb = round(rlb*1000)/1000;\n",
"print \"at section 1-1:R.L of T.E.L = %.2f m.R.L of bed to maintain consmath.tant water depth = %.2f m.\"%(tel,rlb);\n",
"\n",
"#design of contraction transition\n",
"#it is designed on the basis of chaturvedi's formula\n",
"Bo = 20.;\n",
"Bf = 10.;\n",
"L = 10.;\n",
"#from chaturvedi formula we get relation between x and Bx as: x = 15.45(1-(10/Bx)**1.5);\n",
"Bx = linspace(10,20,11)\n",
"print \"design of contraction transition on the basis of chaturvedi formula:\\nBx x\";\n",
"x = zeros_like(Bx)\n",
"for i in range(11):\n",
" x[i] = 15.45*(1-(10/Bx[i])**1.5);\n",
" x[i] = round(x[i]*100)/100;\n",
" print \"%i %.2f\"%(Bx[i],x[i]);\n",
"\n",
"\n",
"#design of expansion transition on the basis of chaturvedi formula\n",
"L = 15.;\n",
"Bf = 10.;Bo = 20.;\n",
"#from chaturvedi formula we get relation between x and Bx as: x = 23.15(1-(10/Bx)**1.5);\n",
"print \"design of expansion transition on the basis of chaturvedi formula:\\nBx x\";\n",
"for i in range(11):\n",
" x[i] = 23.15*(1-(10/Bx[i])**1.5);\n",
" x[i] = round(x[i]*100)/100;\n",
" print \"%i %.2f\"%(Bx[i],x[i]);\n",
"\n",
"\n",
"#design of trough\n",
"print \"design of the trough:\";\n",
"print \"flumed water way of canal = 10 m.trough carrying canal will divide into two \\\n",
"compartments each 5 m wide an dseparated by 0.3 m thick partiions.heigth of trough will be \\\n",
" = 2 m.trough iss constructed umath.sing monolithic reinforced concrete.the outer and inner walls\\\n",
" ca be kept 0.4 m thick.thus,outer width of trough = 11.1 m.\";\n",
"\n",
"#head loss through syphon barrels\n",
"V = 2.05; \t\t\t\t#velocity through barrels\n",
"f1 = 0.505; \t\t\t\t#coefficient of loss of head at entry\n",
"a = 0.00316;\n",
"b = 0.030;\n",
"R = (6*2.5)/(2*(6+2.5));\n",
"f2 = a*(1+b/R);\n",
"L = 11.1; \t\t\t\t#length of barrel\n",
"h = (1+f1+f2*L/R)*V**2/(2*9.81);\n",
"hfl_up = hfl+h;\n",
"h = round(h*1000)/1000;\n",
"hfl_up = round(hfl_up*1000)/1000;\n",
"print \"head loss through syphon barrels = %.2f m.upstream H.F.L = %.2f m.\"%(h,hfl_up)\n",
"\n",
"#uplift pressure on the roof\n",
"bt = gl-0.4; \t\t\t\t#R.L of bottom of the trough\n",
"hl = 0.505*V**2/(2*9.81);\n",
"u = hfl_up-hl-159.6;\n",
"up = u*9.81;\n",
"print \"uplift pressure on the roof = %.2f kN/square m.trough slab is 0.4 m thick and exert a downward load of 9.42 kN.\"%(up);\n",
"print \"th ebalance of the uplift pressure has to be resisted by bending action of \\\n",
"trough slab.so,reinforcement has to be provided at the top of the slab.\";\n",
"\n",
"#uplift on the floor of the barrel and its design\n",
"#(a) static head\n",
"print \"uplift on the floor of the barrel and its design:a static head:\";\n",
"bf = bt-2.5; \t\t\t\t#R.L of barrel floor\n",
"t = 0.8; \t\t\t\t#tentative thickness of floor\n",
"bot = bf-t;\n",
"static = bl_drain-bot;\n",
"static = round(static*100)/100;\n",
"print \"static uplift on the floor = %.2f m.\"%(static);\n",
"\n",
"#(b) seepage head\n",
"L = 10.; \t\t\t\t#length of u/s transition\n",
"bs = 3.; \t\t\t\t#half the barrel span\n",
"df = 11.; \t\t\t\t#end drainage floor\n",
"tcl = 24.; \t\t\t\t#total creep length\n",
"tsh = 161.5-bl_drain; \t\t\t\t#total seepage head\n",
"rs = tsh*(1-13/tcl); \t\t\t\t#residual seepage at B\n",
"tu = (static+rs)*9.81;\n",
"tu = round(tu*100)/100;\n",
"print \"b) seepage head:total uplift = %.2f kN/square m.provide thickness of floor 0.8 m\"%(tu);\n",
"bending = tu-17.58;\n",
"bending = round(bending*100)/100;\n",
"print \"uplift to be resisted by bending action of floor = %.2f kN/square m.\"%(bending);\n",
"\n",
"#design of cut-off and protection works for drainage floor\n",
"print \"design of cut-off and protection works for drainage floor:\";\n",
"Q = 400;f = 1;\n",
"R = 0.47*(Q/f)**(1/3);\n",
"d_up = 1.5*R; \t\t\t\t#depth of u/s cut-off\n",
"bot_up = hfl_up-d_up; \t\t\t\t#R.L of bottom of u/s cut-off\n",
"d_down = 1.5*R; \t\t\t\t#depth of d/s cut-off\n",
"bot_down = hfl-d_down; \t\t\t\t#R.L of bottom of d/s cut-off\n",
"l_down = 2.5*(bl_drain-bot_down);\n",
"l_down1 = 2*(bl_drain-bot_up);\n",
"bot_up = round(bot_up*100)/100;\n",
"bot_down = round(bot_down*100)/100;\n",
"l_down = round(l_down);\n",
"l_down1 = round(l_down1);\n",
"print \"R.L of bottom of u/s cut-off = %.2f m.R.L of bottom of d/s cut-off = %.2f m.\"%(bot_up,bot_down);\n",
"print \"length of d/s protection consisting of 40 cm brick pritching = %.2f m.pitching is \\\n",
"supported by toe wall 0.4 m wide and 1.5 m deep at its d/s end.length of d/s protection consisting\\\n",
" of 0.4 cm brick pritching = %.2f m.pitching is supported by toe wall 0.4 m wide and\\\n",
" 1 m deep at its u/s end.\"%(l_down,l_down1);\n"
],
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{
"output_type": "stream",
"stream": "stdout",
"text": [
"design of drainage water-way:wetted perimeter of river = 95 m.provide 13 spans of 6 m each,separated by 12 piers each of 1.25 m thick.\n",
"total length of water-way = 93 m.\n",
"height of barrels = 2.56 m.provide recmath.tangular barrels 6 m wide and 2.5 m high.actual velocity through barrels = 20.51 m/sec.\n",
"design of canal waterway:Type 3 aqueduct is adopted.\n",
"providing a splay 2:1 in expansion,length of contraction transition = 10 m.providing a splay of 3:1 in expansion,length of expansion transition = 15 m.\n",
"In transition side slopes are warped from original slope of 1.5:1 to vertical.\n",
"design of levels of different sectionn:at section 4-4:\n",
"R.L of T.E.L = 161.56 m. at section 3-3:\n",
"elevation of T.E.L = 161.59 m.R.L of bed to maintain consmath.tant water depth = 159.95 m.\n",
"at section 2-2:R.L of T.E.L = 162.36 m.R.L of bed to maintain consmath.tant water depth = 160.72 m.\n",
"at section 1-1:R.L of T.E.L = 162.38 m.R.L of bed to maintain consmath.tant water depth = 160.88 m.\n",
"design of contraction transition on the basis of chaturvedi formula:\n",
"Bx x\n",
"10 0.00\n",
"11 2.06\n",
"12 3.70\n",
"13 5.03\n",
"14 6.12\n",
"15 7.04\n",
"16 7.82\n",
"17 8.48\n",
"18 9.05\n",
"19 9.55\n",
"20 9.99\n",
"design of expansion transition on the basis of chaturvedi formula:\n",
"Bx x\n",
"10 0.00\n",
"11 3.08\n",
"12 5.54\n",
"13 7.53\n",
"14 9.17\n",
"15 10.55\n",
"16 11.71\n",
"17 12.71\n",
"18 13.56\n",
"19 14.31\n",
"20 14.97\n",
"design of the trough:\n",
"flumed water way of canal = 10 m.trough carrying canal will divide into two compartments each 5 m wide an dseparated by 0.3 m thick partiions.heigth of trough will be = 2 m.trough iss constructed umath.sing monolithic reinforced concrete.the outer and inner walls ca be kept 0.4 m thick.thus,outer width of trough = 11.1 m.\n",
"head loss through syphon barrels = 0.33 m.upstream H.F.L = 160.83 m.\n",
"uplift pressure on the roof = 11.01 kN/square m.trough slab is 0.4 m thick and exert a downward load of 9.42 kN.\n",
"th ebalance of the uplift pressure has to be resisted by bending action of trough slab.so,reinforcement has to be provided at the top of the slab.\n",
"uplift on the floor of the barrel and its design:a static head:\n",
"static uplift on the floor = 1.70 m.\n",
"b) seepage head:total uplift = 32.41 kN/square m.provide thickness of floor 0.8 m\n",
"uplift to be resisted by bending action of floor = 14.83 kN/square m.\n",
"design of cut-off and protection works for drainage floor:\n",
"R.L of bottom of u/s cut-off = 160.13 m.R.L of bottom of d/s cut-off = 159.79 m.\n",
"length of d/s protection consisting of 40 cm brick pritching = -4.00 m.pitching is supported by toe wall 0.4 m wide and 1.5 m deep at its d/s end.length of d/s protection consisting of 0.4 cm brick pritching = -4.00 m.pitching is supported by toe wall 0.4 m wide and 1 m deep at its u/s end.\n"
]
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