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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 11: SPILLWAYS"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.1: EX11_1.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.1\n",
+"//calculate compute the dynamic force on curved section\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"h=1.2; //head of water\n",
+"Cd=2.2; //coefficient of discharge\n",
+"rho=1; //density of water\n",
+"gamma_w=9.81; //unit weigth of water\n",
+"\n",
+"q=Cd*h^1.5;\n",
+"\n",
+"//applying bernaulli's equation at u/s water surface at section A and B\n",
+"//solving it by error and trial method we get\n",
+"v1=13.7;v2=14.7;\n",
+"d1=0.212;d2=0.197;\n",
+"\n",
+"F1=gamma_w*d1^2*cosd(60)/2;\n",
+"F2=gamma_w*d2^2/2;\n",
+"W=gamma_w*60*2*%pi*3*((d1+d2)/2)/360;\n",
+"Fx=rho*q*(v2-v1*cosd(60))-F1/2+F2;\n",
+"Fy=rho*q*(v1*sind(60))+F1*sind(60)+W;\n",
+"F=(Fx^2+Fy^2)^0.5;\n",
+"F=round(F*100)/100;\n",
+"mprintf('Resultant force=%f kN/m.',F);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.2: EX11_2.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.2\n",
+"//calculate discharge over oggy weir\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"C=2.4; //coefficient of discharge\n",
+"H=2; //head\n",
+"L=100; //length of spillway\n",
+"wc=8; //heigth of weir crest above bottom\n",
+"g=9.81; //acceleration due to gravity\n",
+"h=H+wc;\n",
+"Q1=C*L*H^(1.5); //neglecting approach velocity and end contractions\n",
+"va=Q1/(h*L);\n",
+"ha=va^2/(2*g);\n",
+"Ha=ha+H;\n",
+"Q=C*L*Ha^1.5;\n",
+"Q=round(Q*10)/10;\n",
+"mprintf('discharge over oggy weir=%f cumecs.',Q);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.3: EX11_3.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.3\n",
+"//calculate\n",
+"//capacity of siphon\n",
+"//head required in oggy spillway\n",
+"//length of oggy weir required\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"t=6; //tail water elevation\n",
+"h=1; //heigth of siphon spillway\n",
+"w=4; //width of siphon spillway\n",
+"hw=1.5; //head water elevation\n",
+"C=0.6; //coefficient of discharge\n",
+"Co=2.25; //coefficient of discharge of oggy spillway\n",
+"lo=4; //length of oggy spillway\n",
+"hc=1.5; //head on weir crest\n",
+"g=9.81; //acceleration due to gravity\n",
+"\n",
+"//part (a)\n",
+"Q=C*h*w*(2*g*(t+hw))^0.5;\n",
+"Q=round(Q*10)/10;\n",
+"mprintf('capacity of siphon=%f cumecs.',Q);\n",
+"\n",
+"//part (b)\n",
+"h1=(Q/(Co*lo))^(2/3);\n",
+"h1=round(h1*100)/100;\n",
+"mprintf('\nhead required in oggy spillway=%f m',h1);\n",
+"\n",
+"//part (c)\n",
+"L=Q/(Co*(hc)^1.5);\n",
+"L=round(L*100)/100;\n",
+"mprintf('\nlength of oggy weir required=%f m.',L);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.4: EX11_4.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.4\n",
+"//calculate number of siphons units required\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"rl=435; //full reservior level\n",
+"cl=429.6; //level of centre of siphon\n",
+"hfl=435.85; //high flood level\n",
+"hfd=600; //high flood discharge\n",
+"w=4; //width of throat\n",
+"h=2; //heigth of throat\n",
+"C=0.65; //coefficient of discharge\n",
+"g=9.81; //acceleration due to gravity\n",
+"\n",
+"H=hfl-cl;\n",
+"Q=C*w*h*(2*g*H)^0.5;\n",
+"n=hfd/Q;\n",
+"n=round(n*100)/100;\n",
+"mprintf(' number of siphons units required=%f.\nhence provide 11 siphons units.',n);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.5: EX11_5.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.5\n",
+"//design oggy spillway for concrete gravity dam\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"rbl=250; //avarage river bed level\n",
+"rlc=350; //R.L of spillway crest\n",
+"s=0.75; //slope on downstream side\n",
+"Q=6500; //discharge\n",
+"L=5*9; //length of spillway\n",
+"Cd=2.2; //coefficient of discharge\n",
+"t=2; //thickness of each pier\n",
+"\n",
+"//step 1. computation of design head\n",
+"H=(Q/(Cd*L))^(2/3);\n",
+"P=rlc-rbl;\n",
+"\n",
+"//P/H=6.15,which is<1.33;it is a high overflow spillway\n",
+"\n",
+"//H+P/H=7.15>1.7; hence discharge coefficient is not affected by downstream apron interface\n",
+"\n",
+"Kp=0.01;Ka=0.1;N=4;\n",
+"He=17.5; //assumed\n",
+"Le=L-2*(N*Kp+Ka)*He;\n",
+"He1=(Q/(Cd*Le))^(2/3);\n",
+"He1=round(He1*100)/100;\n",
+"//He1 is almost equal to He\n",
+"mprintf('crest profile will be designed for Hd=%f m.',He1);\n",
+"\n",
+"//step 2. determination of d/s profile\n",
+"\n",
+"//equating the slope of d/s side and derivative of profile equation suggested by WES\n",
+"x=27.03;\n",
+"y=0.04372*x^1.85;\n",
+"mprintf('\n\ndownstream profile:');\n",
+"x=[1:1:26]\n",
+"for i=1:26\n",
+" y(i)=0.04372*x(i)^1.85;\n",
+" y(i)=round(y(i)*1000)/1000;\n",
+"end\n",
+"mprintf('\nx y');\n",
+"for i=1:26\n",
+" mprintf('\n%i %f',x(i),y(i));\n",
+"end\n",
+"mprintf('\n27.03 19.48');\n",
+"\n",
+"\n",
+"//step 3. determination of u/s profile\n",
+"// cosidering equation for vertical u/s face and Hd=17.58\n",
+"\n",
+"mprintf('\n\nupstream profile:');\n",
+"x=[-0.5 -0.1 -1.5 -2.0 -3.0 -4.0 -4.75];\n",
+"for i=1:7\n",
+" y(i)=0.0633*(x(i)+4.7466)^1.85+2.2151-1.2643*(x(i)+4.7466)^0.625;\n",
+" y(i)=round(y(i)*1000)/1000;\n",
+"end\n",
+"mprintf('\nx y');\n",
+"for i=1:7\n",
+" mprintf('\n%f %f',x(i),y(i));\n",
+"end\n",
+"\n",
+"//step 4.design of d/s bucket\n",
+"\n",
+"R=P/4;\n",
+"mprintf('\n\nradius of bucket=%i m.',R);\n",
+"mprintf('\nbucket will subtend angle of 60 degree at the centre.');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.6: EX11_6.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.6\n",
+"//design length and depth of stilling basin\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"q=1; //discharge of spillway\n",
+"Cd=0.7; //coefficient of discharge\n",
+"h1=10; //heigth of crest above downstream silting basin\n",
+"g=9.81; //acceleration due to gravity\n",
+"Cv=0.9; //coefficient of velocity\n",
+"\n",
+"h=(3*q/(2*Cd*(2*g)^0.5))^(2/3);\n",
+"H=h1+h/2;\n",
+"vt=(2*g*H)^0.5;\n",
+"v1=Cv*vt;\n",
+"y1=q/v1;\n",
+"F1=v1/(g*y1)^0.5;\n",
+"//F>1, flow is super-critical\n",
+"y2=1;\n",
+"v2=q/y2;\n",
+"F2=v2/(g*y2)^0.5; //<1\n",
+"y2=(y1/2)*((1+8*F1^2)^0.5-1);\n",
+"de=y2-1;\n",
+"le=5*(y2-y1);\n",
+"de=round(de*1000)/1000;\n",
+"le=round(le*10)/10;\n",
+"mprintf('stilling basin should be depressed by %f m.',de);\n",
+"mprintf('\nlength of stilling basin=%f m.',le);\n",
+"\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.7: EX11_7.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.7\n",
+"//calculate leading dimension of hydraulic jump stilling basin\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"q=7.83; //discharge through spillway\n",
+"w=12.5; //width of fall\n",
+"d=2; //depth of water in downstream\n",
+"g=9.8;\n",
+"\n",
+"y1=0.5;\n",
+"v1=q/y1;\n",
+"F1=v1/(g*y1)^0.5;\n",
+"\n",
+"//F>1,flow is super-critical\n",
+"v2=q/d;\n",
+"F2=v2/(g*d)^0.5;\n",
+"y2=(y1/2)*((1+8*F1^2)^0.5-1);\n",
+"de=y2-d;\n",
+"le=5*(y2-y1);\n",
+"de=round(de*100)/100;\n",
+"le=round(le*10)/10;\n",
+"mprintf('stilling basin should be depressed by %f m.',de);\n",
+"mprintf('\nlength of stilling basin=%f m.',le); "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.8: EX11_8.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.8\n",
+"//calculate force to be exerted to lift the gate\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"Ag=5*2.5; //area of gate\n",
+"miu=0.25; //coefficient of friction\n",
+"w=0.5; //weigth of gate\n",
+"h=2; //head of water over crest\n",
+"g=9.81; //acceleration due to gravity\n",
+"gamma_w=1000; //unit weigth of water\n",
+"\n",
+"m=w*g*1000;\n",
+"F=gamma_w*Ag*h*h*g/10;\n",
+"ff=miu*F;\n",
+"tf=(m+ff)/1000;\n",
+"mprintf('force to be exerted to lift the gate=%f kN.',tf);\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.9: EX11_9.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"\n",
+"\n",
+"//example 11.9\n",
+"//calculate depth of flow at both end of jumps\n",
+"clc;funcprot(0);\n",
+"//given\n",
+"q=19; //dischrge through spillway\n",
+"E=1; //energy loss\n",
+"\n",
+"//from energy loss equation;E=(y2-y1)^3/4y2y1; and solving it we get\n",
+"//x=0.5*(-1+(1+294.39*(x-1)^9/64*x^3))\n",
+"//by trial and error method x=2.806\n",
+"x=2.806;\n",
+"y1=4*x/(x-1)^3;\n",
+"y2=x*y1;\n",
+"y1=round(y1*1000)/1000;\n",
+"y2=round(y2*1000)/1000;\n",
+"mprintf('depth of flow at both end of jumps=%f m and %f m. respectively.',y1,y2);\n",
+""
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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