<HTML>
<HEAD>
<TITLE>Calculation of normal depth in a prismatic channel using the Manning equation, Victor Miguel Ponce, San Diego State University</TITLE>
<STYLE TYPE="text/css">
a {text-decoration:none}
a:hover {color: #cc0000; background: #ffffcc; text-decoration: none}
body {font-family: helvetica; font-size: 12pt; color: #000055; background:#114466}
.heading1 {font-size: 11pt; font-family: bookman; color: #880000}
.heading2 {font-size: 10pt; font-family: helvetica; color: #004400}
.heading3 {font-size: 10pt; font-family: courier; color: #770000}
.heading4 {font-size: 10pt; font-family: roman; color: #770000}
.heading5 {font-size: 10pt; font-family: helvetica; color: #000055}
</STYLE>
</HEAD>
<?php
if (!IsSet($_POST['Submit']) || $_POST['Submit'] == 'Reset')
{
$_POST["discharge"] = "";
$_POST["bottomwidth"] = "";
$_POST["sideslope"] = "";
$_POST["bottomslope"] = "";
$_POST["manningsn"] = "";
$_POST["unitsystems"] = "";
$_POST["lengthunits"] = "";
$_POST["areaunits"] = "";
$_POST["velocityunits"] = "";
$_POST["dischargeunits"] = "";
$_POST["accelerationunits"] = "";
$_POST["unitsystemsname"] = "";
$_POST["x"] = "";
$_POST["xr"] = "";
$_POST["y"] = "";
$_POST["yp"] = "";
$_POST["dx"] = "";
$_POST["tol"] = "";
$_POST["yn"] = "";
$_POST["an"] = "";
$_POST["pn"] = "";
$_POST["tn"] = "";
$_POST["rn"] = "";
$_POST["vn"] = "";
$_POST["dn"] = "";
$_POST["fn"] = "";
$_POST["iflag"] = "";
$_POST["jflag"] = "";
$_POST["kflag"] = "";
}
elseif($_POST["Submit"] == 'Calculate')
{
$discharge = $_POST["discharge"];
$bottomwidth = $_POST["bottomwidth"];
$sideslope = $_POST["sideslope"];
$bottomslope = $_POST["bottomslope"];
$manningsn = $_POST["manningsn"];
$unitsystems = $_POST["unitsystems"];
$lengthunits = $_POST["lengthunits"];
$areaunits = $_POST["areaunits"];
$velocityunits = $_POST["velocityunits"];
$dischargeunits = $_POST["dischargeunits"];
$accelerationunits = $_POST["accelerationunits"];
$unitsystemsname = $_POST["unitsystemsname"];
$x = $_POST["x"];
$xr = $_POST["xr"];
$y = $_POST["y"];
$yp = $_POST["yp"];
$dx = $_POST["dx"];
$tol = $_POST["tol"];
$yn = $_POST["yn"];
$an = $_POST["an"];
$pn = $_POST["pn"];
$tn = $_POST["tn"];
$rn = $_POST["rn"];
$vn = $_POST["vn"];
$dn = $_POST["dn"];
$fn = $_POST["fn"];
$iflag = $_POST["iflag"];
$jflag = $_POST["jflag"];
$kflag = $_POST["kflag"];
//check for input errors
if($_POST["discharge"] <= 0)
{
if($_POST["Submit"] == 'Calculate')
{
echo "<P><br><P><br><P><br><P><br><table align=\"center\" bgcolor=\"ffffcc\" width=\"50%\" border=\"2\" cellpadding=\"15\"><tr><td>";
echo "<font color=\"000066\" face=\"arial\" size=\"+2\"><b>
onlinechannel01: *** Error message 1 *** Please enter only positive number for discharge.
Execution stops here. </b></font>";
echo "</td></tr></table>";
die;
}
}
if($_POST["manningsn"] <= 0)
{
if($_POST["Submit"] == 'Calculate')
{
echo "<P><br><P><br><P><br><P><br><table align=\"center\" bgcolor=\"ffffcc\" width=\"50%\" border=\"2\" cellpadding=\"15\"><tr><td>";
echo "<font color=\"000066\" face=\"arial\" size=\"+2\"><b>
onlinechannel01: *** Error message 2 *** Please enter only positive number for manning's n.
Execution stops here. </b></font>";
echo "</td></tr></table>";
die;
}
}
if($_POST["bottomslope"] <= 0)
{
if($_POST["Submit"] == 'Calculate')
{
echo "<P><br><P><br><P><br><P><br><table align=\"center\" bgcolor=\"ffffcc\" width=\"50%\" border=\"2\" cellpadding=\"15\"><tr><td>";
echo "<font color=\"000066\" face=\"arial\" size=\"+2\"><b>
onlinechannel01: *** Error message 3 *** Please enter only positive number for bottom slope.
Execution stops here. </b></font>";
echo "</td></tr></table>";
die;
}
}
if($_POST["bottomwidth"] < 0)
{
if($_POST["Submit"] == 'Calculate')
{
echo "<P><br><P><br><P><br><P><br><table align=\"center\" bgcolor=\"ffffcc\" width=\"50%\" border=\"2\" cellpadding=\"15\"><tr><td>";
echo "<font color=\"000066\" face=\"arial\" size=\"+2\"><b>
onlinechannel01: *** Error message 4 *** Please enter only nonnegative number for bottom width.
Execution stops here. </b></font>";
echo "</td></tr></table>";
die;
}
}
if($_POST["sideslope"] < 0)
{
if($_POST["Submit"] == 'Calculate')
{
echo "<P><br><P><br><P><br><P><br><table align=\"center\" bgcolor=\"ffffcc\" width=\"50%\" border=\"2\" cellpadding=\"15\"><tr><td>";
echo "<font color=\"000066\" face=\"arial\" size=\"+2\"><b>
onlinechannel01: *** Error message 5 *** Please enter only nonnegative number for side slope.
Execution stops here. </b></font>";
echo "</td></tr></table>";
die;
}
}
if(($_POST["bottomwidth"] == 0) && ($_POST["sideslope"] == 0))
{
if($_POST["Submit"] == 'Calculate')
{
echo "<P><br><P><br><P><br><P><br><table align=\"center\" bgcolor=\"ffffcc\" width=\"50%\" border=\"2\" cellpadding=\"15\"><tr><td>";
echo "<font color=\"000066\" face=\"arial\" size=\"+2\"><b>
onlinechannel01: *** Error message 6 *** Bottom width and side slope cannot be zero at the same time.
Execution stops here. </b></font>";
echo "</td></tr></table>";
die;
}
}
//set unit systems
$unitsystems = 0; // default value
if(isset($_POST["unitsystems"]))
{
$unitsystems = $_POST["unitsystems"];
}
if ($unitsystems == 1)
{
$g= 32.17;
$c= 1.486;
$lengthunits = "ft";
$areaunits = "ft<sup>2</sup>";
$velocityunits = "fps";
$dischargeunits = "cfs ";
$accelerationunits = "ft s<sup>-2</sup>";
$unitsystemsname = "U.S. Customary";
}
elseif($unitsystems == 0)
{
$g = 9.81;
$c = 1.0;
$lengthunits = "m";
$velocityunits = "m s<sup>-1</sup>";
$areaunits = "m<sup>2</sup>";
$dischargeunits = "m<sup>3</sup> s<sup>-1</sup>";
$accelerationunits = "m s<sup>-2</sup>";
$unitsystemsname = "SI (metric)";
}
//main calculations
$iflag= 0.;
$kflag= 0.;
$tol= 0.0001;
$x = 0.;
$dx = 1.;
$q = $_POST["discharge"];
$b = $_POST["bottomwidth"];
$z = $_POST["sideslope"];
$s = $_POST["bottomslope"];
$xn = $_POST["manningsn"];
//main while loops
while($kflag == 0)
{
$y = + pow(($x*(0.5*$b + 0.5*$z*$x)),2.5)
- 0.5*pow(($q*$xn/(2*$c*pow($s,0.5))),1.5)*$b;
$jflag = 0;
while($jflag == 0)
{
if($y < 0.)
{
$x = $x + $dx;
$jflag = 1;
}
else
{
while($iflag == 0)
{
$y = + pow(($x*(0.5*$b + 0.5*$z*$x)),2.5)
- 0.5*pow(($q*$xn/(2*$c*pow($s,0.5))),1.5)*$b;
$yp = + 1.25*$z*pow($x,2.5)*pow((0.5*$b + 0.5*$z*$x),1.5)
- pow(($q*$xn/(2*$c*pow($s,0.5))),1.5)*pow((1 + pow($z,2)),0.5);
$xr = $x - $y/$yp;
if(abs($xr - $x) < $tol)
{
$iflag= 1;
$jflag= 1;
$kflag= 1;
}
$x = $xr;
}
}
}
}
$yn = $x;
$an = ($b + $z*$yn)*$yn;
$pn = $b + 2*$yn*pow((1 + pow($z,2)),0.5);
$tn = $b + 2*$z*$yn;
$rn = $an/$pn;
$vn = $q/$an;
$dn = $an/$tn;
$fn = $vn/(pow(($g*$dn),0.5));
}
?>
<BODY link="000066" vlink="555555" alink="555555">
<P><br><P>
<table width="80%" align="center" border="2" cellpadding="10" bgcolor="ffffee"><tr><td>
<DIV align="center" class="heading1"><b>onlinechannel_01: Normal depth in a prismatic channel </b></DIV><hr color="000066">
<center>
<table align="center" width="90%" cellpadding="10"><tr><td>
<table bgcolor="880000" cellpadding="5"><tr><td align="center">
<IMG SRC="onlinechannel_fig05.jpg"><br><font face="helvetica" size="-1" color="ffff66">Definition sketch for a prismatic channel</font>
</td>
</tr></table>
</td><td align="center"><b>Formulas</b> <P>
<div align="center" class="heading3">
<hr color="440000" size="1">
A = y(b + zy)
<hr color="440000" size="1">
P = b + 2y(1 + z<sup><font size="-1">2</font></sup>)<sup><font size="-1">1/2</font></sup>
<hr color="440000" size="1">
T = b + 2zy
<hr color="440000" size="1">
R = A/P
<hr color="440000" size="1">
D = A/T
<hr color="440000" size="1">
Q = (C/n) AR<sup><font size="-1">2/3</font></sup>S<sup><font size="-1">1/2</font></sup>
<hr color="440000" size="1">
V = Q/A
<hr color="440000" size="1">
F = V/(gD)<sup><font size="-1">1/2</font></sup>
<hr color="440000" size="1">
</div>
</td>
</td>
</tr></table>
</center>
<hr color="000066">
<FORM ACTION="<?php echo $_SERVER['PHP_SELF']; ?>" METHOD="POST">
<table width="100%" cellpadding="5"><tr><td valign="top">
<b>INPUT DATA:</b>
<P>Select:
<SELECT NAME="unitsystems" size="2">
<OPTION VALUE="0">SI units (metric)</OPTION>
<OPTION VALUE="1">U.S. Customary units</OPTION>
</SELECT>
<P>Flow discharge Q:
<INPUT TYPE="text" SIZE="08" MAXLENGTH="12" NAME="discharge" VALUE="<?php echo $_POST['discharge']; ?>"> <?php echo $dischargeunits ?>
<P>Bottom width b:
<INPUT TYPE="text" SIZE="08" MAXLENGTH="12" NAME="bottomwidth" VALUE="<?php echo $_POST['bottomwidth']; ?>"> <?php echo $lengthunits ?>
<P>Side slope z:
<INPUT TYPE="text" SIZE="06" MAXLENGTH="12" NAME="sideslope" VALUE="<?php echo $_POST['sideslope']; ?>">
<P>Bottom slope S:
<INPUT TYPE="text" SIZE="08" MAXLENGTH="12" NAME="bottomslope" VALUE="<?php echo $_POST['bottomslope']; ?>">
<P>Manning's n:
<INPUT TYPE="text" SIZE="08" MAXLENGTH="12" NAME="manningsn" VALUE="<?php echo $_POST['manningsn']; ?>">
</td><td valign="top">
<p><b>INTERMEDIATE CALCS:</b><P>
<P>Units selected: <?php echo $unitsystemsname; ?>
<P>Gravitational acceleration g: <?php echo $g; ?> <?php echo $accelerationunits ?>
<P>Units constant C: <?php echo round($c,3); ?>
<P>Wetted perimeter P: <?php echo round($pn,3); ?> <?php echo $lengthunits ?>
<P>Top width T: <?php echo round($tn,3); ?> <?php echo $lengthunits ?>
<P>Flow area A: <?php echo round($an,2); ?> <?php echo $areaunits ?>
<P>Hydraulic radius R: <?php echo round($rn,3); ?> <?php echo $lengthunits ?>
<P>Hydraulic depth D: <?php echo round($dn,3); ?> <?php echo $lengthunits ?>
</td><td valign="top">
<p><b>OUTPUT:</b><P>
<P>Normal flow depth y<sub>n</sub>: <?php echo round($yn,3); ?> <?php echo $lengthunits ?>
<P>Normal flow velocity V<sub>n</sub>: <?php echo round($vn,3); ?> <?php echo $velocityunits ?>
<P>Normal Froude number F<sub>n</sub>: <?php echo round($fn,3); ?>
</td></tr></table>
<hr color="000066">
<P>
<table cellpadding="4" bgcolor="ffffee" align="center">
<tr>
<td bgcolor="880000"><INPUT TYPE="submit" NAME="Submit" VALUE="Calculate"></td>
<td> </td>
<td bgcolor="880000"><INPUT TYPE="submit" NAME="Submit" VALUE="Reset"></td>
</tr>
</table>
</FORM>
<P>
<?php
echo "<p> Your request was processed at ";
echo " ";
echo date('h:i:s a \o\n F jS, Y');
?>
[
<?php
echo date("ymd");echo (" ");echo date("H:i:s");
?> ].
<P><hr color="000066">
<DIV align="center" class="heading2"><b>Thank you for running onlinechannel_01. Please call again. [091005]</b></DIV>
</td></tr></table>
<P>
<center>
<IMG SRC="http://ponce.sdsu.edu/cgi-bin/Count.cgi?cache=F&expires=0" ALT="Count">
</center>
<P><br>
</BODY>
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