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22 changes: 12 additions & 10 deletions OpenHPL/Waterway/Gate.mo
Original file line number Diff line number Diff line change
Expand Up @@ -74,7 +74,8 @@ Equation numbers and figure numbers given below are in sync with the numbers of
<p>
The free flow can be calculated with:

$$Q_A = \\mu_A \\cdot A \\cdot \\sqrt{2g\\cdot h_0} \\tag{8.24} $$
$$ Q_A = \\mu_A \\cdot A \\cdot \\sqrt{2g\\cdot h_0} \\tag{8.24} $$

(valid for gate opening higher than the downstream water level)
</p>
<p>
Expand All @@ -86,17 +87,17 @@ With
<dt> $$ \\mu_A = \\frac{\\psi}{\\sqrt{1+\\frac{\\psi\\cdot a}{h_0}}} \\tag{8.23}$$ </dt>
<dd>Contraction coefficient sluice gate (\\(\\alpha=90^\\circ\\))</dd>
<dt> $$ \\psi_{90^\\circ}= \\frac{1}{1+0.64\\cdot \\sqrt{1-(a/h_0)^2}} \\tag{8.25}$$ </dt>
<dd>Contraction coefficient radial gate (for \\(a/h_0 \\rightarrow 0\\))</dd>
<dd>Contraction coefficient radial gate (for \(a/h_0 \\rightarrow 0\))</dd>
<dt> $$ \\psi_0(\\alpha)= 1.3 -0.8\\cdot\\sqrt{1-\\left(\\frac{\\alpha -205^\\circ}{220^\\circ}\\right)^2} \\tag{8.25a}$$ </dt>
<dd> The edge angle \\(\\alpha\\) of the gate </dd>
<dd> The edge angle \(\\alpha\) of the gate </dd>
<dt> $$ \\alpha = \\left( \\frac{\\pi}{2} - \\arcsin(\\frac{h_h-a}{r})\\right) \\cdot \\frac{180^\\circ}{\\pi} $$ </dt>
</dl>
<blockquote>
With:
<ul>
<li> \\(a \\ldots\\) Vertical gate opening </li>
<li> \\(h_h \\ldots\\) Height of the hinge above gate bottom\"</li>
<li> \\(r \\ldots\\) Radius of the gate arm </li>
<li> \(a \\ldots\) Vertical gate opening </li>
<li> \(h_h \\ldots\) Height of the hinge above gate bottom</li>
<li> \(r \\ldots\) Radius of the gate arm </li>
</ul>
</blockquote>

Expand Down Expand Up @@ -148,11 +149,12 @@ With

<h5>Boundary between free and backed-up flow</h5>
<p>
The boundary of the height of the water level \\(h_2\\) behind the gate from which on the calculation switches to the backed-up flow (8.29) can be derived from:
The boundary of the height of the water level \(h_2\) behind the gate from which on the calculation switches to the backed-up flow (8.29) can be derived from:

$$ \\frac{h_2^*}{a} = \\frac{\\psi}{2} \\cdot \\left( \\sqrt{ 1 + \\frac{16}{\\psi\\cdot\\left(1+\\frac{\\psi\\cdot a}{h_0}\\right)}\\cdot\\frac{h_0}{a}} - 1 \\right) \\tag{8.26}$$

So when \\(\\frac{h_2}{a} \\geq \\frac{h_2^*}{a}\\) then we have back-up flow.
So when \(\\frac{h_2}{a} \\geq \\frac{h_2^*}{a}\) then we have back-up flow.
</p>
</html>"));
end Gate;
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end Gate;
3 changes: 2 additions & 1 deletion OpenHPL/Waterway/Gate_HR.mo
Original file line number Diff line number Diff line change
Expand Up @@ -88,5 +88,6 @@ $$Q = C_{dx} A \\sqrt{2gH} \\tag{3}$$
<strong>Note:</strong>
The use of <code>Cdx</code> is different to the implementaion as done in HEC-RAS. This was done in order to have a smoother transition from the partially to fully submerged region.
</p>
</html>"));
</html>",
__OpenModelica_infoHeader = "<script type=\"text/javascript\" src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-AMS_CHTML\"></script>"));
end Gate_HR;