Friction head loss |
For General cross section
\begin{equation}
h_{f1}=f'\times \cfrac{L}{R}\times \cfrac{v{}^2}{2 g} \qquad f'=\cfrac{2 g n^2}{R^{1/3}}
\end{equation}
$h_{f1}$ | : friction head loss |
$v$ | : mean flow velocity |
$f'$ | : friction loss coefficient |
$L$ | : length of waterway |
$R$ | : hydraulic radius |
$n$ | : Manning's roughness coefficient |
$g$ | : gravity acceleration (=9.8 m/s$^2$) |
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For Circular cross section
\begin{equation}
h_{f2}=f\times \cfrac{L}{D}\times \cfrac{v{}^2}{2 g} \qquad f=\cfrac{124.5 n^2}{D^{1/3}}
\end{equation}
$h_{f2}$ | : friction head loss |
$v$ | : mean flow velocity |
$f$ | : friction loss coefficient |
$L$ | : length of waterway |
$D$ | : internal diameter of waterway |
$n$ | : Manning's roughness coefficient |
$g$ | : gravity acceleration (=9.8 m/s$^2$) |
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Branch or Confluence head loss |
Branch head loss
\begin{equation}
h_{br1}=f_{br1}\times \cfrac{v_1{}^2}{2 g}
\end{equation}
$h_{br1}$ | : branch head loss |
$v_1$ | : mean flow velocity before branch |
$f_{br1}$ | : branch loss coefficient (=0.4) |
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Confluence head loss
\begin{equation}
h_{br2}=f_{br2}\times \cfrac{v_2{}^2}{2 g}
\end{equation}
$h_{br2}$ | : confluence head loss |
$v_2$ | : mean flow velocity after confluence |
$f_{br2}$ | : confluence loss coefficient (=0.4) |
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Entrance or Exit head loss |
Entrance head loss
\begin{equation}
h_{e}=f_{e}\times \cfrac{v_2{}^2}{2 g}
\end{equation}
$h_{e}$ | : entrance head loss |
$v_2$ | : mean flow velocity after flow-in |
$f_{e}$ | : entrance loss coefficient |
Type of entrance | $f_e$ |
Square cornered | 0.5 |
Cut cornered | 0.25 |
Rounded cornered (circular) | 0.1 |
Rounded cornered (rectangular) | 0.2 |
Bell mouth of 1/4 ellipse | 0.01-0.05 |
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Exit head loss
\begin{equation}
h_{se}=f_{se}\times \cfrac{v_1{}^2}{2 g}
\end{equation}
$h_{se}$ | : exit head loss |
$v_1$ | : mean flow velocity before flow-out |
$f_{se}$ | : exit loss coefficient (=1.0) |
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Reducing or Enlarging head loss |
Reducing head loss
\begin{equation}
h_{gc}=f_{gc}\times \cfrac{v_2{}^2}{2 g}
\end{equation}
$h_{gc}$ | : reducing head loss |
$v_2$ | : mean flow velocity after reducing |
$f_{gc}$ | : reducing loss coefficient |
Loss coefficient of reducer by Gardel
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Enlarging head loss
\begin{equation}
h_{ge}=f_{ge}\times \cfrac{(v_1-v_2)^2}{2 g}
\end{equation}
$h_{ge}$ | : enlarging head loss |
$v_1$ | : mean flow velocity before enlarging |
$v_2$ | : mean flow velocity after enlarging |
$f_{ge}$ | : enlarging loss coefficient |
Loss coefficient of enlargement by Gibson
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Bending head loss |
\begin{equation}
h_{b}=f_{b1}\times f_{b2}\times \cfrac{v_2{}^2}{2 g} \qquad f_{b1}=0.131+0.1632 \left(\cfrac{D}{\rho}\right)^{7/2} \qquad f_{b2}=\left(\cfrac{\theta}{90}\right)^{1/2}
\end{equation}
$h_{b}$ | : bending head loss |
$v$ | : mean flow velocity |
$f_{b1}$ | : loss coefficient determined by ratuo of bending radius $\rho$ to pipe diameter $D$ |
$f_{b2}$ | : loss ratio for center angle $\theta$ (degrees) to loss for center angle 90 degrees |
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Screen head loss |
\begin{equation}
h_{r}=f_{r}\times \cfrac{v_1{}^2}{2 g} \qquad f_{r}=\beta\times \sin\theta\times\left(\cfrac{t}{b}\right)^{4/3}
\end{equation}
$h_{r}$ | : screen head loss |
$v_1$ | : mean flow velocity at upstream of screen |
$f_{r}$ | : screen head loss coefficient |
$\beta$ | : coefficient determined by shape of screen bar (=1.6) |
$\theta$ | : inclined angle of screen |
$t$ | : screen bar thickness (=16 mm) |
$b$ | : space between screen bars (=134 mm) |
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