Head Loss Calculation Formulas



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$^2$)

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$^2$)
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)

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)
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

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)











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

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              Loss coefficient of reducer by Gardel

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

png

              Loss coefficient of enlargement by Gibson

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
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)


inserted by FC2 system