For General cross section

$$h_{f1}=f'\times \cfrac{L}{R}\times \cfrac{v{}^2}{2 g} \qquad f'=\cfrac{2 g n^2}{R^{1/3}}$$
 $h_{f1}$ : 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

$$h_{f2}=f\times \cfrac{L}{D}\times \cfrac{v{}^2}{2 g} \qquad f=\cfrac{124.5 n^2}{D^{1/3}}$$
 $h_{f2}$ : 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$^2$)

$$h_{br1}=f_{br1}\times \cfrac{v_1{}^2}{2 g}$$
 $h_{br1}$ : branch head loss $v_1$ : mean flow velocity before branch $f_{br1}$ : branch loss coefficient (=0.4)

$$h_{br2}=f_{br2}\times \cfrac{v_2{}^2}{2 g}$$
 $h_{br2}$ : confluence head loss $v_2$ : mean flow velocity after confluence $f_{br2}$ : confluence loss coefficient (=0.4)

$$h_{e}=f_{e}\times \cfrac{v_2{}^2}{2 g}$$
 $h_{e}$ : 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

$$h_{se}=f_{se}\times \cfrac{v_1{}^2}{2 g}$$
 $h_{se}$ : exit head loss $v_1$ : mean flow velocity before flow-out $f_{se}$ : exit loss coefficient (=1.0)

$$h_{gc}=f_{gc}\times \cfrac{v_2{}^2}{2 g}$$
 $h_{gc}$ : reducing head loss $v_2$ : mean flow velocity after reducing $f_{gc}$ : reducing loss coefficient

Loss coefficient of reducer by Gardel

$$h_{ge}=f_{ge}\times \cfrac{(v_1-v_2)^2}{2 g}$$
 $h_{ge}$ : enlarging head loss $v_1$ : mean flow velocity before enlarging $v_2$ : mean flow velocity after enlarging $f_{ge}$ : enlarging loss coefficient
$$h_{b}=f_{b1}\times f_{b2}\times \cfrac{v_2{}^2}{2 g} \qquad f_{b1}=0.131+0.1632 \left(\cfrac{D}{\rho}\right)^{7/2} \qquad f_{b2}=\left(\cfrac{\theta}{90}\right)^{1/2}$$
 $h_{b}$ : 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
$$h_{r}=f_{r}\times \cfrac{v_1{}^2}{2 g} \qquad f_{r}=\beta\times \sin\theta\times\left(\cfrac{t}{b}\right)^{4/3}$$
 $h_{r}$ : 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)