### Major Loss / Friction Loss in Open Channel Flow

As described in pipe flow, the head loss in open channel flow is also categorized into two parts as Major Loss (or friction loss) & Minor Loss. The friction loss in open channel is calculated from Manning's equation as below:

$$v=\frac{1}{n}R^{2/3}S^{1/2}$$

$$or, v=\frac{1}{n}R^{2/3}(\frac{h_f}{L})^{1/2}$$

$$\therefore h_f=\frac{n^2v^2}{R^{4/3}}L \tag{1}$$

where,

$n$ = Manning's Constant

$R=\frac{A}{P}$

= Hydraulic Radius

$L$ = Length of Channel

$v$ = Velocity of flow

Equation (1) gives the head loss in open channel caused by friction.

### Minor Loss / Local Loss in Open Channel Flow

Minor head loss occurs due to change in velocity of flow either in magnitude or in direction such as at channel contraction and enlargements, at bends, etc. Minor losses in open channel flow can be formulated as below:

**1. Head loss due to channel enlargement**

$$h_m=k_e\left(\frac{v_1^2}{2g}-\frac{v_2^2}{2g}\right)$$

**2. Head loss due to channel contraction**

$$h_m=k_c\left(\frac{v_2^2}{2g}-\frac{v_1^2}{2g}\right)$$

where,

$k_e$= Enlargement coefficient

$k_c$= Contraction coefficient

The value of these coefficients can be adopted as below:

**3. Head loss at channel bends**

Tests on large canals showed that losses due to bends could be estimated from following equation:

$$h_m=0.001(\Sigma \Delta^{\circ})\frac{v^2}{2g}$$

where, $\Sigma \Delta^{\circ}$ is summation of deflection angles in the reach.