Evaluating losses in intakes

The head loss in an intake is the sum of the following parts. Each is computed as a coefficient times a velocity head, except friction.

1. Trash rack loss (Kirschmer):

$$h_t=\beta\left(\frac{s}{b}\right)^{4/3}\frac{V_a^2}{2g}\sin\theta$$

with $\beta$ = bar shape factor (2.42 rectangular, 1.79 circular), $s$ = bar thickness, $b$ = clear spacing, $V_a$ = approach velocity and $\theta$ = rack inclination to the horizontal. For a partly clogged rack, increase the loss by using the blocked area (net velocity).

2. Entrance loss: $h_e=k_e\dfrac{V^2}{2g}$, where $k_e=0.5$ for a sharp-edged entrance, 0.2 for a rounded one, and 0.05-0.1 for a well-shaped bell-mouth.

3. Gate slot loss: $h_g=k_g\dfrac{V^2}{2g}$, with $k_g\approx0.1$ (nil for a fully open gate with flush slots).

4. Transition loss (contraction or expansion): $h_{tr}=k\dfrac{\left|V_2^2-V_1^2\right|}{2g}$, with $k\approx0.1$ for a gradual contraction and 0.2-0.3 for a gradual expansion.

5. Bend loss: $h_b=k_b\dfrac{V^2}{2g}$, where $k_b\approx0.1-0.25$ depends on the bend radius and angle.

6. Friction loss in the intake conduit (Manning or Darcy):

$$h_f=\frac{n^2V^2L}{R^{4/3}}\quad\text{or}\quad h_f=f\frac{L}{D}\frac{V^2}{2g}$$

Total loss

$$h_L=h_t+h_e+h_g+h_{tr}+h_b+h_f$$

The loss is kept small by a low velocity at the rack (about 0.8-1.0 m/s), a bell-mouthed entrance, smooth gradual transitions and few gate slots. For a typical RoR intake the total is of the order of 0.1-0.3 m; it is subtracted from the gross head when the net head of the plant is worked out.