jet.md

# Jet impact

The downstream fish evacuation outlet ends with a device that empties into the plant's tailrace. This module calculates the position and velocity at the point of impact of the free fall or water vein on the surface of the tailrace water taking into account the initial angle and velocity of the jet and the drop height.

Excerpt from Courret, Dominique, and Michel Larinier. Guide for the design of ichthyocompatible water intakes for small hydroelectric power plants, 2008. https://doi.org/10.13140/RG.2.1.2359.1449, p.24:

> Speeds in the structure and at the point of impact in the tailrace must remain below about 10 m/s, with some organizations even recommending that they not exceed 7-8 m/s (ASCE 1995). (...) The head between the outlet and the water body must not exceed a dozen metres to avoid any risk of injury to fish on impact, whatever their size and mode of fall (free fall or fall in the water vein) (Larinier and Travade 2002). The discharge must also be made in an area of sufficient depth to avoid any risk of injury from mechanical shock. Odeh and Orvis (1998) recommend a minimum depth of about a quarter of the fall, with a minimum of about 1 m.

## Formula

With \(g\): gravity acceleration = 9.81 m.s-2

### Fall height

$$H = 0.5 * g * \frac{D^{2}}{\cos \alpha^{2} * V_0^{2}} - \tan \alpha * D$$

### Impact abscissa (horizontal distance covered)

$$D = \frac{V_0}{g * \cos \alpha} \left ( V_0 * \sin \alpha + \sqrt{ \left ( V_0 * \sin \alpha \right )^{2} + 2 * g * H } \right )$$

### Flight time

$$t = \frac{D}{V_0 \cos \alpha} $$

### Horizontal speed at impact

$$V_x = V_0 \cos \alpha$$

### Vertical speed at impact

$$V_z = V_0 \sin \alpha - t * g$$

### Speed at impact

$$V_t = \sqrt{ \V_x^{2} + V_z^{2} }$$