Suspended particles (scattering materials) are moving at the same velocity as the water

ADCP instruments cannot measure water velocity directly. The instruments utilize the Doppler effect by transmitting a wave/sound pulse and listening for the return. The pulse does not reflect from the water itself, but from small suspended particles in the water known as scattering materials. The scattering materials float passively and it is assumed that they move with the same speed as the water - the measured velocity of the particles is the velocity of the water surrounding the particle. The instrument relates the change in frequency of the acoustic pulse to a relative velocity of the scattering particle as the particle moves relative to the instrument. Only changes in the distance between the instrument and the scattering material (radial motion, along the path of the acoustic pulse) can be measured since this is the only motion that affects the Doppler shift.

At a given depth, water velocities are constant and horizontally homogeneous

In the ocean, currents may vary rapidly with depth but vary slowly over horizontal displacements. By assuming horizontal homogeneity it allows the instrument to measure the Doppler shift along each beam individually and determine the velocity in multiple dimensions. 

Salinity is constant

Salinity is a key component in determining the speed of sound in water, a necessary variable in calculating current velocities. The speed of sound increases as salinity, temperature and pressure increase, however, it is much more sensitive to temperature and pressure variations so salinity is assumed to be constant. The salinity is predetermined prior to deployment and in ocean applications is often set to 35 ppt (35 grams of dissolved salts in one kilogram of water). This is also the standard for Nortek software.