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Influence | strength – When a fluid's velocity is being calculated, there are two calculations in play: the terminal velocity specified by the speed parameters on this rollout, and the simulator's calculation of fluid velocity based on fluid dynamics. The Influence parameter determines the degree to which terminal velocity is used instead of fluid dynamics when calculating speed and direction. A value of 0 relies entirely on fluid dynamics while a value of 1 means the fluid's velocity is set immediately to terminal velocity. Intermediate values give the fluid a certain degree of freedom to respond to fluid dynamics, which provides some natural variation while giving a degree of predictability.

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 To simulate liquid that is constantly accelerating (such as free-falling liquid reacting to gravity), use a high terminal velocity and a very low Influence value.

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Liquid - affects the Liquid particles in a Liquid simulation.
Splashes - affects the Splash particles in a Liquid simulation.
Foam - affects the Foam particles in a Liquid simulation.
Mist - affects the Mist particles in a Liquid simulation.
Air 
- affects the space in a Liquid simulation where there are no Liquid particles, when Simulate Air Effects is enabled in the Dynamics rollout. All particles such as Foam, Splash or Mist outside the liquid volume will be influenced.
Temperature - affects the voxels in a Fire/Smoke simulation where the Temperature is different than the default 300 Kelvins. The higher the temperature above 300 or the lower it is below 300, the stronger the effect of the force would be. You can find out more about Phoenix Grid Channel Ranges here.
Smoke - affects the voxels in a Fire/Smoke simulation where there is Smoke. The denser the smoke, the stronger the effect of the force would be.
Fuel - affects the voxels in a Fire/Smoke simulation where there is Fuel. The denser the fuel, the stronger the effect of the force would be.

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 Affect Names are not case sensitive and any unknown element found in the list is ignored.