Newton's laws can be applied to fluids by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighboring pieces. The Euler momentum equation is an expression of Newton's second law adapted to fluid dynamics. A fluid is described by a velocity field, i.e., a function v ( x , t ) that assigns a velocity vector to each point in space and time. A small object being carried along by the fluid flow can change velocity for two reasons: first, because the velocity field at its position is changing over time, and second, because it moves to a new location where the velocity field has a different value. Consequently, when Newton's second law is applied to an infinitesimal portion of fluid, the acceleration a has two terms, a combination known as a total or material derivative. The mass of an infinitesimal portion depends upon the fluid density, and there is a net force upon it if the fluid pressure varies from one side of it to another. Accordingly, a = F / m becomes ∂ ∂ v ∂ ∂ t + ( ∇ ∇ ⋅ ⋅ v ) v = − − 1 ρ ρ ∇ ∇ P + f , where ρ ρ is the density, P is the pressure, and f stands for an external influence like a gravitational pull. Incorporating the effect of viscosity turns the Euler equation into a Navier–Stokes equation : ∂ ∂ v ∂ ∂ t + ( ∇ ∇ ⋅ ⋅ v ) v = − − 1 ρ ρ ∇ ∇ P + ν ν ∇ ∇ 2 v + f , where ν ν is the kinematic viscosity.