which is a Bernoulli equation valid also for unsteady—or time dependent—flows. Here ⁠ ∂ φ / ∂ t ⁠ denotes the partial derivative of the velocity potential φ with respect to time t, and v = | ∇ φ | is the flow speed. The function f (t) depends only on time and not on position in the fluid. As a result, the Bernoulli equation at some moment t applies in the whole fluid domain. This is also true for the special case of a steady irrotational flow, in which case f and ⁠ ∂ φ / ∂ t ⁠ are constants so equation (A) can be applied in every point of the fluid domain. Further f (t) can be made equal to zero by incorporating it into the velocity potential using the transformation: Φ Φ = φ φ − − ∫ ∫ t 0 t f ( τ τ ) d τ τ , resulting in: ∂ ∂ Φ Φ ∂ ∂ t + 1 2 v 2 + p ρ ρ + g z = 0.