It is used in continuum mechanics, when a continuum occupies a simply-connected region and is irrotational. In such a case, ∇ ∇ × × u = 0 , where u denotes the flow velocity. As a result, u can be represented as the gradient of a scalar function Φ : u = ∇ ∇ Φ Φ = ∂ ∂ Φ Φ ∂ ∂ x i + ∂ ∂ Φ Φ ∂ ∂ y j + ∂ ∂ Φ Φ ∂ ∂ z k .