## 2.2Velocity

Like force, velocity is a vector with direction and magnitude, with SI units of . Using the vector to denote the position of a particle of ﬂuid, its velocity is (2.4) ### Vector ﬁelds

While can be used to denote a single velocity with magnitude and direction, it can also denote a vector ﬁeld of velocity which varies from point to point across a spatial domain. A vector is represented by 3 numbers, relating to the co-ordinate system being used, e.g. , , , in the Cartesian system. While the magnitude and direction of a vector is ﬁxed, it is not invariant since the 3 values depend on the co-ordinate system used. We represent a vector without reference to the co-ordinate system by bold text, e.g. ” (compared to scalar “ ”).

### Basic vector algebra

Addition and subtraction of 2 vectors is performed by operating on respective components. Subtraction of two vectors and is performed by Multiplication of any vector by a scalar is performed by multiplying all the components by the scalar, e.g. Addition and multiplication are commutative, i.e. variables can be in any order ( ). Subtraction is not commutative. Products between scalars and vectors are distributive, i.e. and with additional scalar , Division between a vector and a scalar is only relevant when the scalar is the second argument of the operation, i.e. Notes on CFD: General Principles - 2.2 Velocity 