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