Microfluidics: Modeling, Mechanics and Mathematics

Chapter 7

Vector Calculus

7.1 Scalars and Vectors

7.1.1 Introduction

Scalar Quantities. There are two types of quantities describing fluid flows: scalar and vector quantities. Scalar quantities are quantities that are described only by a magnitude. They do not have a direction of action. For fluids the relevant scalar quantities are

• temperature T , measured in K

• density ρ, measured in kg m^− 3

• pressure p, measured in Pa

In the following we will use the symbol ψ whenever referring to a scalar quantity.

Vector Quantities. Vector quantities have both magnitude and a direction of action. The relevant vector quantities of fluid flows are

• position $\overrightarrow{s}$, measured in m

• velocity $\overrightarrow{v}$, measured in m s^− 1

• acceleration $\overrightarrow{a}$, measured in m s^− 2

In the ...