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 s, measured in m

 velocity v, measured in m s 1

 acceleration a, measured in m s 2

In the ...

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