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 $\stackrel{\to }{s}$, measured in m

velocity $\stackrel{\to }{v}$, measured in m s 1

acceleration $\stackrel{\to }{a}$, measured in m s 2

In the ...

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