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Introduction to Fluid Mechanics. Engineering 1h Prof Bill Easson. Definition of a Fluid. A fluid is a substance that flows under the action of shearing forces. If a fluid is at rest, we know that the forces on it are in balance.

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introduction to fluid mechanics

Introduction to Fluid Mechanics

Engineering 1h

Prof Bill Easson

definition of a fluid
Definition of a Fluid

A fluid is a substance that flows under the action of shearing forces. If a fluid is at rest, we know that the forces on it are in balance.

A gas is a fluid that is easily compressed. It fills any vessel in which it is contained.

A liquid is a fluid which is hard to compress. A given mass of liquid will occupy a fixed volume, irrespective of the size of the container.

A free surface is formed as a boundary between a liquid and a gas above it.

density
Density

The density of a fluid is defined as its mass per unit volume. It is denoted by the Greek symbol, .

kg

 water= 998 kgm-3

m

 =

V

air =1.2kgm-3

kgm-3

m3

If the density is constant (most liquids), the flow is incompressible.

If the density varies significantly (eg some gas flows), the flow is compressible.

(Although gases are easy to compress, the flow may be treated as incompressible if there are no large pressure fluctuations)

pressure
Pressure

Pressure is the force per unit area, where the force is perpendicular to the area.

N

pa= 105 Nm-2

F

p=

Nm-2

(Pa)

A

1psi =6895Pa

m2

This is the Absolute pressure, the pressure compared to a vacuum.

The pressure measured in your tyres is the gauge pressure, p-pa.

pressure5
Pressure

Pressure in a fluid acts equally in all directions

Pressure in a static liquid increases linearly with depth

p=

g  h

increase in depth (m)

pressure increase

The pressure at a given depth in a continuous, static body of liquid is constant.

p3

p1 = p2 = p3

p1

p2

measuring pressure 1 manometers
Measuring pressure (1)Manometers

(negligible pressure change in a gas)

p1 = px

p1

(since they are at the same height)

px = py

p2=pa

z

pz= p2 = pa

h

x

y

py - pz = gh

liquid

density 

p1 - pa = gh

So a manometer measures gauge pressure.

measuring pressure 2 barometers
Measuring Pressure (2)Barometers

vacuum

p1 = 0

A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid.

h

p2 - p1 = gh

p2 = pa

pa = gh

examples

water: h = pa/g =105/(103*9.8) ~10m

mercury: h = pa/g =105/(13.4*103*9.8) ~800mm