Introduction to Fluid Mechanics

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Introduction to Fluid Mechanics

• Benno Rahardyan

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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.
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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
m3
kgm-3
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)
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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.
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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
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Measuring pressure (1)Manometers
(negligible pressure change in a gas)
p1 px
p1
(since they are at the same height)
px py
p2pa
z
pz p2 pa
h
x
y
py - pz ?gh
liquid density ?
p1 - pa ?gh
So a manometer measures gauge pressure.
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Measuring Pressure (2)Barometers
p1 0
vacuum
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/(1039.8) 10m
mercury h pa/?g 105/(13.41039.8) 800mm