Geoscience Reference
In-Depth Information
(a)
y
(a)
Object 1
u
constant
P
t
1
5
Speed-time graph
6
y
t
2
5
t
3
5
3
x
x
-
x
5
t
4
5
Steady motion
Any position, P, can
be described by 2
measures of length
t
5
5
t
1
t
2
t
3
t
4
t
5
Time,
t
-
y
(b)
(b)
Object 1
u
constant
y
5
x
1
Speed-distance graph
P
5
x
2
5
y
u
r
x
3
5
5
x
4
5
Uniform motion
-
3
x
-
x
O
x
5
x
5
If we regard P as
directed from the
origin, O, then the line
OP may also be
specified by its length
r
and angle
u
.
OP is a
position vector
x
1
x
2
x
3
x
4
x
5
Distance,
x
Fig. 2.14
(a) Vectors for steady west to east motion at velocity
u
5ms
1
for times
t
1
t
5. (b) Vectors for uniform west to east
5ms
1
for positions
x
1
motion at velocity
u
x
5.
-
y
The description of steadiness depends upon the frame of
reference being fixed at a local point. We may take instan-
taneous velocity measurements down a specific length,
s
,
of the flow. In such a case the flow is said to be
uniform
when there is no velocity change over the length, that is,
z
(c)
P
y
u
r
6
z
0 (Fig. 2.14b).
This division into steady and uniform flow might seem
pedantic but in Section 3.2 it will enable us to fully explore
the nature of acceleration, a topic of infinite subtlety.
u
/
s
-
x
O
3
x
-3
y
f
x
-
y
2.4.6
Fields
Vector OP is either:
(3
x
, -3
y
, 6
z
) or (
r
,
)
u
f
A
field
is defined as any region of space where a physical
scalar or vector quantity has a value at every point. Thus
we may have scalar speed or temperature fields, or, a
vectorial velocity field. Crustal scale rock velocity
(Figs 2.15 and 2.16), atmospheric air velocity, and labora-
tory turbulent water flow are all defined by fields at various
scales. Knowledge of the distribution of velocities within a
flow field is essential in order to understand the dynamics
of the material comprising the field (e.g. Fig. 2.16).
-
z
Fig. 2.13
Coordinate systems: (a) Two dimensions; (b) two dimen-
sions with polar notation, and (c) three dimensions.
velocity is unchanged with time,
t
, then the flow is said to
be
steady
(Fig. 2.14a). Mathematically we can write that
the change of
u
over a time increment is zero, that is,
u
/
t
0.
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