Environmental Engineering Reference
In-Depth Information
Coriolis force
2
. The result is the menacing spiralling motion familiar from satellite
pictures; the rotation always occurring in opposite directions in the northern and
southern hemispheres.
Example 8.2.3
The effect of the Coriolis force on smaller bodies moving at every-
day speeds is usually negligible. In this example we are asked to compute the size of
the Coriolis force on a car of mass 1500 kg travelling due North across Manchester
at a speed of 100 km h
−
1
.
Solution 8.2.3
Let us first convert the speed into SI units, i.e.
10
3
100
×
ms
−
1
28 ms
−
1
.
v
=
=
60
×
60
53
◦
.Now,since
the car is travelling due North, the Coriolis force is simply given by
In addition we need to know that Manchester is at a latitude λ
=
1
m
F
Cor
=
2
ωv
sin
λ
10
−
5
sin 53
◦
ms
−
1
=
2
×
7
.
3
×
×
28
×
=
4
.
9N
.
(8.33)
PROBLEMS 8
8.1 The centrifugal force acting on a particle of mass
m
at position
r
in a frame
that is rotating with angular velocity
ω
is
−
m
ω
×
(
ω
×
r
)
and it appears at first sight to depend upon the position of the origin. Convince
yourself that this is not the case provided the origin lies somewhere on the
rotation axis.
8.2 A bucket of water rotates about its symmetry axis in the Earth's gravitational
field (the symmetry axis is vertical). In a frame which rotates with the bucket,
determine the direction of the net force that acts on a small mass of water
(which lies a distance
r
from the rotation axis) due to its weight and the
centrifugal force which acts on it. You may assume that all elements rotate
with the same angular velocity
. Convince yourself that the tangent to the
surface of the water at radius
r
should be orthogonal to this force and hence
prove that the surface of the water forms a paraboloid of revolution.
8.3 A particle is released from rest at the top of a tall building of height 150m.
If the building is at a latitude of 53
◦
N, determine that the particle strikes the
ground with a small easterly deflection and compute the size of the deflection.
You may neglect air resistance.
ω
2
Anti-cyclones are regions of high pressure and the air is correspondingly pushed away from the centre.
