A
2
. If the falling stream is continuous it is clear
that conservation of matter dictates that
Q v
1
A
1
v
2
A
2
v
3
A
3
etc:
where subscript 3 can refer to any downstream
location for the local values of the area of the
stream and its velocity (for instance the area and
velocity at the gates). Since the velocities are
now known from the height that the melt has
fallen (neglecting any losses at this stage), and Q
has been decided, each of the areas of the filling
system can now be calculated.
In nearly all previous treatises on running
systems the important dimension of the sprue for
controlling the precise rate of flow has been
assumed to be the area of the exit. This part of the
system has been assumed to act as `the choke',
regulating the rate of flow of metal throughout
the whole running system. It is essential to revise
this thinking. If the sprue is correctly designed to
just touch the surface of the falling liquid at all
points, the whole sprue is controlling. There is
nothing special about the narrowest part at the
sprue exit. We shall continue this concept so far
as we can throughout the rest of the filling sys-
tem. If we achieve the target of fitting the
dimensions of the flow channels in the mould just
to fit the natural shape of the flowing stream, it
follows that no one part is exerting control. The
whole system is all just as large as it needs to be;
the channels of the filling system just touch the
flowing stream at all points.
Even so, after such features as bends and
filters and other complications, the energy losses
are not known precisely. Thus there is a sense in
which the sprue (not just its exit, remember) is
doing a good job of controlling, but beyond this
point the precision of control may be lost to
some extent after those features that introduce
imponderables to the flow. (In the fullness of
time we hope to understand the features better.
Even now, computers are starting to make
useful inroads to this problem area.)
Thus, as long as the caster pours as fast as
possible, attempting to fill the pouring basin as
quickly as possible, and keeping the basin full
during the whole of the pour, then he or she will
have no influence on the rate of filling inside the
mould; the sprue (the whole sprue, remember)
will control the rate at which metal fills the
mould.
For most accurate results it is best to calcu-
late the sprue dimensions using the formulae
given above, and using the alloy density to
obtain the initial volume flow rate Q.
However, for many practical purposes we
can take a short cut. It is possible to construct a
useful nomogram for Al assuming a liquid
density of 2500 kg m
ÿ3
and for the dense alloys
based on Fe and Cu assuming a liquid density
around 7500 kg m
ÿ3
(Figure 2.62). Thus areas of
sprues at the top and bottom can be read off,
and the sprue shape formed simply by joining
these areas by a straight taper. Using the dia-
gram it is simple to read off areas of the sprue at
any other intermediate level if it is desired to
provide a more accurately formed sprue having
a curved taper. Recall that the heights are
measured in every case from the level of metal in
the pouring basin, regarding this as the zero
datum.
The nomogram is easy to use. For instance if
we wish to pour an aluminium alloy casting at
an average rate of 1.0 kg s
ÿ1
, corresponding, of
course, to an initial rate of 1.5 kg s
ÿ1
, Figure 2.62
is used as follows. The 1.5 kg s
ÿ1
rate with a
depth in the basin (the top level down to the
level of the sprue entrance) of 100 mm, and a
sprue length of 200 mm (total head height to the
top of the melt in the basin of 300 mm), then its
entrance and exit areas can be read from the
figure as approximately 440 mm
2
and 250 mm
2
respectively. Remember from section 2.3.2.3
that it is advisable to increase the area of the
entrance by approximately 20 per cent to com-
pensate for errors, particularly the error intro-
duced if the sprue shape is approximated to a
straight taper. Thus the final sprue entrance
should be close to 500 mm
2
.
As a check on the nomogram read-outs for our
aluminiumalloy casting, we can now calculate the
dimensions numerically using the equations given
above. At 1.0 kg s
ÿ1
average fill rate, corre-
sponding to an initial rate 1.5 kg s
ÿ1
, assuming
a liquid density of 2500 kg m
ÿ3
, we obtain an
initial volume flow rate Q 1.5/2500 0.6
10
ÿ3
m
3
s
ÿ1
. We can calculate that the falls
of 100 mm and 300 mm are seen to cause the
melt to accelerate to a velocity of 1.41 and
2.45 m s
ÿ1
, giving areas of 424 and 245 mm
2
respectively. These values are in reasonable
agreement with those taken directly from the
nomogram.
The cross-section of the filling system can, of
course, be round or square, or even some other
shape, provided the area is correct (we are
neglecting the small corrections required as a
result of increased drag as sections deviate fur-
ther from a circle). However, in view of making
the best junction to the runner, a slot sprue and
slot runner are strongly recommended for most
purposes. (Multiple sprues might be useful to
connect to a number of runners. Several such
sprues would be expected to work better than
one large sprue as a result of improved con-
straint of the metal during its fall as shown in
Figure 2.63.)
98 Castings Practice: The 10 Rules of Castings