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9.8 During pouring into a sand mold, the molten metal can be poured into the downsprue at a constant
flow rate during the time it takes to fill the mold. At the end of pouring the sprue is filled and there
is negligible metal in the pouring cup. The downsprue is 15 cm long. Its crosssectional area at the
top = 5 cm
2
and at the base = 3.75 cm
2
. The crosssectional area of the runner leading from the
sprue also = 3.75 cm
2
, and it is 20 cm long before leading into the mold cavity, whose volume =
1015 cm
3
. The volume of the riser located along the runner near the mold cavity = 390 cm
3
. It takes
a total of 3.0 sec to fill the entire mold (including cavity, riser, runner, and sprue. This is more than
the theoretical time required, indicating a loss of velocity due to friction in the sprue and runner.
Find (a) the theoretical velocity and flow rate at the base of the downsprue; (b) the total volume of
the mold; (c) the actual velocity and flow rate at the base of the sprue; and (d) the loss of head in
the gating system due to friction.
Solution
: (a) Velocity
v
= (2 × 9.8 × 100 × 15)
0.5
=
171.5 cm/sec
Flow rate
Q
= 171.5 × 3.75 =
643.1 cm
3
/sec
(b) Total
V
= 1015 + 390 + 0.5 (5 + 3.75)(15) + (3.75)(20) =
1545.6 cm
3
(c) Actual flow rate
Q
= 1545.6/3 =
515.2 cm
3
/sec
Actual velocity
v
= 515.2/3.75 =
137.4 cm/sec
(d)
v
= (2 × 9.8 × 100 × h)
0.5
= 44.3 h
0.5
= 137.4 cm/sec
h
0.5
= 137.4/44.3 = 3.102
h
= 3.102
2
= 9.622 cm
Head loss = 15
−
9.622 =
5.378 cm
9.11 A flat plate is to be cast in an open mold whose bottom has a square shape that is 200 mm by 200
mm. The mold is 40 mm deep. A total of 1,000,000 mm
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This note was uploaded on 02/12/2012 for the course MCE 311 taught by Professor Diab during the Fall '11 term at American Dubai.
 Fall '11
 diab

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