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MCE311_HW01_sol_Fall2011

MCE311_HW01_sol_Fall2011 - 9.8 During pouring into a sand...

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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 cross-sectional area at the top = 5 cm 2 and at the base = 3.75 cm 2 . The cross-sectional 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
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