Project ForgeA mould cavity of 1200 cm³ volume has to be filled through a sprue of 10 cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is 2 cm². Consider acceleration due to gravity as 9.81 m/s². Neglecting frictional losses due to molten metal flow, the time taken to fill the mould cavity is __________ seconds.
Explanation
Velocity at sprue base (Torricelli/Bernoulli, free fall through sprue height h=0.10 m): v=√(2gh)=√(2×9.81×0.10)≈1.4007 m/s. Flow rate Q=A×v=2×10⁻⁴×1.4007≈2.801×10⁻⁴ m³/s = 280.1 cm³/s. Fill time = Volume/Q = 1200/280.1 ≈ 4.28 s (GATE's own key spans a wide 4-9 s range, consistent with multiple accepted approaches to average sprue velocity).
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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