Project ForgeManufacturing Engineering
Metal Casting
GATE 2017
Medium
A sprue in a sand mould has a top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/s. Assume acceleration due to gravity as 9.8 m/s² and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is __________ m/s.
2.055 m/s(± 0.015 accepted)
Explanation
By Bernoulli's equation (free-fall energy conservation) through the sprue: v_bottom = √(v_top² + 2gh) = √(0.5² + 2×9.8×0.2) = √(0.25+3.92) = √4.17 ≈ 2.042 m/s.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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