GATE 2017 ME (ME1) – Question 64

Casting, Forming and Joining Processes · Plastic deformation and yield criteria, hot and cold working · 2 marks · Numerical answer

A sand-mould sprue has top diameter 20 mm and height 200 mm. Molten metal enters at 0.5 m/s. The mould is well ventilated; take g = 9.8 m/s² and neglect losses. Find metal speed at the sprue bottom in m/s, to three decimal places.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 2.04 to 2.07

Explanation

Top and bottom are at atmospheric pressure under the stated ventilation assumption. Bernoulli’s equation gives $v_b^2=v_t^2+2gh=0.5^2+2(9.8)(0.2)=4.17$. Thus $v_b=\sqrt{4.17}=2.04206$ m/s, or 2.042 m/s. The top diameter determines flow rate but cancels from this lossless energy relation.

More Plastic deformation and yield criteria, hot and cold working questions

GATE 2025 ME Q22 – The yield stress of a metal in uniaxial tension is 200 MPa. According to von Mises yield…
GATE 2019 ME (ME1) Q44 – The plane-strain forging block shown has zero z strain and uniaxial-compression yield…
GATE 2018 ME (ME1) Q60 – A bar is compressed to half its original length. True-strain magnitude, to two decimals,…
GATE 2018 ME (ME2) Q56 – A metal’s true stress (MPa)–true strain relation is =10200.4. Its initial cross-sectional…
GATE 2016 ME (ME2) Q33 – The value of true strain produced in compressing a cylinder to half its original length is

All Plastic deformation and yield criteria, hot and cold working questions →