GATE 2024 PI – Question 54
A sand-mold sprue has height h₂ = 200 mm and flow $10^6$ mm³/s. Liquid height above point 2 is h_c = 25 mm. Areas at 2,3 are A₂,A₃; points 1,3 are atmospheric. Set gauge pressure at 2 to zero at the limiting aspiration-free condition. Find A₃/A₂ (two decimals).
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Correct answer: 0.31 to 0.35
Explanation
Bernoulli from the reservoir surface gives $v_2=\sqrt{2gh_c}$ and $v_3=\sqrt{2g(h_c+h_2)}$. Continuity gives $A_3/A_2=v_2/v_3=\sqrt{25/(25+200)}=1/3$, or **0.33**.