GATE 2020 MT – Question 63
A top-gated mold receives a freely falling liquid-metal stream from height 0.5 m. Neglect viscous and directional losses. Mold volume is 10 m³, gate area 0.2 m² and g = 9.8 m/s². Find filling time in seconds, nearest integer.
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Correct answer: 14 to 18
Explanation
The ideal gate speed is $v=\sqrt{2gh}=\sqrt{2(9.8)(0.5)}=3.1305$ m/s. Volumetric flow is $Q=Av=0.2(3.1305)=0.6261$ m³/s. Constant-flow filling time is $t=V/Q=10/0.6261=15.97$ s, or 16 s.