GATE Papers >> Mechanical >> 2017 >> Question No 54

Question No. 54 Mechanical | GATE 2017

A sprue in a sand mould has 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

Answer : 2.04 to 2.07

Solution of Question No 54 of GATE 2017 Mechanical Paper

Taking bottom of sprue as reference datum

$ \begin{array}{l}{\mathrm P}_1={\mathrm P}_\mathrm{atm}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\mathrm P}_2={\mathrm P}_\mathrm{atm}\\{\mathrm h}_1\;=200\mathrm{mm}=0.2\mathrm m\;\;\;\;\;\;{\mathrm h}_2=0\\{\mathrm v}_1=0.5\;\mathrm m/\mathrm s\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\mathrm v}_2=?\end{array} $

Apply Bernoulli's principle

$ \begin{array}{l}\frac{{\mathrm P}_1}{\mathrm{ρg}}+\frac{\mathrm v_1^2}{2\mathrm g}+{\mathrm h}_1=\frac{{\mathrm P}_2}{\mathrm{ρg}}+\frac{\mathrm v_2^2}{2\mathrm g}+{\mathrm h}_2\\\frac{\mathrm v_1^2}{2\mathrm g}+{\mathrm h}_1=\frac{\mathrm v_2^2}{2\mathrm g}\\{\mathrm v}_2=\sqrt{\mathrm v_1^2+2{\mathrm{gh}}_1}\\{\mathrm v}_2=\sqrt{\left(0.5\right)^2+2\left(9.81\right)\left(0.2\right)}\\{\mathrm v}_2=2.0420\;\mathrm m/\mathrm s\end{array} $

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