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JCECE Engineering JCECE Engineering Solved Paper-2013

  • question_answer
    Equal volume of two immiscible liquids of densities \[p\] and \[2p\] are filled in a vessel as shown in figure. Two small holes are made at depth \[\frac{h}{2}\] and \[\frac{3h}{2}\] from the surface of lighter liquid. If \[{{v}_{1}}\] and \[{{v}_{2}}\] are the velocities of efflux at these two holes, then \[{{v}_{1}}/{{v}_{2}}\] will be.

    A) \[\frac{1}{\sqrt{2}}\]                                     

    B) \[\frac{1}{2\sqrt{2}}\]

    C)  \[\frac{1}{2}\]                                  

    D)  \[\frac{1}{4}\]

    Correct Answer: A

    Solution :

    We have\[{{v}_{1}}=\sqrt{2gh(h/2)}=\sqrt{gh}\]               ... (i) and by using Bernoulli's theorem                 \[\rho gh+2\rho g\left( \frac{h}{2} \right)=\frac{1}{2}(2\rho )v_{2}^{2}\] \[\Rightarrow \]                               \[{{v}_{2}}=\sqrt{2}gh\]                                ... (ii) From Eqs. (i) and (ii)                                 \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1}{\sqrt{2}}\]


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