Two immiscible liquid are filled in conical flask as shown in figure. The area of cross section is shown, a small hole of area a is made in lower end of cone. Find speed of liquid flow from hole
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$P_{0}+\frac{1}{2} 2 \rho v^{2}=P_{1}+2 \rho g h+\frac{1}{2}(2 \rho)\left(\frac{a v}{A}\right)^{2}$
$P_{0}+\frac{1}{2} \rho\left(\frac{a v}{4 A}\right)^{2}+\rho g h=P_{1}+O+\frac{1}{2} \rho\left(\frac{a v}{A}\right)^{2}$
$\Rightarrow \rho v^{2}-\frac{\rho}{32} \frac{a^{2} v^{2}}{A^{2}}+\rho g h=2 \rho g h+\rho \frac{a^{2} v^{2}}{A^{2}}-\frac{\rho}{2} \frac{a^{2} v^{2}}{A^{2}}$
$v^{2}\left[1-\frac{a^{2}}{32 A^{2}}-\frac{a^{2}}{A^{2}} v^{2}+\frac{a^{2} v^{2}}{2 A^{2}}\right]=g h$
$v=\sqrt{\frac{3 g h}{1-\frac{17 a^{2}}{32 A^{2}}}}$
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