Question
Two cylindrical vessels $V_{1}$ and $V_{2}$ placed same horizontal level. Each vessel contains the same liquid of density $\rho$. Initially the vessels are not connected (valve closed). the height of liquid in vessel $v_{1}$ is $h_{1}$ and that in vessel $V_{2}$ is $h_{2}$. The diameter of vessels $V_{1}$ and $V_{2}$ are 2d and d respectively. When vessels are interconnected (valve opened) at the bottom, the height h of liquid in each vessel (neglecting the volume of liquid in connecting tube) will be
Options
Solution
Sol. Key concept: Equal hydrostatic levels and conservation of liquid volume.
Once connected, the same liquid in the two open vessels settles to a common height h. The diameters are in the ratio 2:1, so their cross-sectional areas are in the ratio 4:1.
$$4Ah_{1} + Ah_{2} = (4A + A)h$$
$$h = \frac{4h_{1} + h_{2}}{5}$$
The final height is an area-weighted average, not the simple mean of the initial heights. Hence (b).
Create a free account to view solution
View Solution Free