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Question
A U-tube containing a liquid is accelerated horizontally with a constant acceleration a0. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.
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Solution
Let a0 be the acceleration with which U-tube is accelerated horizontally. So, the horizontal part will experience some inertial force.
Also,
pa = Atmospheric pressure
A = Area of cross section
h = Increase in height of the liquid
According to the question,
\[p_a A + A \times l \times \rho \times a_0 = p_a A + h\rho g \times A\]
\[ \Rightarrow hg = a_0 l\]
\[ \Rightarrow h = \frac{a_0 l}{g}\]
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