Question

A U-tube containing a liquid is accelerated horizontally with a constant acceleration $a_0$. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.

Answer 1

Since, the U tube is accelerated horizontally, inertia force will be experienced by the horizontal part.

If $P_a\to$ atm pressure
A $\to$ area of cross section
h $\to$ Increase in height

$P_{a}A+A\times L\times P\times a_0$

= $P_{a}A+h\rho g\times A$

$\Rightarrow hg=a_{0}L$

$\Rightarrow h=\frac{a_{0}L}{g}$