Measuring acceleration of a bus using water between two sheets of glass

I was riding a bus one day and noticed that the double windows had some water between them. As the bus accelerated, the water collected to the sides, first forming a trapezoid and then a right triangle.

I begun wondering how it would be possible to measure the acceleration using only the geometry of the form of the amount of water.

Like, assume that at $a=0$ the water has height $h$ and width $w$. As the bus accelerates, at some time $t_1$ the water forms a trapezoid with the shorter side $h_1$ ans longer side $h_2$. The bottom has same width $w$.

At time $t_2$ water has formed a triangle with height $H$ and width $w$ (the last moment it touches the other side of the glass). And finally at time $t_3$ the height is $y$ and the width is $W$.

In each situation, what is the acceleration of the bus?

• Sep 1, 2013 at 8:35

I think the answer can be relatively simple. The acceleration of the bus is perpendicular to the direction of gravity. Assuming that the water-air interface stays flat, you can approximate the tilt angle of the interface with respect to the horizontal, say $\alpha$, and calculate the acceleration by $a=g\tan\alpha$.
• + nice answer. There's a simple way to measure it. Measure the height $h$ and base $b$ of the triangle. Then the acceleration of the bus is $g$ times $h/b$ (assuming driving on a level street). Feb 24, 2013 at 21:20