Water level in tilted container I have a rectangular container of water. I know the container size (2 dimensions). Let's say, when the container stays on a flat plane the water level is 10 cm. How to correctly calculate the water level for this container if I tilt it 30 degrees? Or just point me to the topic of what I should learn about it.
I see that I could have two cases, when water is low and I tilt the container - water forms a triangle, when I have more water - it forms a trapezoid.
 A: $\newcommand{\bl}[1]{\boldsymbol{#1}} 
\newcommand{\e}{\bl=}
\newcommand{\p}{\bl+}
\newcommand{\m}{\bl-}
\newcommand{\gr}{\bl>}
\newcommand{\les}{\bl<}
\newcommand{\greq}{\bl\ge}
\newcommand{\leseq}{\bl\le}
\newcommand{\plr}[1]{\left(#1\right)}
\newcommand{\tl}[1]{\tag{#1}\label{#1}}
$
Hint :
Consider that
\begin{equation}
\begin{split}
\mathrm w & \e \texttt{container width}\\
\mathrm h_0 & \e \texttt{water level on flat plain}\\
\theta & \e \texttt{tilt angle}\\
\mathrm h\plr \theta & \e \texttt{water level in the tilted by $\theta$ container }\\
\end{split}
\tl{01}
\end{equation}
First, try to find $\:\mathrm h\plr \theta\:$ under the hypothesis of trapezoidal section. Find the condition on $\:\theta\:$ to have a trapezoid.
Second, try to find $\:\mathrm h\plr \theta\:$ under the hypothesis of triangular section. Find the condition on $\:\theta\:$ to have a triangle.
Your results must agree to the fact that the section is trapezoidal or triangular for $\:\theta\les\theta_0\:$ or $\:\theta\greq\theta_0\:$ respectively where
\begin{equation}
\tan\theta_0\stackrel{???}{\e\!\!\!\!\e} f\plr{\mathrm h_0,\mathrm w}
\tl{02}
\end{equation}



A: The key is that water can be considered incompressible, i e.,  having a constant density, and hence constant volume. For a cylindrical container the volume is trivially calculated as a product of the container area and water level:
$$V=Ah_0.$$
In a tilted container the dependence of volume on the level will be more complex. Suppose it is given by $f(h)$, then you find the level by solving
$$f(h)=V$$
for $h$. Most of the work thus goes into calculating the dependence $f(h)$.
