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\begin{document}

\frame{\frametitle{\b Fluids - 1} \medskip

{\bf Car in a Lake (1):} Density of water $\rho=10^3\,kg/m^3$,
$$ M = V\,\rho\,,~~~F_{outside}=M\,g+A\,atm $$
with $V$ volume and $A$ area. $F_{inside}$ is then obvious.
\bigskip

{\bf Ballon (2):} $M=V\,(\rho_a-\rho_g)\,.$ \bigskip

{\bf Ballon II (3):} 
$$ F_B = M\,g\,,~~M=V\,\rho\,. $$
Then:
$$ F_w+F_r = F = V\,g\,(\rho-\rho_b) $$
and solve for for $\rho_b$.
\bigskip

{\bf Specific Gravity (4):} 
$$ sg = \rm \frac{weight\ of\ object\ in\ air}{weight\ 
   loss\ when\ submerged\ in\ water}\,. $$
Then multiply $sg$ with the density of water.
\vskip 20pt }


\frame{\frametitle{\b Fluids - 2} \bigskip

{\bf Debris in Ocean (5).} Visible volume:
$$ V_{out} = V\ \frac{\rho_{sw}-\rho}{\rho_{sw}}\,.$$
\bigskip

{\bf Floating Hollow Sphere (6):} Let the number $m$ and $n$ 
be given, (i.e., $m\,R$ and $n\,\rho_0$). Solve
$$ \frac{4\pi}{3}\left[(m\,R)^3-R^3\right]\,\rho_0+
   \frac{4\pi}{3}\,R^3\,\rho_m = \frac{4\pi}{3}\,(m\,R)^3\,n\rho_0 $$
for $\rho_m$.  \bigskip

{\bf Hurricane Force (7):} Use Bernoulli's equation
$$ \triangle P = \frac{1}{2}\,\rho\,v^2\,.$$
\vskip 20pt }
\end{document}
