Exercise 1.2.21

Question

At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in$^2$. Below the surface, the water pressure increases by 4.34 lb/in$^2$ for every 10 ft of descent.
    \begin{enumerate}[label=(\alph*)]
        \item Express the water pressure as a function of the depth below the ocean surface.
        \item At what depth is the pressure 100 lb/in$^2$?
    \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
    \item Let $h$ be the depth below the ocean surface, $p$ - the water pressure on the depth $h.$ We define the function $p$ as follows:
    $$\forall h\in [0,35814]:\quad p(h)=15+\frac{h}{10}\cdot 4.34,$$
    where 35,814 feet is the depth of Challenger Deep - the deepest point known on Earth.
    \item Now, we must find $h$ for $p(h)=100 	ext{ lb/in}^2:$
    $$15+\frac{h}{10}\cdot 4.34=100.$$
    $$\frac{h}{10}\cdot 4.34=85.$$
    Thus, we have:
    $$h\approx 196\mathrm{~ft}.$$
\end{enumerate}

Exercise 1.2.21

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Exercise 1.2.21

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