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Question

At what depth below the surface of water total pressure would be equal to $$1.5$$ atmosphere?
$$1\;atmosphere=10^5\;Nm^{-2}$$.


Solution

Total pressure at depth $$h$$ below the water surface
$$=atmospheric\;pressure+water\;pressure$$.
Let atmospheric pressure be $$P$$. Then, total pressure $$=1.5\;P$$
$$\therefore\;1.5\;P=P+hdg\Rightarrow hdg=0.5\;P$$
$$\Rightarrow h=\displaystyle\frac{0.5\,P}{dg}=\displaystyle\frac{0.5\times10^5\;Nm^{-2}}{(10^3\,kgm^{-2})\times9.8\;ms^{-2}}$$
$$=\displaystyle\frac{5\times10^5}{10^3\times98}m=\displaystyle\frac{500}{98}m=5.1\;m$$

Physics

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