Calculating Depth Below the Surface of Water: What Depth of Water Creates the Same Pressure as the Entire Atmosphere?

Calculate the depth below the surface of water at which the pressure due to the weight of the water equals 1.00 atm.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We begin by solving the equation $P = hρg$ for depth $h$ :

$h = \frac{P}{ρg} .$
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Then we take $P$ to be 1.00 atm and $ρ$ to be the density of the water that creates the pressure.
Solution
Entering the known values into the expression for $h$ gives

$h = \frac{1 . 01 \times 10^{5} {N/m}^{2}}{(1 . 00 \times 10^{3} {kg/m}^{3}) (9.80 {m/s}^{2})} = 10 . 3 m .$
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Discussion
Just 10.3 m of water creates the same pressure as 120 km of air. Since water is nearly incompressible, we can neglect any change in its density over this depth.

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