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At what depth beneath the surface of the lake is the pressure in the water equal to twice atmospheric pressure?
  1. 10 m
  2. 100 m
  3. 1000 m
  4. 10,000 m
Question by OpenStax is licensed under CC BY 4.0.
Final Answer

(a)

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OpenStax College Physics Solution, Chapter 12, Problem 3 (Test Prep for AP® Courses) (1:08)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We're looking for the depth in a lake such that the absolute pressure is equal to twice atmospheric pressure. So I've had P subscript atm for atmospheric pressure. And this is the absolute pressure in the water, that's depth h. And so we have the gauge pressure which is rho gh to the atmospheric pressure to get the absolute pressure. And this absolute pressure has equal two times atmospheric pressure. So we subtract the Patm from both sides. So this makes one Patm on the right side. And then divide both sides by rho g and we get the height is atmospheric pressure divided by density of water times gravitational field strength. So it's 1.013 times ten to the five Newton's per square meter divided by one thousand kilograms per cubic meter times 9.81 Newton's per kilogram which gives the depth of 10.3 meters. So at ten meters, the absolute pressure in the water would be twice atmospheric pressure.