Question

At what depth beneath the surface of the lake is the pressure in the water equal to twice atmospheric pressure?

- 10 m
- 100 m
- 1000 m
- 10,000 m

Final Answer

(a)

Solution Video

#### Sign up to view this solution video!

View sample solution## Calculator Screenshots

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.