How Deep Must You Dive to Match Venus's Surface Pressure?

[lmannoia]

Homework Statement

Water has a density of 1000kg/m^3, so a column of water n meters tall and 1 meter square at its base has a mass of nx1000kg. On either Earth or Venus, which have nearly the same surface gravity, a mass of 1 kg weighs about 9.8 Newtons. Calculate how deep you would have to descend into Earth's oceans for the pressure to equal the atmospheric pressure on Venus's surface, about 9 x 10^6 N/m^2.

Homework Equations

Density = mass/volume
Pressure = force/unit of surface area

The Attempt at a Solution

I'm confused as to how to relate pressure to density or mass. Any hint or push in the right direction would be greatly appreciated. Thanks!

 

[zhermes]

Remember that pressure is force per unit area. So (for instance), what would be the pressure underneath the column of water in the beginning of the problem?

 

[lmannoia]

Would the pressure equal (n meters)(1000kg)(9.8m/s^2)/m^3?

 

[zhermes]

Would the pressure equal (n meters)(1000kg)(9.8m/s^2)/m^3?

You're on the right track, but not quite.

If we're looking for pressure, we should start with force---provided by gravity, thus F = mg. Mass m is then density times volume. Try to keep everything symbolic here (i.e. use $$\rho$$ instead of 1000). So what's the volume of the column? Then plug in for the force. Now, over what area is that force being distributed?---the pressure is then P = F/A

 

[rwisz]

Density, pressure, and confusion are all related to each other through the concept of fluid mechanics. Density is a measure of how tightly packed the particles of a substance are, while pressure is the force exerted on a surface by a fluid. In this scenario, we are dealing with the fluid properties of water and how they differ on Earth and Venus. The given information about density and mass allows us to calculate the force of gravity on a 1kg mass on both planets. This force, along with the given atmospheric pressure on Venus, can be used to calculate the depth at which the pressure in Earth's oceans would equal the atmospheric pressure on Venus's surface. You can use the equation P = ρgh, where P is pressure, ρ is density, g is the acceleration due to gravity, and h is the depth. From there, you can set the pressure on Earth equal to the atmospheric pressure on Venus and solve for h. I hope this helps clarify the relationship between density, pressure, and confusion in this problem. Keep in mind that understanding these concepts and their relationships is crucial in many areas of science, including fluid mechanics and atmospheric science.