Underwater Pressure: 9.42 ATM, Find Vessel's Depth

• cchiapuzio
In summary, underwater pressure is measured in atmospheres (ATM) or pounds per square inch (PSI), with 1 ATM being equivalent to the pressure at sea level. The formula for calculating underwater pressure is P = ρgh, and a pressure gauge is used to determine a vessel's depth. A depth of 9.42 ATM is not safe for humans, as it is too great for the body to withstand without proper equipment and training.
cchiapuzio

Homework Statement

The pressure exerted on an underwater vessel is 9.42 ATM. If the vessel is in fresh water, to what depth has the vessel descended?

2. Formula

P=Po + pgh

It is fresh water so p=1000 kg/m^3

Last edited:
Hi cchiapuzio and welcome to the forum!
Do you know any formula that relates pressure vs depth? If yes, post it here and try to use it.
Also, what is water density?

Po= atmospheric pressure= 1 ATM

g= gravitational acceleration= 9.8 m/s^2

Solution:

To find the depth of the vessel, we can rearrange the formula to solve for h (depth):

h = (P - Po)/pg

Substituting the given values, we get:

h = (9.42 ATM - 1 ATM)/ (1000 kg/m^3 * 9.8 m/s^2)

= 0.042 ATM / 9800 kg/m^2s^2

= 4.2857 * 10^-6 m

Therefore, the vessel has descended to a depth of approximately 4.2857 micrometers. It is important to note that this calculation assumes the vessel is in a completely enclosed environment and there are no other factors affecting the pressure. In real-world scenarios, there may be other variables that need to be taken into account.

1. How is underwater pressure measured?

Underwater pressure is measured in atmospheres (ATM) or pounds per square inch (PSI). 1 ATM is equivalent to the pressure at sea level, which is 14.7 PSI.

2. What is the formula for calculating underwater pressure?

The formula for calculating underwater pressure is P = ρgh, where P is the pressure, ρ is the density of the fluid (in this case, water), g is the acceleration due to gravity, and h is the depth.

3. What does 9.42 ATM mean in terms of underwater pressure?

9.42 ATM means that the pressure at a certain depth underwater is 9.42 times greater than the pressure at sea level. This is equivalent to a depth of approximately 94.2 meters (308.4 feet).

4. How is a vessel's depth determined using underwater pressure?

A vessel's depth can be determined using a pressure gauge, which measures the pressure exerted by the water at a certain depth. The pressure reading is then used in the formula P = ρgh to calculate the depth of the vessel.

5. Is it safe for humans to be at a depth of 9.42 ATM?

No, it is not safe for humans to be at a depth of 9.42 ATM. The recommended maximum depth for recreational scuba diving is approximately 40 meters, or 4 ATM. At a depth of 9.42 ATM, the pressure would be too great for the human body to withstand without proper equipment and training.

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