Calculating the Depth for 1 atm Gauge Pressure in Fresh Water

In summary, gauge pressure under water is the pressure exerted by the weight of water relative to atmospheric pressure. It is different from absolute pressure, which takes into account the pressure of the atmosphere. Gauge pressure under water can be calculated using the formula P = ρgh, and it can be affected by factors such as depth, density, and gravitational force. This measurement is important in scientific research, specifically in fields such as oceanography, hydrology, and engineering, to study water pressure's effects on structures, marine life, and ocean currents.
  • #1
rasen58
71
2

Homework Statement


Approximately how deep into water must a diver dive to reach the point where the gauge pressure is 1 atm. (1 atm = 1.013 x 10^5 N/m^2) (assume fresh water)

Homework Equations


gauge pressure = pgd
density of fresh water p = 1 kg/m^3

The Attempt at a Solution


pgd = (1 kg/m^3)(10 m/s^2)(d) = 1.013 x 10^5 N/m^2
d = 10130 m

But the answer is actually 10 m. So what did I do wrong?
 
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  • #2
Confirm your figure for water density. A cubic meter is a pretty big container!
 
  • #3
Oh wow, I forgot that density of water is 1000 kg/m^3.
Thanks.
 

FAQ: Calculating the Depth for 1 atm Gauge Pressure in Fresh Water

1. What is gauge pressure under water?

Gauge pressure under water is the pressure exerted by the weight of the water above a certain point, measured relative to atmospheric pressure. It is typically expressed in units of pounds per square inch (psi) or kilopascals (kPa).

2. How is gauge pressure under water different from absolute pressure?

Gauge pressure under water is a measurement of pressure relative to atmospheric pressure, while absolute pressure takes into account the pressure of the atmosphere itself. This means that absolute pressure will always be higher than gauge pressure under water, since it includes the weight of the atmosphere as well.

3. How is gauge pressure under water calculated?

Gauge pressure under water can be calculated using the formula P = ρgh, where P is the pressure in pascals, ρ is the density of the water in kilograms per cubic meter, g is the acceleration due to gravity in meters per second squared, and h is the depth of the water in meters.

4. What factors can affect gauge pressure under water?

The main factors that can affect gauge pressure under water are the depth of the water, the density of the water, and the strength of the gravitational force. Other factors such as temperature, salinity, and the presence of other substances in the water can also have an impact.

5. How is gauge pressure under water used in scientific research?

Gauge pressure under water is an important measurement in many areas of scientific research, including oceanography, hydrology, and engineering. It is used to study the effects of water pressure on structures, marine life, and water flow. It is also used to measure the depth and pressure of the ocean in order to better understand ocean currents and climate patterns.

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