Absolute pressure. depth

In summary, the correct formula for calculating the depth at which the absolute pressure is 6 times the atmospheric pressure of 1.01 x 105 Pa is h = 5P/ρg, where P is the atmospheric pressure and ρ is the density of water. The mistake made in the calculation was that the depth was calculated for a pressure change of 6 times the surface pressure, rather than the absolute pressure at that depth being 6 times the surface pressure.
  • #1
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At what depth beneath the surface of a lake is the absolute pressure 6 times the atmospheric pressure of 1.01 x 105 Pa that acts on the lake's surface?

pressure = density * g * h

I thought to multiply 6 * 1.10 X 10^5 pa. Then divide that answer by 1000 kg/m3 (density of water, right?) * 9.8 m/s/s.

This was marked wrong my webassign.
Can someone help me figure out what I did wrongly?

Thank you.
 
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  • #2
cavery4 said:
At what depth beneath the surface of a lake is the absolute pressure 6 times the atmospheric pressure of 1.01 x 105 Pa that acts on the lake's surface?

You were almost right, but you calculated the depth at which the change in pressure was six times the surface pressure. This makes the total pressure at that depth slightly more than six times the surface value.

[tex]h\ =\ depth[/tex]

[tex]P-P_s=\Delta P=\rho gh[/tex]

[tex]\frac{P+\Delta P}{P}=6=1+\frac{\rho gh}{P}[/tex]

[tex]h=\frac{5P}{\rho g}[/tex]

Just a little smaller than your value. :smile:
 
  • #3


To find the depth at which the absolute pressure is 6 times the atmospheric pressure, we can use the formula for pressure: P = ρgh, where P is pressure, ρ is density, g is acceleration due to gravity, and h is the depth. We know that the atmospheric pressure acting on the surface of the lake is 1.01 x 10^5 Pa. So, to find the depth at which the absolute pressure is 6 times this atmospheric pressure, we can set up the equation:

6 * 1.01 x 10^5 Pa = ρ * 9.8 m/s^2 * h

Now, we need to find the density of water at the given depth. The density of water changes with depth due to the increasing pressure, so we cannot simply use the density of water at the surface. Instead, we can use the fact that the density of water at a depth of 1 meter is approximately 1000 kg/m^3. This means that at a depth of h meters, the density of water would be approximately 1000 kg/m^3 * h. Substituting this into our equation, we get:

6 * 1.01 x 10^5 Pa = 1000 kg/m^3 * h * 9.8 m/s^2 * h

Simplifying, we get:

6.06 x 10^5 Pa = 9800 kg/m^3 * h^2

Solving for h, we get:

h = √(6.06 x 10^5 Pa / 9800 kg/m^3) = 7.17 meters

Therefore, at a depth of 7.17 meters below the surface of the lake, the absolute pressure would be 6 times the atmospheric pressure. It seems like you may have made a calculation error in your answer, which is why it was marked wrong. I hope this explanation helps you understand the correct way to solve this problem.
 

What is absolute pressure?

Absolute pressure is the total pressure exerted by a fluid, including both the atmospheric pressure and the pressure caused by the weight of the fluid itself.

What is the difference between absolute pressure and gauge pressure?

The main difference is that absolute pressure includes the atmospheric pressure, while gauge pressure only measures the pressure above atmospheric pressure. Absolute pressure is also commonly measured in units of absolute pressure (such as pascals or bar) while gauge pressure is often measured in units of pressure relative to atmospheric pressure (such as psi or bar).

How is depth related to absolute pressure?

The deeper an object is submerged in a fluid, the greater the weight of the fluid above it and therefore the greater the absolute pressure. This is because the weight of the fluid above an object creates a force that contributes to the absolute pressure at that depth.

What instruments are used to measure absolute pressure at different depths?

Instruments such as barometers, manometers, and pressure gauges can measure absolute pressure at different depths. Specialized instruments such as depth gauges and submersible pressure sensors are also used to measure absolute pressure in underwater environments.

Why is it important to consider absolute pressure when working with fluids?

Absolute pressure provides a more accurate measure of the total pressure exerted by a fluid, which is important in many applications such as diving, aviation, and hydraulic systems. It also allows for more accurate calculations and predictions of fluid behavior at different depths.

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