Calculating pressure in high altitude?

In summary, the change in pressure on a special-op soldier who must scuba dive at a depth of 20 m in seawater one day and parachute at an altitude of 7.6 km the next day can be calculated using the formula p=p0 + ρgh. The solution manual incorrectly ignores atmospheric pressure, resulting in an incorrect final answer. The correct calculation takes into account the atmospheric pressure at the surface, which is significantly lower at 7.6 km.
  • #1
dmk90
8
0

Homework Statement


What is the change in pressure on a special-op soldier who must scuba dive at a depth of 20 m in seawater one day and parachute at an altitude of 7.6 km the next day? Assume that the average air density within the altitude
range is 0.87 kg/m3.

Homework Equations


p=p0 + ρgh

The Attempt at a Solution


I understand how to calculate pressure using the above formula for something at the surface, but how do I apply it to a high altitude? In the solution manual, they just ignore atmospheric pressure, so I am confused. At that high altitude, doesn't it mean the person is not affected by the usual atmospheric pressure of 1 atm?
 
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  • #2
Pressure is less at the top of the sea than at the bottom of the sea ...
we live on the bottom of a "sea of air" that's only about 8km deep.
Pressure is zero at the "top" of the atmosphere, the edge of space.
 
  • #3
dmk90 said:
In the solution manual, they just ignore atmospheric pressure, so I am confused. At that high altitude, doesn't it mean the person is not affected by the usual atmospheric pressure of 1 atm?

I doubt that the solution manual ignored the atmospheric pressure at the surface of the earth. Please show us how the manual solution got the pressure at 7.6 km.

Chet
 
  • #4
This is from the solution manual:

The gauge pressure at a depth of 20 m in seawater is
p1swgd = 2.00 x 105 Pa
On the other hand, the gauge pressure at an altitude of 7.6 km is
p2airgh=6.48 x 104 Pa
Therefore, the change in pressure is
Δp = p1 - p2 = 1.4 x 105 Pa
 
  • #5
dmk90 said:
This is from the solution manual:

The gauge pressure at a depth of 20 m in seawater is
p1swgd = 2.00 x 105 Pa
On the other hand, the gauge pressure at an altitude of 7.6 km is
p2airgh=6.48 x 104 Pa
Therefore, the change in pressure is
Δp = p1 - p2 = 1.4 x 105 Pa
The result for 7.6 km from the solution manual is incorrect. They have the sign wrong. It should be p2= - ρairgh= - 6.48 x 104 Pa. The absolute pressure at 7.6 should be 1. x 105 - 6.48 x 104 Pa. This is where the atmospheric pressure at the surface comes in.

Of course, this error makes the final answer incorrect also.

Chet
 
  • #6
Isn't 105 only applies to things at roughly sea level? Wouldn't something at 7.6 km up not be subjected to this pressure?
 
  • #7
dmk90 said:
Isn't 105 only applies to things at roughly sea level? Wouldn't something at 7.6 km up not be subjected to this pressure?
Sure. It''s less. That's what I calculated.

Chet
 

Related to Calculating pressure in high altitude?

1. What is high altitude and how does it affect pressure?

High altitude refers to a location that is above sea level. As altitude increases, the air becomes less dense, resulting in a decrease in atmospheric pressure. This means that there are fewer air molecules present, making it more difficult to breathe and causing a decrease in oxygen levels.

2. How do you calculate pressure at high altitude?

The pressure at high altitude can be calculated using the barometric formula, which takes into account the altitude, temperature, and the universal gas constant. The formula is P = P0 * e-Mgh/RT, where P is the pressure at high altitude, P0 is the pressure at sea level, M is the molar mass of air, g is the acceleration due to gravity, h is the altitude, R is the universal gas constant, and T is the temperature in Kelvin.

3. How does pressure change with increasing altitude?

As altitude increases, the atmospheric pressure decreases. This is because the weight of the air above decreases as there are fewer air molecules present. The decrease in pressure with altitude is not linear - it decreases more rapidly at lower altitudes and levels off at higher altitudes.

4. What are the units of pressure at high altitude?

The SI unit for pressure is pascals (Pa), which is equal to one newton per square meter. However, for high altitude calculations, the unit used is often hectopascals (hPa) or millibars (mb). 1 hPa is equal to 100 Pa, while 1 mb is equal to 1 hPa.

5. How does pressure at high altitude affect the human body?

The decrease in atmospheric pressure at high altitude can have adverse effects on the human body. It can cause altitude sickness, which can range from mild symptoms such as headache and nausea to more severe conditions like pulmonary edema and cerebral edema. It is important to acclimatize to high altitude gradually to avoid these effects on the body.

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