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Fluid MechanicsLast Fall, researchers using an unmanned submarine discovered a coral reef at the unprecenented depth of 1/2 mile. The density of seawater at the surface of the ocean is 1025kg/m3 and the bulk modulus of elasticty of seawater is 2.34*109 Pa. A volume of air is taken downward to the coral reef. Assuming an absolute air pressure at the ocean surface of 1 atm, and that the air taken to the reef behaves as an isothermal gas.Find the pressure  of the air at that depth.Find the fractional change in denisity and volume of the air at that depth.

Question

Fluid Mechanics

Last Fall, researchers using an unmanned submarine discovered a coral reef at the unprecenented depth of 1/2 mile. The density of seawater at the surface of the ocean is 1025kg/m3 and the bulk modulus of elasticty of seawater is 2.34*109 Pa. A volume of air is taken downward to the coral reef. Assuming an absolute air pressure at the ocean surface of 1 atm, and that the air taken to the reef behaves as an isothermal gas.

  • Find the pressure  of the air at that depth.
  • Find the fractional change in denisity and volume of the air at that depth. 
check_circleAnswer
Step 1

The acceleration due to gravity (g) is 9.81 m/s2.

Calculate the pressure of the air at the depth.

Pressure pgh
1
milex
2
1609.34m
1025kg/mx9.81m/s
1mile
-8.09 x106 N/m2
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Pressure pgh 1 milex 2 1609.34m 1025kg/mx9.81m/s 1mile -8.09 x106 N/m2

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Step 2

Calculate the fractional change in density.

Ap
Bulk modulus
Δρ
8.09x10 N/m2
Ap
2.3x10 Pax 1N/m2
1Pa
Ap0.00352
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Ap Bulk modulus Δρ 8.09x10 N/m2 Ap 2.3x10 Pax 1N/m2 1Pa Ap0.00352

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Step 3

Calculate the fractional ...

Ap
Bulk modulus
AV
V
8.09x10 N/m2
AV
2.3 x10 Pax IN/m2
1Pa
V
AV
-0.00352
V
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Ap Bulk modulus AV V 8.09x10 N/m2 AV 2.3 x10 Pax IN/m2 1Pa V AV -0.00352 V

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