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Pressure in Fluids

Pressure is force per unit area and increases with depth in an incompressible fluid.

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The Pressure Under Water

The Pressure Under Water

License: CC BY-NC 3.0

A deep sea navy diver searches the crash site of a WWII military aircraft near Palau. These deep sea divers are exposed to tremendous amounts of pressure, that without their protective gear, they wouldn’t be able to survive. For every meter they descend, the pressure increases by nearly 10,000 Pascals!

Amazing But True

  • The pressure felt by deep sea divers is due to water being incompressible. In other words, you can’t squeeze water. The further you are under the surface of a body of water, the more water there is on top of you. If you were to imagine the water as concrete, you can easily see that as you place more on top of you, effective increasing the distance between yourself and the top of the concrete, there is more weight pressing down on you.
  • This principle of the transmission of fluid pressure is the basis for Pascal’s law. Mathematically, the change in pressure of an enclosed fluid is equally transmitted to all points in a fluid. Pascal’s law is given as:

\begin{align*}\triangle P = \rho g \triangle h\end{align*}

  • Where the change is pressure is simply due to the acceleration due to gravity, the density of the fluid in question and the displacement, or the distance, from the surface of the fluid.

Can You Apply It?

Using the information provided above, answer the following questions.

  1. While underwater, you swim 10 meters to the left of your current position without changing your vertical displacement. How much has the pressure on your body changed by?
  2. What are the units of Pascals made of?
  3. If you were to dive 10 meters below the surface of the Earth, how many times greater would the pressure on your body be?

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  1. [1]^ License: CC BY-NC 3.0

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