Question

The depth of the Cariaco Trench, in the Caribbean Sea, is about 4708 ft. What is the gauge pressure at this depth? The specific gravity of seawater is 64.48 lb/ft ³.

 

 

Answer 1

 

Step 1

Nomenclature:

h is the depth

\( \gamma \) is the specific gravity of the seawater.

\( \Delta P \) is the gauge pressure.

 

Step 2

Let's determine the gauge pressure at the bottom of the Cariaco trench from the fundamental law of hydrostatics.

\( \Delta P = \gamma\ h \ \)

 

Step 3

Substituting the known values and simplifying:

\( \Delta P = \rm (64.48\ lb/ft^3)(4708\ ft)\times \cfrac{1\ ft^2}{144\ in^2} = \rm 2108\ lb/in^2 \ \)

\( = \boxed{\rm 2108\ psig} \ \)

 

 

The gauge pressure at the bottom of the Cariaco pit is about 2108 psig.