Express the water pressure as a function of the depth below the ocean surface.

Question

At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in². Below the surface, the water pressure increases by 4.34 lb/in² for every 10 ft of descent.

(a) Express the water pressure as a function of the depth below the ocean surface.
(b) At what depth is the pressure 100 lb/in² ?

Answer 1

Step 1:

The water pressure at the surface of the ocean is ,

Let is the water pressure and is the depth of the water level.

The pressure and depth are linearly related.

Where is the slope.

At surface of the ocean, the depth is zero and Pressure is .

The water pressure is .

Step 2:

(a)

The water pressure increases by for every .

Slope .

Substitute  value in .

The water pressure as a function of depth is .

Step 3:

(b)

Water pressure .

Substitute in the Pressure function .

The depth of water is .

Solution :

(a) The water pressure as a function of depth is .

 (b) The depth of water at pressure is .