Calculus, 8th Edition,stewart; page 34 problem 19

Question

At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in^2. Below the surface, the water pressure increases by 4.34 lb/in^2 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/in^2 ?

Answer 1

Step:1

The water pressure at the surface of the ocean is  lb/in.

(a)

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

Pressure and depth are linearly related : .

Where  is the slope.

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

The water pressure is .

The water pressure increases by  lb/in for every  ft.

Slope is .

Substitute  in .

The water pressure as a function of depth is .

Step:2

(b)

Water pressure  lb/in.

Substitute  in the Pressure function.

The depth of water is  ft.

Solution:

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

(b) The depth of water at pressure  lb/in is  ft.