Question

A vertical off-shore structure is built to withstand a maximum stress of 10⁹ Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.

Answer 1

Yes

The maximum allowable stress for the structure, P = 10⁹ Pa

Depth of the ocean, d = 3 km = 3 × 10³ m

Density of water, ρ = 10³ kg/m³

Acceleration due to gravity, g = 9.8 m/s²

The pressure exerted because of the sea water at depth, d = ρdg

= 3 × 10³ × 10³ × 9.8

= 2.94 × 10⁷ Pa

The maximum allowable stress for the structure (10⁹ Pa) is greater than the pressure of the sea water (2.94 × 10⁷ Pa). The pressure exerted by the ocean is less than the pressure that the structure can withstand. Hence, the structure is suitable for putting up on top of an oil well in the ocean.

Answer 2

Here, Maximum stress = 10⁹ Pa, h = 3 km = 3 x 10³ m;

p (water) = 10³ kg/m³ and g = 9.8 m/s².

The structure will be suitable for putting upon top of an oil well provided the pressure exerted by sea water is less than the maximum stress it can bear.

Pressure due to sea water, P = hρg = 3 x 10³ x 10³x 9.8 Pa = 2.94 x 10⁷ Pa

Since the pressure of sea water is less than the maximum