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.
Pressure at ocean floor:
$$P = \rho g h$$ $$P = 1000 \times 10 \times 3000 = 3 \times 10^7 \, \text{Pa} = 30 \, \text{MPa}$$
\(P = 30 \times 10^6\) Pa = 30 MPa
| Pressure/Stress | MPa | |
|---|---|---|
| Water pressure | \(3 \times 10^7\) Pa | 30 |
| Max allowable | \(1 \times 10^9\) Pa | 1000 |
$$\frac{P_\text{max allowable}}{P_\text{water}} = \frac{10^9}{3 \times 10^7} \approx 33.3$$
Yes! 30 MPa << 1000 MPa safety margin of ~33×.