Question

At what depth in the ocean would the water pressure be three times atmospheric pressure? What would be the force on a portion of the hull of a submarine that is 10 cm by 10 cm? If a bubble of air has diameter 5.0 cm starting at that depth, what will be its diameter just as it reaches the surface (assume temperature stays the same)?

Answer 1

At what depth in the ocean the water pressure would be three times atmospheric pressure:

$$\rho gD=3p_a,\\\space\\ D=\dfrac{3p_a}{\rho g}=31\text{ m}.$$

The force on a portion of the hull of a submarine that is 10 cm by 10 cm would be

$$F=3p_aA=3p_ax^2=3040\text{ N}.$$

The new volume of the bubble:

$$3p_aV_1=p_aV,\\\space\\ V=4V_1=262\text{ cm}^3.$$