Question

If a submarine is built to withstand a pressure of 42 barg before it collapses due to the pressure of the water surrounding it, to what depth can it safely dive (give your answer in meters beneath the surface of the ocean)?

Answer 1

Solution:

Pressure, P = 42 bar gauge = 4200 kPa (given)

Now, If the submarine is at a height 'h' from the ocean then:

$P_{P} = P_{Q}$ + $\rho$  g h                  (1)

where,

$P_{P}$ = pressure at point P(depth)

$P_{Q}$ = atmospheric pressure

$\rho$ = density of water = 1000 kg/$m^{3}$

h = height of submarine from the depth of ocean

Now, using eqn (1):

$P_{P} - P_{Q}$ = 1000$\times 9.8\times h$

4200$\times 10^{3}$ = 1000$\times 9.8\times h$

h = 428.13 m