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24 May, 20:16

A research submarine has a 30-cm-diameter window that is 8.6cm thick. The manufacturer says the window can withstand forces up to 1.2*10^6 N. What is the submarine's maximum safe depth in salt water?

The pressure inside the submarine is maintained at 1.0 atm.

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  1. 24 May, 23:58
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    What is missing is the density of salt water. Let's denote it ρ.

    The pressure at depth d then is:

    p = p0 + ρ g d

    , where p0 is the atmospheric pressure at the surface of the sea. We assume it is equal to the 1 atm inside the sub.

    Hence the pressure difference between inside and outside of the window is:

    Δp = ρ g d

    The force on the window is this pressure difference, multiplied by the area of the circular window of diameter D. The latter equals

    A = ¼ π D².

    So

    F = p A = ¼ π D ²ρ g d.

    This should be less than Fmax.

    Hence d < Fmax / (¼ π D ²ρ g).
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