A research submersible rated for a maximum allowable absolute pressure of operates in…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Fluids · Fluids

Problem

A research submersible rated for a maximum allowable absolute pressure of

2.40\times10^{5}\,\text{Pa}

operates in two environments. • Environment A: a mountain lake located

3000\,\text{m}

above sea level, where the atmospheric pressure is

7.00\times10^{4}\,\text{Pa}

. The lake water has density

1000\,\text{kg}\,\text{m}^{-3}

. • Environment B: the open ocean at sea level, where the atmospheric pressure is

1.01\times10^{5}\,\text{Pa}

and the seawater density is

1025\,\text{kg}\,\text{m}^{-3}

. Take

g = 9.80\,\text{m}\,\text{s}^{-2}

in both environments. (a) Determine the maximum depth to which the submersible can descend in Environment A without exceeding its pressure rating. (b) Determine the maximum depth for Environment B under the same constraint. (c) Compare the two depths by calculating

h_{\!B} - h_{\!A}

and explain, using physical reasoning, why the difference has that sign and magnitude. (d) The lake’s maximum depth is

150\,\text{m}

. If the submersible descends to the lake bottom, calculate the absolute pressure it experiences and evaluate whether this depth is within the safety margin implied by its rating.

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