Question

The Mariana trench is located in the Pacific Ocean at a depth of about 11 000 m below the surface of the water. The density of seawater is 1025 kg/m³. (a) If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle's observation window (radius = 0.178 m)? (b) For comparison, determine the weight of a jetliner whose mass is 7.25 × 10⁵ kg.

Answer 1

Use as an estimate

p = patm + rho*g*z

patm = 101325 N/m^2

p = 101325+(1025 kg/m*3)*(9.8 m/sec^2)*11,000 m

p = 110,596,325 N/m^2

Now the area of the window is pi*0.178^2 = 0.09954 m^2

The force on the window is approximately 110,596,325 N/m^2*0.09954 m^2 = 11.008 x 10^6 Newtons

The weight of the jetliner is (7.25 x 10^5 kg)*(9.8m^2) = 7.105 x 10^6 Newton

So the force on the window is about 1.55 times the weight of the plane.

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