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A submarine is at an ocean depth of 3.00 km.

(a) Calculate the absolute pressure at this depth. Assume that the density of water is 1.025 ✕ 103 kg/m3 and that atmospheric pressure is 1.01 ✕ 105 Pa.
Pa
(b) Calculate the total force exerted at this depth on a circular submarine window with a diameter of 35.0 cm.
N

User Lucan
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1 Answer

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Final answer:

The absolute pressure at a depth in a fluid is obtained with the formula P = P_0 + ρgh. For a circular window, the force due to this pressure is found by F = P × A, where A is the area of the window calculated as πr².

Step-by-step explanation:

To answer this question, we will need to calculate the absolute pressure and the total force exerted on a submarine window.

Absolute Pressure Calculation

The absolute pressure at a depth in a fluid is given by the equation P = P_0 + ρgh, where:

  • P is the absolute pressure
  • P_0 is the atmospheric pressure
  • ρ is the density of the fluid
  • g is the acceleration due to gravity (9.81 m/s²)
  • h is the depth below the surface

Using the given values, P_0 = 1.01 × 10⁵ Pa, ρ = 1.025 × 10³ kg/m³, and h = 3000 m, the absolute pressure P can be calculated.

Now let's move on to the force calculation.

Force on Submarine Window Calculation

The force (F) exerted by the pressure on a surface is given by F = P × A, where A is the area of the surface. The area of the circular window can be calculated using the formula A = πr², with r being the radius of the window.

Given the diameter of the window is 35.0 cm (0.35 m), the radius r is 0.175 m. Once we have the pressure from the previous calculation, we can calculate the total force exerted on the window.

User Peter Kim
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