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.