Question

a submersible is sent to explore the bottom of a lake that is 472 m deep. the density of water is 1000 kg/m3. the submersible has a window that is 14 cm wide and 21 cm tall. assume that the atomospheric pressure is 101.3 kpa. what is the force on the window due to the pressure of the water and atmosphere? give the answer in kn.

Answer 1

The force on the window due to the pressure of the water and atmosphere is 146.6 kN.

Step-by-step explanation:

To calculate the force on the window due to the pressure of the water and atmosphere, we first need to calculate the pressure.

The pressure due to the water is given by the equation P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water.

Substituting the given values, we get

P = (1000 kg/m3)(9.8 m/s2)(472 m)

= 4,627,600 N/m2.

The pressure due to the atmosphere is given by the equation P = Patm, where Patm is the atmospheric pressure. Substituting the given value, we get P = (101,300 N/m2).

Since the window has an area of 0.14 m x 0.21 m = 0.0294 m2, the force on the window is given by the equation F = PA, where A is the area of the window.

Substituting the calculated pressures and area, we get

F = (4,627,600 N/m2 + 101,300 N/m2)(0.0294 m2)

= 146,601 N

= 146.6 kN.

Therefore, the force on the window is 146.6 kN.