you are designing a diving bell to withstand the pressure of sea water at a depth of 250m. a)what is the quage pressure at the depth(you can ignor the small changes in the density of the water with depth.) b)at the 250m depth, what is the net force due to the water outside and the air inside the bell on the circular glass window 30.0cm in diameter if the pressure inside the diving bell equals the pressure at the surface of the water?(you may ignor the small variation in pressure over the surface of the window)

a) 2.52x10^3Pa

a) Oh, diving into the depths of sea water, are we? At a depth of 250m, the gauge pressure would be about 25.8 atmospheres, or roughly equal to the number of times I've accidentally hit myself with a rubber chicken.

b) Ah, the circular glass window is definitely going to feel some pressure at that depth! Assuming the pressure inside the diving bell is equal to the pressure at the surface (which is very considerate, by the way), the net force on the window would be approximately 11,715 newtons. That's like asking a clown to balance an elephant on a unicycle - quite a bit of force! So, better hope that window is up to the task or we might have a soggy clown on our hands!

a) To find the gauge pressure at a given depth in sea water, we can use the hydrostatic pressure equation, which states that the pressure at a depth in a fluid is given by the product of the density of the fluid, the acceleration due to gravity, and the depth.

The gauge pressure refers to the pressure relative to atmospheric pressure at the surface. Since we are ignoring small changes in density with depth, we can assume that the density of sea water remains constant.

Therefore, the gauge pressure at a depth of 250m can be calculated as:

Gauge Pressure = Density of Sea Water * Acceleration due to Gravity * Depth

b) To find the net force on the circular glass window, we need to consider the pressure difference between the water outside and the air inside the bell. The net force can be obtained by multiplying the pressure difference by the area of the circular window.

Let's calculate these values step by step:

a) Gauge Pressure:
To find the gauge pressure at a depth of 250m, we need the density of sea water (ρ) and the acceleration due to gravity (g).

1. Density of Sea Water: The typical average density of sea water is around 1025 kg/m³.

2. Acceleration due to Gravity: The standard value for acceleration due to gravity is 9.8 m/s².

Now, we can calculate the gauge pressure:

Gauge Pressure = Density of Sea Water * Acceleration due to Gravity * Depth
= 1025 kg/m³ * 9.8 m/s² * 250m
≈ 2,539,500 Pa (Pascal)

Therefore, the gauge pressure at a depth of 250m is approximately 2,539,500 Pa.

b) Net Force on the Glass Window:
To find the net force on the circular glass window, we need to calculate the pressure difference between the water outside and the air inside the bell, and then multiply it by the area of the window.

1. Pressure difference: The pressure difference is the gauge pressure at the given depth.

Pressure difference = Gauge Pressure = 2,539,500 Pa

2. Area of the circular window: The area can be calculated using the formula for the area of a circle: π * (radius)². Since the diameter is given as 30.0 cm, the radius would be half of that value.

Radius = Diameter / 2 = 30.0 cm / 2 = 15.0 cm = 0.15 m

Area of the circular window = π * (0.15 m)²

Now, we can calculate the net force:

Net Force = Pressure difference * Area of Window
= 2,539,500 Pa * (π * (0.15 m)²)

Performing the calculation will give us the net force on the glass window.

(a) (depth)*(water density)*g

(b) (window area)*(gauge pressure)