A submarine is at a depth of 15.0 m under the ocean surface. The inside of the submarine is kept at atmospheric pressure. What is the net force being exerted on a circular window of the submarine that has a radius of 25 cm? The density of the ocean water is 1030 kg/m3.

I know that the direction of the net force is being exerted into the submarine but I don't know how to calculate it..
Thank you!

net force=(outside pressure-1atm)areawindow

so, the pressure of the water weight from above is...

P= weightwater/area + atmospheric pressure above
= g*density*heigh*area/area+ 1atm
= g*density*15m + 1atm
= 9.8*15*1030 + 101.3kpa

To calculate the net force exerted on the circular window of the submarine, you can use the concept of pressure.

Step 1: Calculate the pressure exerted by the water on the circular window.
Pressure is given by the formula:
Pressure = Density × Acceleration due to gravity × Depth

The density of ocean water is given as 1030 kg/m^3, and the depth is 15.0 m.

Pressure = 1030 kg/m^3 × 9.8 m/s^2 × 15.0 m
= 151,350 N/m^2 (or Pa, Pascal)

Step 2: Calculate the force exerted on the circular window.
The force exerted on an area is given by the formula:
Force = Pressure × Area

The radius of the circular window is given as 25 cm, which is equivalent to 0.25 m.

Area = π × (radius)^2
= π × (0.25 m)^2
= 0.19635 m^2 (approx)

Force = 151,350 N/m^2 × 0.19635 m^2
= 29,708 N

Therefore, the net force being exerted on the circular window of the submarine is approximately 29,708 N, directed into the submarine.

To calculate the net force exerted on the circular window of the submarine, we need to consider the pressure difference between the inside and outside of the window.

The pressure at a given depth in a fluid can be calculated using the equation:

P = P0 + ρgh

Where:
P is the pressure at the given depth,
P0 is the reference pressure at the surface (atmospheric pressure),
ρ is the density of the fluid (in this case, the ocean water),
g is the acceleration due to gravity (9.8 m/s²), and
h is the depth.

In this case, we are given that the submarine is at a depth of 15.0 m. So, using the equation above, we can calculate the pressure at that depth:

P = P0 + ρgh
= 101325 Pa + (1030 kg/m³)(9.8 m/s²)(15.0 m)

Now, we know that pressure is force per unit area. The force exerted on the window can be calculated by multiplying the pressure difference by the area of the circular window.

The area of the circular window can be calculated using the formula:

A = πr²

Where:
A is the area of the circular window, and
r is the radius of the circular window.

In this case, the radius of the circular window is given as 25 cm (or 0.25 m). So:

A = π(0.25 m)²

Now, we can calculate the force exerted on the window:

Force = Pressure × Area

Using the values we have calculated, we can substitute them into the equation to find the net force exerted on the window.