Final answer:
The absolute pressure at an ocean depth of 1000m is approximately 10,136,300 Pa. The force that the frame around the submarine porthole must exert to counterbalance the force exerted by the water is approximately 717,195 N.
Step-by-step explanation:
To calculate the absolute pressure at an ocean depth of 1000m, we can use the formula:
Pressure = atmospheric pressure + pressure due to depth
First, let's calculate the pressure due to depth:
Pressure = density of sea water x gravitational acceleration x depth
Plugging in the values:
Pressure = (1024 kg/m³) x (9.8 m/s²) x (1000m)
Simplifying the calculation, we find that the pressure due to depth is 10,035,200 Pa.
Now, let's calculate the absolute pressure:
Absolute pressure = atmospheric pressure + pressure due to depth
Given that the atmospheric pressure is 101.3 kPa (convert to Pa), we have:
Absolute pressure = (101.3 kPa x 1000) + 10,035,200 Pa
Simplifying the calculation, we find that the absolute pressure at an ocean depth of 1000m is approximately 10,136,300 Pa.
To counterbalance the force exerted by the water on the submarine porthole, the frame around the porthole must exert an equal and opposite force. This force can be calculated using the formula:
Force = pressure x area
The area of the circular porthole can be calculated using the formula for the area of a circle:
Area = π x (radius)²
Given that the diameter of the porthole is 30.0 cm (convert to meters), the radius is 0.15 m. Plugging in the values, we have:
Force = (10,136,300 Pa) x (π x (0.15m)²)
Simplifying the calculation, we find that the force that the frame around the porthole must exert to counterbalance the force exerted by the water is approximately 717,195 N.