jason_r said:A research submarine has a 20.0 cm-diameter window 8.90 cm thick. The manufacturer says the window can withstand forces up to 1.10×10^6 N. What is the submarine's maximum safe depth?
The pressure inside the submarine is maintained at 1.0 atm.
The sub is in salt water
alphysicist said:Hi jason_r,
What have you tried so far?
jason_r said:I''ll show you what I've got so far
please let me know if I am doing this right, because i don't have a key or anything.
thanks
P=P_o + pgh
1.10 x 10^6= 1 + (1030)(9.8)(h)
alphysicist said:There are two problems with this line. You have 1.10 x 10^6 on the left side; that is the force the window experiences, but in this equation you need the pressure that's on the window. So how can you find the pressure on the window if you know the force on the window?
Also, the first term on the right side: you seem to be saying that P_o is 1 atm, which is definitely true; however, to match the other term you need P_o to be in units of Pascals.
jason_r said:ok, so..
this is what i have now:
P=P_o + pgh
35014087.48=(P_o(air) - P_o(sub)) + (1030)(9.8)(h)
h=3.47 x 10^3
(does the pressure of air on top of the sea cancel the pressure of air in the sub?)
Also can you confirm that i have the correct anser?
thanks
alphysicist said:Yes, those pressures will cancel if you calculate it in one step, and that answer looks right to me. (As long as you have the right value for the density of seawater.)
Fluids are substances that can flow and take the shape of their container, while pressure is the force exerted by a fluid on the walls of its container or any object placed in it.
Pressure in fluids is calculated using the formula P = F/A, where P is pressure, F is the force exerted by the fluid, and A is the area over which the force is applied.
The density of a fluid directly affects its pressure. The higher the density of a fluid, the greater the pressure it exerts on its surroundings. This is because the particles in a denser fluid are packed closer together, resulting in more frequent collisions and a greater force exerted on the walls of the container.
Pascal's principle states that pressure applied to a confined fluid is transmitted equally and undiminished in all directions. This means that if a force is applied to a fluid in a closed container, the pressure will increase equally throughout the entire fluid. This principle is the basis for hydraulic systems.
The shape of a container does not affect the pressure of a fluid, as long as the depth and density of the fluid remain constant. This is because pressure in fluids is dependent on the depth and density of the fluid, not the shape of the container.