Question

a) A deep sea diving apparatus (bathyscaphe) can submerge to a depth of approximately     11,000 m. What pressure must its hull withstand at this depth

b)   If the bathyscaphe has circular window of radius 50 cm and it is pressurized to 1 atm pressure, what force must the window withstand at this depth?

c) A climbing expedition sets out to climb Mt.Everest in the Himalayan mountain range. The base camp is at 17,500ft. What is the atmospheric pressure at this altitude?

(You can assume that both g and the air density remain constant between sea level and base camp).

d) In practice both g and air density change over this range in height. If these effect are taken into account, will the answer to part c) be higher or lower?

Answer 1

A deep sea diving apparatus (bathyscaphe) can submerge to a depth of approximately     11,000 m. What pressure must its hull withstand at this depth
let density of water roh = 1,000kg m^-3

pressure at this depth = roh * g * h
                                    = 1000*9.81*11000 Pa

                                  = 1.08*10⁸ Pa
                                  = 1.065 *10³ atm
b)   If the bathyscaphe has circular window of radius 50 cm and it is pressurized to 1 atm pressure, what force must the window withstand at this depth?
area of the window = pi*.5²= .785 m²
pressure difference = 1065 - 1 = 1064 atm
                                 = 1.078*10⁸ Pa
Total force on the window = Pressure difference * area = 1.078*10⁸ * .785 N
                                = 8.47*10⁷   N

c) What is the atmospheric pressure 17,500ft. altitude?
                        let denisity of air roh = 1.225 kg/m³
                               then pressure at sea level^, = 101325 Pa
                                 = pressure at altitude 17,500ft + roh * g * h
   pressure at altitude 17,500ft = pressure at sea level - roh * g * h
                                  = 101325- (1.225*9.81*5334)

                                  = 37225 Pa

d) In practice both g and air density change over this range in height. If these effect are taken into account, will the answer to part c) be higher or lower?

Gravity decreases with altitude as one rises above the earth's surface because greater altitude means greater distance from the Earth's center.
so value of g decreases at 17,500ft height
similarly atmospheric pressure also decreases when altitude increases

so If these effect are taken into account, answer to the previous question will be higher