(390) Problem 14. A certain rigid aluminum container contains a liquid at a gaug
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(390) Problem 14. A certain rigid aluminum container contains a liquid at a gauge pressure ofPo-2.02 x 10° Pa at sea level where the atmospheric pressure is Pa 1.01 × 105 Pa. The volume of the container is 70-2.6 x 10-4 m3. The maximum difference between the pressure inside and outside that this particular container can withstand before bursting or imploding is ?? max 2.53x 10 Pa For this problem, assume that the density of air maintains a constant value of pa 1.20 kg /m3 and that the density of seawater maintains a constant value of ps 1025 kg m3 25% Part (a) The container is taken from sea level where the pressure of air is Pa-1.01 x 105 Pa, to a higher altitude. What is the maximum height h in meters above the ground that the container can be lifted before bursting? Neglect the changes in temperature and acceleration due to gravity with altitude 25% Part (b) If we include the decrease in the density of the air with increasing altitude, what will happen? 25% Part (c) Choose the correct answer from the following options 2596 Part (d) what is the maximum depth dmax in meters below the surface of the ocean that the container can be taken before imploding? Grade Summa Deductions Potential max 0% 100% sinO cosO cotanan acosO tan( ) ? Submissions Attempts remaining:5 5% per attempt) atan) acotan0 sin cosh0 t cotanho is detailed view 0 Degrees Radians Submit Hint I give up! Hints: 2% deduction per hint. Hints remaining: 3 Feedback: 2V% deduction per feedback.Explanation / Answer
If we consider decrease in density of air with increasing altitude, pressure will decrease at slower rate with increase in altitude. As a result pressure difference between inside and outside the container will increase at slower rate, with increase in altitude. As a result, maximum height of container, before it bursts, will increase.
Gauge pressure, d distance below sea surface = d rho g
= d 1025*9.8 = 10045 d Pa
Container will burst when this gauge pressure is 2.53x105 Pa more than the gauge pressure inside the container.
Container burst when gauge pressure = (2.02 +2.53)x105
10045 dmax= 4.55x105
dmax = 45.3 m
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