Problem 5: A certain rigid aluminum container contains a liquid at a gauge pressure equal to Po = 2.02 x 10° Pa at sea level where the atmospheric pressure P 1.01 x 10° Pa. The volume of the container is Vo = 3.35 x 104 m³. The maximum difference between the pressure inside and outside the container that this particular container can withstand before bursting or imploding is AP = 2.28 x 105 Pa. For this problem, assume that the density of air maintains a constant value of o, = 1.20 kg / m and that the density of seawater maintains a constant value of o, = 1025 kg / m³. Randomized Variables AP = 2.28 x 105 Pa Vo = 3.35 x 10-4 m³ Part (a) The container is taken from sea level, where the pressure of air is P = 1.01 x 10 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. Numeric A numeric value is expected and not an expression. h =

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Chapter14: Fluid Mechanics
Section: Chapter Questions
Problem 49CP
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9.5 please answer parts a and e, other parts are answered. The hints for part a are: (1) The change in pressure with altitude is related to the density, the change in height, and the acceleration due to gravity. (2) As the container is taken to higher altitudes, the pressure exerted by the atmosphere decreases. (3) There is an initial difference in pressure between the inside and outside of the container before the container is lifted. The hints for part e are: (1) The change in pressure with depth in a medium is re lated to the density of the medium and the acceleration due to gravity. (2)Just below the surface of the ocean (at, say, 1 m), the pressure in the container is greater than the pressure exerted by the ocean water.
(3) The pressure between the container and the surrounding ocean will be equal at a nonzero depth below the surface; the container will then need to be taken to a greater depth for which the difference in pressure is the maximum possible value.

Part (e) What is the maximum depth h in meters below the surface of the ocean that the container can be taken before imploding?
Numeric : A numeric value is expected and not an expression.
h =
Part (f) Choose the correct answer from the following options.
MultipleChoice :
1) The volume of the rigid container decreases as the container is taken to greater ocean depths.
2) There is not enough information.
3) If the container were not rigid, its volume would decrease as it is taken to greater ocean depths.
+ The volume of the rigia container increases as the containeris telken to gicac OTtali depthiS.
5) If the container were not rigid, its volume would increase as it is taken to greater ocean depths.
6) If the container were not rigid, its volume would stay the same as it is taken to greater ocean depths.
Transcribed Image Text:Part (e) What is the maximum depth h in meters below the surface of the ocean that the container can be taken before imploding? Numeric : A numeric value is expected and not an expression. h = Part (f) Choose the correct answer from the following options. MultipleChoice : 1) The volume of the rigid container decreases as the container is taken to greater ocean depths. 2) There is not enough information. 3) If the container were not rigid, its volume would decrease as it is taken to greater ocean depths. + The volume of the rigia container increases as the containeris telken to gicac OTtali depthiS. 5) If the container were not rigid, its volume would increase as it is taken to greater ocean depths. 6) If the container were not rigid, its volume would stay the same as it is taken to greater ocean depths.
Problem 5: A certain rigid aluminum container contains a liquid at a gauge pressure equal to Po= 2.02 x 10° Pa at sea level where
the atmospheric pressure P, = 1.01 × 10° Pa. The volume of the container is Vo = 3.35 × 10-4 m³. The maximum difference
between the pressure inside and outside the container that this particular container can withstand before bursting or imploding is
AP = 2.28 × 10° Pa.
For this problem, assume that the density of air maintains a constant value of gg = 1.20 kg / m' and that the density of seawater
maintains a constant value of o, = 1025 kg / m'.
Randomized Variables
AP = 2.28 x 10 Pa
Vo = 3.35 x 10-4 m3
Part (a) The container is taken from sea level, where the pressure of air is P, = 1.01 x 10° 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.
Numeric : A numeric value is expected and not an expression.
h =
Part (b) If we include the decrease in the density of the air with increasing altitude, what will happen?
MultipleChoice :
1) The container would implode at a maximum altitude.
2) There is not enough information.
3) The height that the container could be lifted to without bursting would increase.
4) The container would not burst.
5) The height that the container could be lifted to without bursting would not change.
6) The height that the container could be lifted to without bursting would decrease.
Part (c) Choose the correct answer from the following options.
MultipleChoice :
1) The volume of the rigid container decreases as the container is lifted to greater altitudes.
2) There is not enough information.
3) If the container were not rigid, its volume would increase as it is lifted to greater altitudes.
4) The volume of the rigid container mcreases as the container is lifted to greater alutudes.
5) If the container were not rigid, its volume would decrease as it is lifted to greater altitudes.
6) If the container were not rigid, its volume would stay the same as it is lifted to greater altitudes.
Part (d) Choose the correct answer from the following options.
MultipleChoice :
1) The depth below the surface of the ocean the container can reach before exploding is the same as the altitude in the atmosphere the container
can reach before imploding.
2) The depth below the surface of the ocean the container can reach before imploding is the same as the altitude in the atmosphere the container
can reach before exploding.
3) The depth below the surface of the ocean the container can reach before exploding is less than the altitude in the atmosphere the container can
reach before imploding.
4) The depth below the surface of the ocean the container can reach before imploding is less than the altitude in the atmosphere the container can
reach before exploding.
5) There is not eHough information.
6) The depth below the surface of the ocean the container can reach before imploding is greater than the altitude in the atmosphere the container
can reach before exploding.
7) The depth below the surface of the ocean the container can reach before exploding is greater than the altitude in the atmosphere the container
can reach before imploding.
Transcribed Image Text:Problem 5: A certain rigid aluminum container contains a liquid at a gauge pressure equal to Po= 2.02 x 10° Pa at sea level where the atmospheric pressure P, = 1.01 × 10° Pa. The volume of the container is Vo = 3.35 × 10-4 m³. The maximum difference between the pressure inside and outside the container that this particular container can withstand before bursting or imploding is AP = 2.28 × 10° Pa. For this problem, assume that the density of air maintains a constant value of gg = 1.20 kg / m' and that the density of seawater maintains a constant value of o, = 1025 kg / m'. Randomized Variables AP = 2.28 x 10 Pa Vo = 3.35 x 10-4 m3 Part (a) The container is taken from sea level, where the pressure of air is P, = 1.01 x 10° 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. Numeric : A numeric value is expected and not an expression. h = Part (b) If we include the decrease in the density of the air with increasing altitude, what will happen? MultipleChoice : 1) The container would implode at a maximum altitude. 2) There is not enough information. 3) The height that the container could be lifted to without bursting would increase. 4) The container would not burst. 5) The height that the container could be lifted to without bursting would not change. 6) The height that the container could be lifted to without bursting would decrease. Part (c) Choose the correct answer from the following options. MultipleChoice : 1) The volume of the rigid container decreases as the container is lifted to greater altitudes. 2) There is not enough information. 3) If the container were not rigid, its volume would increase as it is lifted to greater altitudes. 4) The volume of the rigid container mcreases as the container is lifted to greater alutudes. 5) If the container were not rigid, its volume would decrease as it is lifted to greater altitudes. 6) If the container were not rigid, its volume would stay the same as it is lifted to greater altitudes. Part (d) Choose the correct answer from the following options. MultipleChoice : 1) The depth below the surface of the ocean the container can reach before exploding is the same as the altitude in the atmosphere the container can reach before imploding. 2) The depth below the surface of the ocean the container can reach before imploding is the same as the altitude in the atmosphere the container can reach before exploding. 3) The depth below the surface of the ocean the container can reach before exploding is less than the altitude in the atmosphere the container can reach before imploding. 4) The depth below the surface of the ocean the container can reach before imploding is less than the altitude in the atmosphere the container can reach before exploding. 5) There is not eHough information. 6) The depth below the surface of the ocean the container can reach before imploding is greater than the altitude in the atmosphere the container can reach before exploding. 7) The depth below the surface of the ocean the container can reach before exploding is greater than the altitude in the atmosphere the container can reach before imploding.
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