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We will consider the case of real transport with a given flow rate $J=\rho u$. We assume that all compressors are identical, capable of maintaining a given air flow. Specifications: the flow velocity is limited by the condition $1\le u\le 10$ m/s. It is necessary to determine how many compressors are needed and how to optimally position them when ...

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If you have a pressurized container of sufficient size, would there be a pressure gradient due to gravity? There will always be a pressure gradient due to gravity. How significant it is, however, depends on what you mean by "sufficient size". For example, for the first 1000 meters above sea level, the increase in atmospheric pressure due to gravity is 11....

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A balloon is comprised of surface patches that expand with hydrostatic pressure and taken on a certain shape. If the material shape and properties are known, the direct problem of finding out what shape it takes at a given pressure and thus the volume is straight forward. The inverse problem; however, isn't. In this case one would normally model the volume ...

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As explained in other answers, a tank can fail under internal or external pressure if the material strength is exceeded. The critical pressure differential of a thin spherical shell for this failure mode can be calculated using the following formula (to derive it, one can consider equilibrium of a half of the shell): $$2\pi R h\sigma=\pi R^2 \Delta p,$$ ...

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Expanding tank vs contracting tank is the comparison. Since the collapsing tank may not tear, and therefore technically not be destroyed in that it could be reinflated and still be usable to some extent (search for images of 'tank collapse under vacuum' on web), a different way to look at the problem is useful. Two questions can be posed: "Which tank would ...

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Adding on to what others have said, this is very non-straightforward. As others mention, the failure criteria for a vacuum vessel and a pressurized vessel is quite different. There is one very large factor that no one seems to have mentioned yet. When the spherical vessel is under a vacuum, it develops compression, and if it's a ductile material, it is ...

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Though failure with the sphere evacuated is highly unlikely given a maximum pressure difference of one atmosphere, if there were no limit to the external pressure, then It would probably depend on the material. With positive pressure inside a spherical tank, the walls are subjected to tensile stress. If negative, compressive stress. Failure may depend on ...

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There's no physics principle that gives a single answer here. First of all, a vacuum can never achieve more than a 1atm pressure difference across a vessel (assuming we're doing this here in a normal workshop). So if you have a vessel that can withstand 5atm without any yield, then it will never have a problem with a vacuum, but would fail if pressurized ...

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Shouldn't the can still start moving from the moment we make the opening and until the air pressure inside the can is equalized with the outside air? Indeed it will, but that takes very little time. If that in fact happens, why would it stop and return ("a momentary slight oscillation about the center of mass") and not simply continue moving ...

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If the pressure difference between inside and outside is the same (but opposite) then the force on the can in both situations is equal and opposite. If the geometry is the same then the pressure difference evolves in the same way but with opposite sign. The motion of the can, opposite, is only different due to difference in the amount of gas resistance. So ...

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The easiest way to answer this problem is by thinking about conservation of momentum. Consider the still closed can with vacuum inside, and the air outside. The can is at rest, hence it has momentum $\vec{p}_\text{can} = \vec{0}$. The air is at rest too, hence it has momentum $\vec{p}_\text{air} = \vec{0}$. Therefore total momentum is \vec{p}_{\text{...

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Because gas is compressible, you must specify its pressure along with the volume it happens to occupy in order to properly define its state. And since heating a gas causes its pressure to increase, a complete description of any gas will necessarily include calling out its temperature as well. Since more gas atoms in a fixed volume will exert more pressure ...

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If you are considering a gas/partial vacuum that is not confined in a well-defined 'container', you would presumably want use specific volume (aka inverse density) instead. I.e. consider the amount of volume occupied per unit mass of the substance.

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