Flux Calculations for Open and Closed Cylinders?

In summary, the conversation involves a question about the wording of a problem, specifically the difference between finding the flux of a given vector field through a closed cylinder and through the curved sides of an open cylinder. The speaker notes that "open" and "closed" have precise topological meanings, but in this context, it likely refers to whether the cylinder has caps on the ends or not.
  • #1
quaker
14
0
I have a quick question about the wording of a problem I have. It's in two parts.

The first part asks me to find the flux of a given vector field through the closed cylinder of given dimensions. That's fine, no problem.

The second part then asks me to find the flux of the same field through the curved sides of the open cylinder in the previous part.


Is this just poor wording, or is there actually a difference that I am not seeing?

Thanks for your help!
 
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  • #2
I'm guessing the closed one has caps on it (ie, it includes the disk at each end of the cylinder) and the open one one doesn't. "Open" and "closed" have precise topological meanings, but no surface can be open in R^3, so this can't be what they mean.
 

FAQ: Flux Calculations for Open and Closed Cylinders?

What is the difference between an open cylinder and a closed cylinder?

An open cylinder is a three-dimensional shape that has two circular bases at either end and a curved surface connecting them. The two bases are not connected, creating an opening. A closed cylinder, on the other hand, has two circular bases that are connected by a curved surface, creating a solid shape with no openings.

How do open and closed cylinders differ in terms of volume and surface area?

The volume of an open cylinder is calculated by multiplying the area of the base by the height, while the volume of a closed cylinder is calculated by multiplying the area of the base by the height and adding the area of the curved surface. In terms of surface area, an open cylinder has a larger surface area than a closed cylinder because it includes the area of the opening.

What are the real-life examples of open and closed cylinders?

Open cylinders can be found in objects such as cans, pipes, and straws. Closed cylinders can be seen in everyday objects like soda cans, water bottles, and soup cans. They are also commonly used in engineering and architecture, such as in the design of towers, columns, and pillars.

Which type of cylinder is more stable?

A closed cylinder is more stable than an open cylinder because the connected bases provide more support and distribute the weight evenly. An open cylinder relies on the strength of the curved surface to hold its shape, making it less stable.

Can an open cylinder be transformed into a closed cylinder?

Yes, an open cylinder can be transformed into a closed cylinder by covering the opening with a circular base. This process is commonly seen in the production of cans and bottles, where the open end is sealed to create a closed cylinder shape.

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