Flux through cylinder problem: Finding the lateral area using vector calculus

In summary, flux through a cylinder is a measure of the flow of a property through the surface of a cylinder, represented by the symbol Φ and calculated by taking the integral of the property over the surface area of the cylinder. This measurement can be affected by factors such as the size, shape, material, temperature, pressure, and external forces of the cylinder. It is significant in understanding and predicting fluid behavior and is used in various real-world applications, including heat exchangers, fluid dynamics, and industrial processes.
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Homework Statement



Hey guys.

I have this question:

http://img122.imageshack.us/img122/2936/84391716.jpg

I think that the flux through the top and bottom is zero and that because A does not have a component in the z axis direction.
So all that got left is the lateral area.
Well, I get 0 and I don't know why. I'm suppose to get 120, I obviously have a mistake and I don't know where.
Can I please have some help?

Thanks


Homework Equations





The Attempt at a Solution

 
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  • #2
The normal vector to your cylinder certainly isn't (1,0,0), is it?
 

1. What is flux through a cylinder?

Flux through a cylinder is a measure of the flow of a property (such as heat or fluid) through the surface of a cylinder. It is usually represented by the symbol Φ and is measured in units of the property per unit time.

2. How is flux through a cylinder calculated?

The flux through a cylinder is calculated by taking the integral of the property over the surface area of the cylinder. This can be represented mathematically as Φ = ∫∫S F · dS, where S is the surface of the cylinder and F is the property being measured.

3. What factors can affect the flux through a cylinder?

The flux through a cylinder can be affected by several factors, including the size and shape of the cylinder, the properties of the material it is made of, the temperature and pressure of the fluid or substance flowing through it, and any external forces acting on the cylinder.

4. What is the significance of calculating flux through a cylinder?

Calculating the flux through a cylinder allows scientists to better understand and predict the behavior of fluids and substances as they flow through cylindrical objects. It can also be used to design and optimize systems that involve the use of cylinders, such as heat exchangers or pipes.

5. How is flux through a cylinder used in real-world applications?

Flux through a cylinder has many practical applications, such as in the design of heat exchangers and refrigeration systems, the study of fluid dynamics in pipes and channels, and the analysis of flow in blood vessels and other cylindrical structures in the human body. It is also used in industries such as oil and gas, chemical processing, and manufacturing.

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