How is "cross sectional area" different from "area"?

[untitledm9]

How is "cross sectional area" different from "area"?

I don't understand what cross sectional area is and there is no explanation about it in my textbook.I cannot find this anywhere and am really desperate right now. Can someone please help me?

 

[Tide]

Imagine cutting a (spherical!) grapefruit into two equal parts. The area of each of the flat circles you just created is called the cross sectional area. That differs from the (surface) area of the original grapefruit only in that you are calculating the area of different things (i.e. area is area!).

 

[untitledm9]

So cross sectional area is the area of just part of an object?

 

[Tide]

Not exactly. We could talk about the cross sectional area of that grapefruit without actually doing the cutting. It's the area it would have if we cut it.

With respect to hydrodynamics it is often useful to talk about things like the cross sectional area of a flow such as through a pipe. So, for example, if a fluid is flowing through a pipe the diameter of the pipe may vary from place to place and we can use the concept of cross sectional area to infer things like flow velocity or pressure at a location given the velocity and/or pressure at another location.

If the flow is steady then $\rho A v$ is a constant with $\rho$ being the mass density, A is the cross sectional area and v is the flow speed which simply says that the flow through any cross section is the same at any point along the pipe. We don't actually have to cut the pipe to make use of the concept of cross section.

 

[untitledm9]

Thank you so much for helping me. I was getting so frustrated that I couldn't find what cross sectional area is anywhere. Thank you!

 

[Tide]

You are very welcome!