Undergrad Can the volume of a control volume change with time?

[Amin2014]

Can an expanding balloon be considered a control volume?

 

[dRic2]

Yes

 

[russ_watters]

I would answer no. The point of a control volume is that it is open, enabling you to track mass flows in and out. A balloon is closed: it is a control mass.

 

[dRic2]

What about water evaporating from a a glass (for example). I'd take the control volume to be the liquid water's volume rather than the volume of the glass, even if it is changing in time...

I'm mean it's just a definition

 

[Amin2014]

I would answer no. The point of a control volume is that it is open, enabling you to track mass flows in and out. A balloon is closed: it is a control mass.

I meant a balloon that can be blown into

 

[dRic2]

Why didn't I think of that... it's even in the title... I feel so dumb

 

[russ_watters]

Why didn't I think of that... it's even in the title... I feel so dumb

No, I don't think so - I read it the same way you first did: as expanding without changing mass. E.G., heating a balloon. Because...

I meant a balloon that can be blown into

I don't think so, but I'm not certain. A balloon that can be blown into is a transient process, not a continuous one, which seems to me to defeat the definition. The throat on the other hand is a control volume.

 

[Chestermiller]

Usually, a control volume is treated as fixed. However, I had seen developments where a portion of a control volume interface (across which no mass passes) can be moving. I have also seen moving and deforming (material) control volumes across which no mass passes.

 

[Amin2014]

Usually, a control volume is treated as fixed. However, I had seen developments where a portion of a control volume interface (across which no mass passes) can be moving. I have also seen moving and deforming (material) control volumes across which no mass passes.

Did the volume change as well, or just the shape of the control surface?

 

[Amin2014]

No, I don't think so - I read it the same way you first did: as expanding without changing mass. E.G., heating a balloon. Because...

I don't think so, but I'm not certain. A balloon that can be blown into is a transient process, not a continuous one, which seems to me to defeat the definition. The throat on the other hand is a control volume.

Control volumes are used to analyze transient and continuous processes alike; Refer to an engineering thermodynamics textbook. The point is that it's a mathematical tool that provides a different point of view from the lagrangian/control mass viewpoint. A transient process can lend itself to either analysis. For transient processes, changes in quantities are normally expressed with Δ, such as ΔU, where as in continuous processes time derivatives are used; $dU/dt$

My real concern is that if the volume of a control volume can change, then what's the distinction between "control volume" and "open system"? Seems redundant to me.

 

[dRic2]

I think you are overthinking it. I mean, what's the problem in practice ? Do you have in mind a scenario where you don't know how to choose the control volume ?

 

[Amin2014]

I think you are overthinking it. I mean, what's the problem in practice ? Do you have in mind a scenario where you don't know how to choose the control volume ?

The derivations of formulas in textbooks on thermodynamics and fluid mechanics seem to repeatedly make the assumption that the volume of whatever chosen control volume is constant, that's why I had to ask.

 

[256bits]

The derivations of formulas in textbooks on thermodynamics and fluid mechanics seem to repeatedly make the assumption that the volume of whatever chosen control volume is constant, that's why I had to ask.

That is the fixed control volume, such as flow through a pipe.
One can have a moving control volume, such as around an airplane.
One can also have a deformable control volume, as in your balloon case. Here this case the control surface moves with the surface of the balloon.
The control volume separates your area of interest from the surroundings.
Read this
http://user.engineering.uiowa.edu/~...ynolds Transport Theorem_10-11-2013_Final.pdf

 

[Amin2014]

That is the fixed control volume, such as flow through a pipe.
One can have a moving control volume, such as around an airplane.
One can also have a deformable control volume, as in your balloon case. Here this case the control surface moves with the surface of the balloon.
The control volume separates your area of interest from the surroundings.
Read this
http://user.engineering.uiowa.edu/~fluids/posting/Lecture_Notes/Control Volume and Reynolds Transport Theorem_10-11-2013_Final.pdf

Thanks, I thought of this myself. Was wondering why no book suggested these. Good to know White has taken care of it.

 

[Don jennings]

Can an expanding balloon be considered a control volume?

Sure but the diffusion rate of molecules out of the balloon would have to be taken into account if you rely on the mass inside the balloon to be static. It won't be. For instance if the inflating gas is helium you know full well helium gets through very small cracks and the plastic of most balloons is porous and even a metallic mylar balloon will still have some porosity.