Control Volumes - Fluid Mechanics

In summary, the conversation discusses the confusion surrounding control volumes, specifically in relation to depicting mass flow and momentum in a simple vertical flow scenario. The concept of a control volume is explained as an imaginary region containing volume and the importance of equal entering and exiting mass flow is emphasized. The idea of surface and body forces is also mentioned in relation to steady flow. The conversation concludes with a suggestion to approach the problem using traditional physics principles.
  • #1
sierra52
10
4
After doing extensive research, I am still confused about Control Volumes. Say that there is water flowing into a cup at a steady rate, and I am required to illustrate the momentum and mass flows, as well as the forces, how would I approach this? I have seen examples of Control Volumes but they do not reflect simple vertical flow and do not contain much information.

Thanks.
 
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  • #2
I am honestly not sure what you are asking here. What do you mean by "illustrate the momentum and mass flows"?
 
  • #3
boneh3ad said:
I am honestly not sure what you are asking here. What do you mean by "illustrate the momentum and mass flows"?
So depicting (via an illustration of the control volume) the mass flow and momentum of the fluid as it enters and leaves the control volume, noting that the flow is steady and vertical. I'm not sure at all how I sketch this. I hope this clarifies things. Thanks.
 
  • #4
A control volume represents a basically imaginary region containing volume and as it relates to mass flow, the entering and exiting mass flow from a control volume must always be equal regardless of the shape of the control volume size or configuration between the fluid entry and exit end points.

(Note Edited to remove earlier erroneous statement related to momentum and inlet vs. outlet areas deleted.)
 
Last edited:
  • #5
I am a bad engineer but let's give it a try :P
This question is not very clear, please provide some more information, is the cup stationary or moving, what is the hose dia, what is the velocity of water? Assuming the simplest case, the flow is steady,
you have first imagine a boundary across your cup, let for example the cup is resting on a flat surface and water is entering the cup vertically,

Untitled.jpg
the total amount of forces acting in y directing would be:
Capture.JPG


as the flow is steady C.V term would cancel out,
Fs = surface forces.
Fb = body forces.
from the assumption that the cup is at rest, Fs= Ry ;reaction.
Fb= weight of the cup plus weight of the water.
Capture.JPG


Capture.JPG
 
  • #6
You don't need a control volume (a conceptual thing) if you already have a cup a real thing).
In either case you can then proceed with normal physics, starting with mass/volume conservation.
 

Related to Control Volumes - Fluid Mechanics

1. What is a control volume in fluid mechanics?

A control volume is an imaginary region in space that is used to analyze the flow of fluids. It can be fixed or moving and is often used to study the mass, momentum, and energy transfer in a fluid system.

2. How is a control volume different from a control volume?

A control volume is a region in space, while a control surface is the boundary that encloses the control volume. The control surface can be either real or imaginary and is used to regulate the flow of fluids in and out of the control volume.

3. What is the significance of control volumes in fluid mechanics?

Control volumes are essential in fluid mechanics because they provide a framework for analyzing and understanding fluid flow. They allow us to apply the fundamental laws of conservation of mass, momentum, and energy to a specific region, making it easier to study and predict fluid behavior.

4. How do you determine the flow rate through a control volume?

The flow rate through a control volume can be determined by using the continuity equation, which states that the mass entering the control volume must equal the mass exiting the control volume. This equation is based on the principle of conservation of mass and can be used to calculate the volumetric flow rate or the velocity of the fluid.

5. Can control volumes be used for both steady and unsteady fluid flow?

Yes, control volumes can be used to analyze both steady and unsteady fluid flow. For steady flow, the properties of the fluid within the control volume remain constant over time, while for unsteady flow, these properties can vary with time. In both cases, the fundamental laws of conservation can be applied to the control volume to understand the flow behavior.

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