Why Do Stream Tubes Form in Fluid Mechanics?

[mrmojorizing]

I don't understand why stream tubes exist. Stream tube is defined here: http://www.princeton.edu/~asmits/Bicycle_web/streamline.html

Why can't you have a stream line starting at a point going one way, and then the stream line at the neighboring point going some orthogonal direction, and thus not forming a tube?

 

[Studiot]

Welcome to Physics Forums

Why can't you have a stream line starting at a point going one way, and then the stream line at the neighboring point going some orthogonal direction, and thus not forming a tube?

Stream tubes and lines occur in laminar flow.
How would your example be laminar?

 

[RandomGuy88]

It is just a definition. A streamline is a line that is tangential to the instantaneous velocity vector. A streamtube is a collection of streamlines and by definition there is no flow perpendicular to a streamline so therefore there is no flow through the walls of the streamtube.

 

[boneh3ad]

Welcome to Physics Forums



Stream tubes and lines occur in laminar flow.
How would your example be laminar?

Streamlines are not only present in laminar flow. In fact, the concept of streamlines is completely independent of the concept of viscosity, which means it is also independent of laminar/turbulent flow since they make no sense in an inviscid sense.

I don't understand why stream tubes exist. Stream tube is defined here: http://www.princeton.edu/~asmits/Bicycle_web/streamline.html

Why can't you have a stream line starting at a point going one way, and then the stream line at the neighboring point going some orthogonal direction, and thus not forming a tube?

RandomGuy88 said it pretty well. As he said, streamlines are defined as following along the instantaneous velocity vector. Imagine that two streamlines did somehow cross. That would mean the flow is moving in two directions at once! Clearly, that doesn't really make physical sense, hence streamlines cannot cross one another.

There are more mathematically robust answers, but they aren't as easy to visualize.

 

[PJC01]

Stream tubes exist because they are a mathematical representation of fluid flow that allows us to better understand and analyze the behavior of fluids. They are based on the concept of streamlines, which are imaginary lines that are tangent to the velocity of the fluid at every point. Stream tubes are formed by grouping together these streamlines, creating a tube-like structure that represents the flow of the fluid.

The reason why stream tubes cannot have streamlines going in different directions is because this would violate the fundamental principles of fluid mechanics. Fluids are subject to the laws of conservation of mass and momentum, which means that the flow of a fluid must be continuous and the forces acting on it must balance out. If streamlines were to suddenly change direction, it would create discontinuities and imbalances in the flow, which is not physically possible.

In addition, stream tubes are useful because they allow us to simplify the complex behavior of fluids into a more manageable and understandable form. By using stream tubes, we can visualize and analyze the flow of fluids in a more intuitive way, making it easier to make predictions and design systems that involve fluid flow.

In summary, stream tubes exist as a mathematical tool to help us understand and analyze the behavior of fluids. They are based on the fundamental principles of fluid mechanics and provide a simplified representation of fluid flow, making it easier for scientists and engineers to study and utilize this important aspect of nature.