Question about fluid statics and dynamics

In summary, the conversation discusses the use of tracers to make the flow of a fluid visible. It mentions that each tracer follows a streamline, which is the path that a tiny element of the fluid would take as it flows. The last statement made is that streamlines can never intersect because it would imply a fluid element having two different velocities simultaneously, which is impossible. This is because the streamline is imagined to contain abstract, point-like particles with zero extension, unlike real particles which can touch each other due to their finite size.
  • #1
farleyknight
146
0
This is not a homework assignment but a general question about something I found in my textbook. It pertains to fluid statics and dynamics and it says that:

We can make the flow of a fluid visible by adding a tracer. This might be a dye injected into many points across a liquid stream or smoke particles added to a gas flow. Each bit of a tracer follows a streamline, which is the path that a tiny element of the fluid would take as the fluid flows. Recall from Chapter 4 that the velocity of a particle is always tangent to the path taken by the particle. Here the particle is the fluid element, and it's velocity v is always tangent to the streamline. For this reason, to streamlines can never intersect; if they did, then an element arriving at their intersection would have two different velocities simultaneously - an impossibility.
​

Why is this last statement impossible? Is it saying that two particles floating in water will never touch (something that many people have witnessed, I'm sure)? Or is it more abstract / general than that?
 
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  • #2
Real particles can touch each other as they have some finite size. The streamline is imagined to contain abstract, point-like particles with zero extension.

ehild
 
  • #3
ehild said:
Real particles can touch each other as they have some finite size. The streamline is imagined to contain abstract, point-like particles with zero extension.

ehild

Ah, okay, that makes sense. Thanks for answering.
 

1. What is the difference between fluid statics and fluid dynamics?

Fluid statics is the study of fluids at rest, while fluid dynamics is the study of fluids in motion. Fluid statics deals with forces acting on fluids and their effects on stationary objects, while fluid dynamics focuses on the movement of fluids and the forces causing them to move.

2. What are some real-world applications of fluid statics and dynamics?

Fluid statics and dynamics are used in various industries such as aerospace, automotive, and marine engineering. They are also important in the design of water supply systems, hydraulic systems, and pumps. In addition, understanding fluid statics and dynamics is crucial in weather prediction and climate studies.

3. How does fluid density affect the behavior of fluids?

Fluid density plays a significant role in fluid statics and dynamics. A fluid with higher density will exert more pressure on objects and will require more force to be moved. In fluid dynamics, higher density fluid will have a greater resistance to flow and will require more energy to be moved.

4. Can you explain the concept of buoyancy in fluid statics?

Buoyancy is the upward force exerted by a fluid on an object immersed in it. It is a result of the difference in pressure between the top and bottom of the object. If the buoyant force is greater than the weight of the object, it will float. This principle is used in designing ships and other floating objects.

5. How does Bernoulli's principle apply to fluid dynamics?

Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. This principle is used to explain the lift force generated by airplane wings and the flow of fluids through pipes and nozzles. It is also important in the study of airfoils and the design of wind turbines.

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