Transit time for a fluid particle in potential flow

However, this answer may not be entirely accurate due to the presence of circulation, which can affect the flow patterns and therefore the time taken for the particle to travel from one stagnation point to the other. This is a strange and complex phenomenon, and more research and analysis is needed to fully understand it.
  • #1
deltaquattro
1
0
Hi,

consider classical potential flow without circulation around a
cylinder. Let us follow a fluid particle adjacent to the upper surface
of the cylinder (e.g. on the dividing streamline), starting just a
very tiny bit upstream of the upstream stagnation point. It will go to
the downstream stagnation point, following the surface of the
cylinder. How much time does it take for the particle to get to the
downstream stagnation point? I found an answer, but it's so strange
that I'd like to hear your opinion too. Thanks,


greetings,


deltaquattro
 
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  • #2
The time it takes for a fluid particle to go from the upstream stagnation point to the downstream stagnation point in a classical potential flow without circulation around a cylinder depends on the velocity of the flow. If the flow is faster, the particle will reach the downstream stagnation point more quickly; if the flow is slower, it will take longer. Generally, the time taken will be equal to the distance between the two stagnation points divided by the velocity of the flow.
 
  • #3


I would like to clarify that the concept of "transit time" in potential flow is not well-defined. In potential flow, the fluid particles move along streamlines, which are imaginary lines that represent the direction of flow at any given point. Therefore, the time taken for a fluid particle to move from one point to another will depend on the specific streamline it follows. Additionally, potential flow assumes an idealized scenario without any drag or viscosity, which may not accurately reflect real-world fluid behavior.

That being said, if we consider the scenario described in the question, where the fluid particle is following the upper surface of the cylinder, it will indeed take a finite amount of time to reach the downstream stagnation point. This time will vary depending on the speed of the fluid and the length of the streamline it follows. However, without specific values for these parameters, it is impossible to accurately determine the transit time.

Moreover, the concept of "stagnation points" in potential flow also needs to be clarified. In potential flow, these points represent areas where the fluid velocity is zero, and they are usually located at the leading and trailing edges of the cylinder. However, in real-world situations, the fluid velocity at these points may not be exactly zero due to factors such as boundary layer separation.

In conclusion, while the concept of transit time in potential flow may provide some insights into the behavior of fluid particles, it should be used with caution and not considered as an absolute measure of time. Furthermore, it is essential to consider the limitations and assumptions of potential flow when applying this concept to real-world fluid dynamics problems.
 

1. What is potential flow?

Potential flow is a simplified model used to describe the motion of fluids, assuming that they are inviscid (have no internal friction) and incompressible (their density remains constant). It is a useful tool in fluid dynamics, as it allows for simpler calculations and predictions compared to real fluid flow.

2. How is transit time defined in potential flow?

Transit time is the time it takes for a fluid particle to travel from one point to another in a potential flow. It is a measure of the flow's speed and can be calculated using the Bernoulli equation, which relates the fluid's velocity, pressure, and potential energy.

3. What factors affect the transit time in potential flow?

The transit time in potential flow is affected by the fluid's initial velocity and position, the shape of the flow field, and any obstacles or boundaries present. It is also influenced by the fluid's properties, such as its density and viscosity.

4. How can transit time be used in practical applications?

Transit time in potential flow is a useful concept in various practical applications, such as designing aircraft wings or calculating the flow rate of a liquid through a pipe. It can also be used in meteorology to predict the movement of air masses.

5. Is transit time the same for all fluid particles in potential flow?

In potential flow, all fluid particles follow the same flow pattern, so they will have the same transit time if they are released at the same time and location. However, if the fluid's properties or the flow field changes, the transit time may also vary for different particles.

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