How can the velocity at points of change in pipe systems be determined?

[pipedown]

For minor losses, I read that the pressure drop is equal to the dynamic pressure * loss coefficient. However, in calculating dynamic pressure, it uses a single velocity. How do you determine this velocity when it will vary at the point of change in pipe diameter or direction? I have read somewhere that it would be a mean velocity between the two sides of the change, but how can this be determined? It seems that in these pipe systems, the head loss must be calculated for the system to determine velocities before a mean velocity at these points can be calculated. Is an iterative process the only way to achieve this or am I missing something?

 

[Skrambles]

If you know the volumetric flow rate you can just divide it by the cross-sectional area of the pipe. It really depends on what information you have about the system, sometimes you will have to find the answer through iteration and sometimes you may need to use a table.

 

[Curl]

Actually this depends on how the coefficient is defined. Usually the table you grab it from will tell you if they are referring to the velocity coming out, or the upstream velocity.

 

[pipedown]

Is there a general convention? I am also trying to figure out how to relate this in terms of reservoirs/tanks and entrance flows, though I am starting to see that I should be making assumptions for certain head losses based on relative geometries

 

[PJC01]

I can confirm that determining the velocity at points of change in pipe diameter or direction can be a complex process. In general, the velocity at these points can be determined using a variety of methods such as theoretical calculations, experimental measurements, or numerical simulations. In some cases, an iterative process may be necessary to achieve an accurate estimation of the mean velocity.

One approach to determining the velocity at points of change is to use the continuity equation, which states that the mass flow rate in a pipe is constant. This equation can be used to calculate the mean velocity by equating the mass flow rate on both sides of the change in pipe diameter or direction. However, this method may not be applicable in all cases, such as when the flow is not fully developed.

Another approach is to use empirical correlations or experimental data to estimate the velocity at points of change. These correlations can be based on factors such as the geometry of the pipe, the type of fluid, and the Reynolds number. However, the accuracy of these correlations may be limited and may require adjustments based on specific system conditions.

In some cases, numerical simulations using computational fluid dynamics (CFD) can also be used to determine the velocity at points of change. CFD simulations can provide a detailed understanding of the flow behavior and can account for factors such as turbulence and flow separation. However, this method may require significant computational resources and may not be feasible for all pipe systems.

In summary, determining the velocity at points of change in pipe systems can be a challenging task and may require a combination of theoretical, experimental, and numerical methods. An iterative process may be necessary to achieve an accurate estimation of the mean velocity, and the specific approach may vary depending on the system and its conditions. I would recommend consulting with experts in the field or conducting further research to determine the most suitable method for a specific pipe system.