Problem of holes in straight pipes

1. The question is quite simple: it involves determining the pressure drop upstream and downstream of each hole, and then calculating the diameter of those holes based on the requirement of equal flow rates. 2. The pressure drop distribution within the branch pipes differs significantly; the flow within these pipes is not uniform. Whether parameters such as fluid viscosity and boundary slip, which are difficult to quantify accurately, can be properly determined affects the calculation results. 3. I have seen simulations using CFD software for similar problems; it seems that achieving exact equal flow rates at each hole requires considerable effort. 4 Make it rough; reduce the diameter slightly upstream and increase it slightly downstream

1. I read a document many years ago with the theme of calculating flow distribution pipes of equal diameter; it could serve as a reference, so you might want to search for it online. 2. A simple simulation was conducted using a straight tube with 10 orifices of equal diameter. Under the same inlet flow velocity and the same external pressure conditions, three fluids with different viscosities were used to observe the flow distribution at each nozzle, as shown in the attached figure. 2.1. For general low-viscosity media, the static pressure at the end of the straight pipe is higher than that at the inlet, which means a larger pressure difference at the outlet orifice and thus a higher flow rate ； The flow rate at the inlet nozzle is actually slightly lower. 2.2. When the viscosity of the medium is high enough to cause changes in the distribution of pressure drops within the straight pipe, the flow rates through the 10 nozzles of equal diameter also change. 3. We have encountered similar situations in practice: too low a pressure in the straight pipe at the inlet end leads to backflow at the nozzles. It’s exactly the opposite of what the original poster reported. 4. It is also verified in the experimental section of the recommended literature that the flow rate at the outlet nozzles is greater than that at the inlet nozzles. 5. Of course, the pattern of flow is related to many factors; the phenomenon observed by the original poster may be based on a certain pattern.

For multiple nozzles of the same diameter installed in a straight pipe, the smaller the nozzle aperture, the smaller the difference in flow rate between the various nozzles; of course, the resulting pressure drop also increases. However, the pattern of high flow rates at the outlets remains unchanged

Is there something similar to the principle of a vacuum extractor at work here? The linear velocity in the inlet section should be the highest; vacuum formation is more likely to occur in the short sections near the inlet. Of course, this applies when the medium is gas, as its relative viscosity is much lower than that of liquids!

This should be more related to the resistance of the pipeline corresponding to each opening. By setting the flow rate to be the same and ensuring that the resistance in each pipeline is equal, the diameter of the pipelines can be determined, from which the size of the openings can be calculated. The openings further back can be made slightly larger, which should help improve uneven gas distribution

It has a bit of a vacuum cleaner smell to it. When the total cross-sectional area of the nozzles is much smaller than that of the straight pipe, the pressure difference between the inside and outside of the straight pipe increases, resulting in a positive pressure drop across each nozzle; only then does the backflow phenomenon disappear

Could the shunt tubes be evenly distributed across several circumferential sections? This would reduce the amount of calculation required, and it would basically ensure that the tubes on the same circumference have equal flow rates.

1. Reducing the pressure difference between the nozzles through circumferential distribution is conditional; it depends on whether the manifold is annular or disc-shaped. 2. If it is annular and has a single inlet point, it functions in a similar manner to a straight pipe (with the inlet at the center and nozzles distributed on the sides). 3. If it is disc-shaped with air intake at the center, then all nozzles arranged at the same diameter are at equal distances from the center, resulting in similar pressure drops, which helps to alleviate unevenness.