Fluid mechanics problems
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Everyone is probably familiar with Bernoulli’s equation; in simple terms, the faster the flow rate, the lower the pressure. Essentially, it’s the law of conservation of energy, but there’s a contradiction I haven’t been able to figure out. Suppose there is a main pipe that supplies water outward, and there is a control valve on the end of this main pipe. When we open the control valve wider, the flow rate increases compared to before. This results in a decrease in the main pipe pressure; in other words, it is the situation where the flow rate is high and the pressure is low. But as everyone knows, when the control valve remains unchanged and the flow rate is to be increased, the only way is to raise the pressure, that is, to increase the pressure in the main pipe. Once the pressure in the main pipe increases, the flow rate rises as well, and the flow velocity becomes faster. These two theories are not contradictory; the first one deals with the relationship between flow rate and pressure, while the second deals with the relationship between flow rate and pressure difference (drop). Theoretically, they are not incompatible. However, from my analysis, in the second scenario, as the flow rate increases, the pressure in the main pipe should decrease – so why does it increase? Here, we need to analyze how the point for determining the pressure difference is chosen. Simply put, the pressure in my main pipe has increased. From this perspective, since the source of pressure has increased, the pressure difference should increase as well, which in turn results in a faster flow rate. If we consider only the pressure in the main pipe, an increase in pressure would lead to a decrease in flow rate. It’s quite contradictory, isn’t it? I’m not sure whether there’s an issue with the selection of the analysis points or with my understanding of certain definitions. It’s a simple question, but I just can’t figure it out. I hope my friends from Haichuan can explain to me where I went wrong.
You can’t use Bernoulli when working backwards; increasing the pressure in the main pipe already creates an energy imbalance
Thank you. What you mean is that the second scenario I mentioned involves an increase in flow velocity due to an increase in energy – energy is added from the outside – rather than the relationship between pressure energy and kinetic energy as described by Bernoulli’s principle of energy conservation. Is that what you mean?
Thank you very much, but there is one more thing I don’t understand. The theory I had seen before was that with parallel pumps, the head does not increase while the flow rate does. However, when I worked at a power plant, I found that the head still increased after the pumps were connected in parallel, as the two pumps were connected to the same main pipe, just as shown in the diagram I had drawn earlier. Using two pumps clearly results in much higher pressure than using just one pump. Why is that? Another factor is that with the same pump, different pipe diameters can lead to varying flow rates and pressures; a narrower pipe results in a faster flow rate and higher pressure. (Compared to the thicker one) this is another pump, and energy is also conserved. How is it that this doesn’t match Bernoulli either? Is it because of the diameter? Can’t we use Bernoulli when the pipe diameter and operating conditions are different? I feel that the small tubes here have a high flow rate and high pressure. It’s contrary to Bernoulli, right? Please, the expert in charge, could you tell me? It’s been bothering me for a long time
This question is part of our daily question series; we’ve discussed it intensively on the forum, and I’ll find that post for you later.
This issue relates to the performance curve of the pump and the characteristic curve of the pipeline. Parallel connection of pumps results in a constant head for the pumps on the curve, with the flow rates adding together. In fact, the intersection point with the pipeline characteristic curve shifts, so under unchanged other conditions, both parallel and series connections increase both flow rate and head. For more details, see the post below. Discussion on [Daily Question] Parallel and series operation of centrifugal pumps http://bbs.hcbbs.com/thread-1413143-1-1.html (Source: Haichuan Chemical Industry Forum)