Discussion on fluid transport machinery
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Regarding the gas transfer machinery I’ve been looking at recently, can it really be analyzed using Bernoulli’s equation? It can be simply understood as follows: vacuum creation and pressure increase represent external work done on the system, thereby adding mechanical energy; this leads to a conversion between kinetic energy and static pressure. In the end, there is always some expansion from a small diameter to a larger one, which transforms dynamic pressure into static pressure – it is thus a process of pressure increase； But if I consider things ideally, and look at it from the perspective of the ideal gas law, a rough assessment suggests that the conclusion regarding isothermal compression of an ideal gas is actually the opposite. According to PV=nRT, P1V1=P2V2; as the volume of the compressed gas decreases, the pressure increases. Therefore, the process of expanding the gas seems to be a process of reducing pressure, which is contrary to the conclusion mentioned earlier
Bernoulli’s equation is primarily used to describe the conservation of energy in the flow of incompressible fluids such as water through pipes; it relates the fluid’s pressure energy, kinetic energy, and potential energy. For gas transfer machinery, especially vacuum or pressurization equipment, if we treat gas as an incompressible fluid, Bernoulli’s equation can qualitatively describe the process of energy conversion, namely the transformation between kinetic energy and static pressure energy. In this case, it is indeed possible to observe the conversion of kinetic energy into static pressure energy during the expansion process, thereby achieving pressurization. However, gases are compressible; especially under high-speed flow or significant pressure changes, a simple application of Bernoulli’s equation becomes inaccurate. At this point, the compressibility of the gas needs to be taken into account, which involves the use of the ideal gas law PV=nRT. According to the ideal gas law, as a gas is compressed, its volume decreases while its pressure increases. If the expansion process is considered, from the perspective of an ideal gas, it does appear to be a depressurization process, as the increased volume seems to lead to a decrease in pressure. In fact, the flow of gas in pipes is a complex process that involves various factors such as energy conversion, pressure changes, volume changes, and temperature changes. In gas transfer machinery, especially in pressurization and vacuum pumping equipment, there is usually a series of power devices (such as compressors, fans, etc.) and fluid dynamics designs (such as expanded or constricted pipes) to ensure that the gas flows and is compressed in the desired manner. The expansion process can indeed be used to increase pressure in some cases, but this is based on the principle of kinetic energy being converted into static pressure energy, rather than merely due to an increase in volume. When designing and analyzing these systems, it is usually necessary to use more complex fluid dynamics and thermodynamics theories, rather than relying solely on simplified models based on Bernoulli’s equation or the ideal gas law. .
So, may I ask the senior, how can we simply understand the operation of fluid transfer machinery in engineering design? I usually use the conservation of mechanical energy to analyze these models nowadays
Agree with the second floor; it applies to incompressible fluids.