How to Understand the Relationship Between Pressure and Flow in Piping?

 How to Understand the Relationship Between Pressure and Flow in Piping? Suppose we put a water pump into a fish pond to pump water, and a pipe is connected to the outlet of the water pump. If we increase the power of the water pump, the water from the pipe will spray farther, and the water flow rate will also increase. So it is easy for us to draw a conclusion based on intuition: there is a certain correlation between the flow rate and pressure in the piping. However, in actual industrial production, if we only know that the diameter of a water pipe is DN50 and its internal pressure is 1MPa, we will have no way to calculate the flow velocity and flow rate in the pipe. Why is there such a counterintuitive situation? We can first conduct a simple thought experiment. For the convenience of understanding, we will use compressible gas as an example. Suppose we have a sealed syringe filled with air. When we do not apply any force to the piston, the air pressure in the syringe is equal to the external atmospheric pressure. This is easy to understand because the internal and external air pressures are balanced. From a microscopic perspective, the air pressure in the syringe is the result of the "combined force" formed by the gas molecules inside continuously moving thermally and "colliding" with the inner wall of the syringe. If we press the piston hard to compress the gas in the syringe to a certain volume, the gas pressure will obviously increase. But note that after we complete the compression process, the gas in the syringe remains stationary, that is, the pressure increases but the flow rate is still 0. In this way, we can intuitively understand why the two parameters of pressure and flow rate in the piping can have no connection at all. Smart friends will surely find that replacing air with other gases or liquids in this example will not affect the conclusion at all. Then the question comes: why does the phenomenon mentioned at the beginning of the article make us have the intuition that pressure is related to flow rate? The movement of the water column after spraying is not essentially different from the parabolic movement of a small ball in physics class. The water column sprays farther not because the water pressure is high, but because the water flow velocity is fast. When you slightly pinch the nozzle, that is, reduce the diameter of the pipe, the water will also spray farther and hurt more when it hits a person, which is exactly the effect of the increased flow velocity. However, in actual industrial production, it is impossible to calculate the flow velocity or flow rate in the pipe only by knowing the diameter and pressure of a section of pipe that leads to an unknown place. To establish the relationship between pressure and flow rate in the pipe, it is necessary to exert a specific influence on the fluid in the pipe. For example, open a hole against the incoming flow direction, and measure the dynamic pressure and static pressure of the fluid at the same time to form a "bar" flowmeter (such as Pitotbar, Annubar, etc.). The core principle of differential pressure flowmeters such as Pitotbar and Annubar is to use the Bernoulli equation law of fluid: *Total Pressure = Static Pressure + Dynamic Pressure*. Static pressure is the pressure when the fluid is stationary (also the piping pressure measured by a conventional pressure gauge), representing the potential energy of the fluid; Dynamic pressure is the pressure generated by the fluid flow, which is proportional to the square of the flow velocity, representing the kinetic energy of the fluid. When the upstream hole of the Pitotbar probe is facing the fluid direction, it can measure the total pressure including static pressure and dynamic pressure, while the side hole can only measure the static pressure. The difference between the two is the dynamic pressure. The flow velocity and flow rate can be accurately converted through the dynamic pressure value, combined with parameters such as fluid density and pipe cross-sectional area. This also explains why the piping static pressure alone cannot calculate the flow rate - the key parameter of "flow property", dynamic pressure, is missing. The  Vortex Steam Flow Meter is also a commonly used flow monitoring device in industry. Different from the monitoring logic of differential pressure flowmeters, the   Compressed Air Flow Meter uses the principle of fluid vibration to complete flow measurement, and has strong adaptability in many medium and low pressure fluid piping. Back to the industrial scenario, we can further understand the relationship between pressure and flow rate through the resistance characteristics of the piping. Any piping has along-the-way resistance (such as pipe wall friction) and local resistance (such as elbows, valves), and the resistance is proportional to the square of the flow rate. When the power of the water pump is increased, its total output head (which can be understood as total pressure) will increase. Part of it is used to overcome the piping resistance, and the other part is converted into the kinetic energy of the fluid (increasing the flow velocity and flow rate). For example, for the same DN50 water pipe, if the valve is fully open, the piping resistance is small, and the flow rate is greater under the same water pump pressure; if the valve is closed, the piping resistance increases sharply. At this time, the pressure output by the water pump is mostly used to overcome the resistance, and the fluid flow velocity and flow rate will decrease instead. This is why the same water pump and the same piping can produce the difference of "high pressure and small flow rate" or "low pressure and large flow rate" only by adjusting the valve opening. In this process, if the  Steam Vortex Flow Meter is used for data collection, the real-time data of flow rate changes with pressure and resistance can be clearly seen. The measurement and control products of Auto Instruments are based on these fluid mechanics principles, providing accurate solutions for pressure and flow monitoring of industrial piping. Its intelligent pressure transmitter can capture the static pressure changes of the piping in real time. When paired with a  Vortex Gas Flow Meter or a differential pressure flowmeter (such as the Pitotbar supporting solution), it can realize the linkage monitoring of pressure and flow rate; Among them, the industrial-grade Vortex Flowmeter can adapt to multiple types of fluid media, and can stably monitor common water, air, and some viscous media; For some industrial scenarios with explosion-proof requirements, Auto's explosion-proof  Vapor Flow Meter can also ensure the safety of the monitoring process; There is also a small-caliber Vortex Flowmeter specially designed for small-flow piping, which can cover more industrial monitoring scenarios. All in all, the pressure and flow rate in the piping are not simply linearly related. The establishment of their relationship depends on three core elements: fluid flow state (dynamic pressure), piping resistance characteristics, and physical properties of the medium. Professional measurement and control equipment, such as the Vortex Flowmeter, is the key bridge to convert these complex relationships into accurate data, laying a solid data foundation for the safe and efficient operation of industrial production.