The Bernoulli equation and the issue of pressure rise in pipes immediately after a fluid flow is interrupted
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The physical meaning of Bernoulli’s equation is that the sum of the potential head, static head, and dynamic head at any two points in a fluid flowing continuously within a pipeline is equal. The existing pipeline with a diameter of 100 mm carries a fluid with a specific gravity of 0.9, at a flow rate of 20 cubic meters per hour; when the valve is suddenly closed, the pressure in the pipeline rises sharply to 2 to 6 kilograms. According to the Bernoulli equation, our calculation results should show an increase of only a few tens of kilopascals. I was wondering if any experienced experts could help determine whether it is appropriate to use this equation. If not, then I want to know if the law of inertia is suitable (the length of this pipeline is approximately 200 meters)
Reply to 1# itol1986: The Bernoulli equation is based on the principle that the sum of dynamic pressure and static pressure remains constant along a streamline. In your case, there is already pressure loss due to the valve’s wall thickness; how can the Bernoulli equation be applied at the same point? I personally think it’s not appropriate.
What you mean is that when the pipeline valve is closed, pressure builds up inside the pipeline, and the Bernoulli equation cannot be applied
If the Bernoulli equation cannot be used, then what should be used?
Reply to 4# itol1986: You can check tables; there are empirical data on head loss, and it seems that data on elbow loss is available as well. Then, using Bernoulli’s equation, it should be possible to calculate it.
It is the water hammer phenomenon; the amount of pressure increase depends on the flow rate, the density of the liquid, and the speed at which the valve is closed. The Bernoulli equation is not suitable for calculation here. Water hammer occurs when there is a sudden power outage or when a valve is closed too quickly; due to the inertia of the pressurized water flow, shock waves are generated, similar to the impact of a hammer, which is why it is called water hammer. The force generated by the back-and-forth movement of water flow shock waves can sometimes be very large, thereby damaging valves and pumps. “The \"water hammer effect\" refers to the situation inside a water pipe, where the inner wall is smooth and water flows freely. When an open valve suddenly closes, the water flow exerts pressure on the valve and the pipe walls, with the valve being the main target of this pressure. Due to the smooth wall of the pipe, the subsequent water flow, driven by inertia, quickly reaches its maximum velocity and causes destructive effects; this is what is known in hydraulics as the \"water hammer effect\", or positive water hammer. This factor must be taken into account in the construction of water supply pipelines. On the contrary, when a closed valve is suddenly opened, water hammer occurs as well; this is known as negative water hammer, and it also has a certain degree of destructive power, though less than that of the former. When a motorized water pump starts under voltage, it can accelerate from a stationary state to its rated speed in less than 1 second, while the flow rate in the pipeline increases from zero to the rated value. Due to the momentum of the fluid and its degree of compressibility, sudden changes in flow rate can cause pressure surges or drops within the pipeline, as well as cavitation. The impact of pressure exerts force on the pipe wall, generating noise, similar to a hammer hitting the pipe; this is known as the \"water hammer effect\".
In my opinion, when the valve is closed, the fluid is divided into two halves and is no longer a continuous fluid, whereas Bernoulli’s equation applies to continuous fluids! So after it’s turned off, it’s not usable as a whole! It can be calculated separately: for the part before the valve, Bernoulli’s principle is applied; the area behind the valve and the system downstream form a single unit, for which Bernoulli’s principle is also used. In this way, the pressures before and after the valve can be determined. If a reduction is desired, check whether it’s possible!
OP, can we use Bernoulli’s equation? But one needs to take the derivative with respect to time. :)
Can you help him write out the differential?
That one is more troublesome! The result obtained from the Bernoulli equation is the steady-state condition after the valve is closed! Not only the characteristic curve of the pipeline needs to be considered, but also the specific curve of the pump (especially since the head provided by a centrifugal pump varies with different flow rates).
Without the Bernoulli equation, isn’t it just a simple motion? Can Newton’s laws of motion be used? F=MV, force = mass * velocity?