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What is the relationship between vortex flowmeter and viscosity?

When the fluid reaches A from B, the viscous force of the fluid consumes some energy, which tends to reduce the velocity of the fluid in the boundary layer. In order to maintain the increase of the velocity in the boundary layer, in the region of the step-down speed increase, only the fluid outside the boundary layer transports some energy to supplement. Therefore, in the interval from A to B, the flow in the boundary layer is stable.
After point B, the flow of fluid outside the boundary layer becomes a supercharged deceleration flow, so that the kinetic energy of the fluid outside the boundary layer is converted into a part of the pressure energy, and the flow rate is continuously reduced. Due to the deceleration, it is no longer possible to replenish the fluid in the boundary layer to slow down the deceleration caused by the energy consumption of the fluid viscous retardation. Thus, part of the energy of the fluid in the boundary layer is converted into pressure energy, and a part of it continues to overcome the frictional resistance. Therefore, in the absence of energy replenishment, the remaining energy is insufficient to maintain the slowing of the velocity at the outer boundary of the boundary layer and the increase in pressure, resulting in a more drastic drop in speed. Especially for the part of the fluid close to the surface of the cylinder, the speed is reduced more quickly due to the influence of the wall surface.
After the fluid continues to move to point C, the energy consumed to overcome the friction and the energy converted for the supercharge has exhausted the kinetic energy of the fluid near the surface of the cylinder. This part of the fluid can only stagnate and then reverse. As can be seen from Figure 2-2, the velocity profile is getting narrower and narrower.
From point C to point D, the separation plane C-C' of the boundary layer appears. In this region, the flow of the fluid is extremely unstable, constantly forming a vortex. On the one hand, these vortices are constantly taken away, and on the other hand, they are continuously entangled with some fluids with larger energy to supplement the part of the fluid that is taken away. The incoming flow meets the backflowing fluid in the boundary layer, causing the flow line to be significantly squeezed away from the surface of the cylinder, creating a boundary layer separation phenomenon. This is the reason and process of fluid flow and vortex separation in a vortex flowmeter.

When discussing the flow around a fluid, if the viscosity of the fluid is small (e.g., gas), the fluid motion at a distance from the fluid can be approximated as a non-viscous fluid for vortex-free motion. The movement of a thin layer of fluid near the wall of the fluid is not considered to be such a flow. This thin layer is often referred to as the boundary layer. Fluid flow in the boundary layer has the following characteristics:
(1) The thickness of the boundary layer increases along the length of the fluid in the flow direction.
(2) - Boundary Layer Figure 2-1. Around the fluid boundary layer, no matter how small the viscosity of the fluid, the velocity of the fluid particles at the fluid wall around it is zero. As the distance from the wall increases, as shown in Figure 2-1, after a certain distance from the wall, the velocity increases to the same speed as the non-viscous fluid outside the boundary layer. Therefore, the velocity gradient is large in the boundary layer. According to Newton's internal friction law, the internal friction is proportional to the velocity gradient. Therefore, a large internal friction force is generated in the boundary layer.
(3) Because of the large velocity gradient in the boundary layer, resulting in strong vortices, it is vortex motion.
(4) The pressure values at the points along the normal direction of the fluid wall in the boundary layer are the same. If the y-axis is perpendicular to the direction around the fluid wall, the pressure distribution within the boundary is d/)/dy = 0. The existence of the boundary layer is one of the important reasons for the separation phenomenon when the fluid is moving around.
2. The system of regenerative production i is within a certain range of Reynolds number, and the flow around the fluid will cause vortex separation. Taking a cylinder as an example, the flow around the fluid and the vortex separation process can be explained.
 
The arrow to the left of the cylinder indicates the direction of fluid flow, the flow rate is u, and the pressure is p0.
When the fluid flows through the cylinder, if the viscosity of the fluid is not considered, the fluid begins to decelerate near the leading edge A of the cylinder and then accelerates along the curved surface. At the highest point B, the speed reaches its maximum. Then start to slow down, and finally close together behind the cylinder, the flow does not produce separation.
The actual fluid is viscous, so a boundary layer is created on the surface of the cylinder. At the former stagnation point A, the flow rate is "=0. The boundary layer at this point is still developing in the future, so the thickness of the boundary layer is approximately 0. As the fluid flows around the surface of the cylinder, the front stagnation point A The flow rate gradually increases, the pressure gradually decreases, and the thickness of the boundary layer gradually increases. However, the boundary layer of the region is very thin, so the internal pressure of the boundary layer and the external pressure can be considered to be substantially equal. The flow velocity and pressure in the boundary layer and the outer surface of the boundary layer the same.

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