## What is a Rotameter?

The Rotameter is one of the most commonly used throttling flowmeters. It has the advantages of simple structure, easy manufacturing, wide measuring range (range ratio up to 10:1), high measuring accuracy (error ± 5%), intuitive indication, convenient maintenance, small pressure loss, etc. It is the most widely used measuring instrument in modern life and industrial production.Today, with the increasing development of measurement technology and the increasing demand for measurement accuracy, only when metrologists fully understand the structural principle of rotameter, flow calculation, influencing factors, and correction methods of the measurement value, as well as the selection and installation requirements of flowmeter, can they choose the most suitable measuring instrument to achieve the best measurement effect. We hope that this article will bring some help to metrologists.

## Analysis of the structure and principle of rotameter

### Structural analysis

The rotameter is composed of two parts, one is the tapered tube that expands gradually from bottom to top, and the other is the rotor that can move down the centerline of the tube and has a slightly higher density than the fluid (Figure 1 Schematic Diagram of rotameter).

The tapered tube is made of glass, plastic, or metal. The glass or plastic cone tube is engraved with a flow scale, through which the position of the rotor in the transparent fluid and the corresponding scale value can be seen; The rotor position in the metal tapered tube is transferred outside the tube through magnetic coupling, and the value is displayed on the panel.

### Working principle

When measuring the flow rate of fluid, the fluid flows into the impact rotor from the lower end of the cone tube, which produces a force on it. The force varies with the flow rate; When the flow is large enough, the force generated will lift the rotor and make it rise; The fluid flows out from the upper end through the annular section between the rotor and the tapered pipe wall. When the force exerted by the fluid on the rotor is equal to the weight of the rotor, the rotor stays at a certain position due to force balance; This position has a corresponding relationship with the flow, and the flow value can be obtained according to this position.

### Flow calculation

The flowmeter rotor is subjected to three forces in the conical tube: gravity, dynamic pressure, and buoyancy. When the three forces are balanced, the rotor gravity=dynamic pressure+buoyancy. When the flow rate increases or decreases, the rotor will move up or down, and the cross-sectional area of fluid flow will also change until the corresponding flow rate reaches equilibrium, and the rotor will be stable at a new position.

Therefore, the force relationship formula of the rotor when it is stable is as follows:

Combining Formula (1) and referring to the relationship equation between the flow rate of the orifice flowmeter and the throttling differential pressure:

Flow formula of rotameter:

Where: Qv flow value; A0 - flow coefficient (related to rotor shape, fluid state, flowmeter structure, fluid physical properties, and other factors, which can only be determined by experiments); A0 - Annular clearance area, corresponding to rotor height h; Approximate: A0=ch; The coefficient c is related to the geometric shape and size of the rotor and tapered tube; ρ T - rotor density; ρ F - fluid density; At - maximum sectional area of the rotor.

The flow equation can be written as:It can be seen from Formula (4) that the floating height h of the rotor is corresponding to the flow qv; The flow value can be read in real-time by marking the flow value according to different heights.

## Fluid correlation correction of measured values

### Measurement value correction analysis

It can be seen from Formula (4) that the matching relationship between the flow rate and the rotor height varies with the density of the measured fluid. Due to the limitation of calibration equipment, it is impossible for manufacturers to calibrate all flowmeters with real liquid. Therefore, when measuring non-calibrated media, the measured values read out should be corrected to ensure accuracy.

For liquid, its density is constant, and only needs to correct the influence caused by the difference between the measured liquid and the calibration liquid; Because the gas is compressible, the influence of temperature and pressure when the calibration state is different from the actual state should also be considered.

Generally, the default calibration state is temperature T=293.16K, absolute pressure p=101325Pa. According to the flow calculation formula, the following analysis is made:

On the one hand, the flow formula for measuring the calibration fluid is:

Where: Qv0 - flow indication of calibration fluid in calibration state; A0 Flow coefficient of calibration fluid in calibration state; ρ 0 - Density of fluid in calibration state.

On the other hand, the flow formula for measuring the measured fluid under the working condition of the flowmeter is set as follows:

It can be seen from Eq. (5) and Eq. (6) that under the actual working condition, the actual flow of the fluid to be measured is qv, but when the rotor is at height h, the rotor flowmeter still displays qv0. Comparing Formula (5) and Formula (6), we can get the relationship between Qv and Qv0, that is, the flow correction formula is:

The experiment shows that the flow coefficient a is related to the Reynolds number Re and the structure of the flowmeter. When the viscosity of the measured fluid is not much different from the viscosity of the calibration fluid, or within the flow range where the flow coefficient a is constant, the influence of a can be ignored, that is, a=a0 can be considered, so equation (7) can be simplified as:

If the viscosity of the measured fluid differs greatly from the viscosity of the calibrated fluid, the difference between the actual flow coefficient a and the calibrated flow coefficient a0 due to the viscosity difference shall be considered. The difference shall be corrected or calibrated according to Formula (8). It cannot be simply considered that a=a0.

### Fluid density correction

#### Correction of the measured value of liquid flow

The flowmeter usually uses water as the reference fluid for the measurement indication of liquid fluid, which is calibrated in the calibration state. In the actual measurement of non-aqueous liquid flow, only the influence caused by the density difference between the measured liquid and the calibration liquid (water) needs to be corrected, and the correction and conversion can be carried out according to Formula (8). At this point, ρ 0 is the density of the calibration fluid, and ρ Is the density of the fluid being measured.

#### Correction of the measured value of gas flow

The air is used as the reference for the measurement indicative of the flowmeter for gaseous fluid, and the flowmeter is calibrated under the calibration state. As the density of the gas is greatly affected by temperature and pressure changes, it should not only be converted according to the different densities between the measured gas and the calibration gas but also be corrected and converted according to the different temperatures and pressures under working conditions and calibration conditions. In order to simplify the correction of gas flow value, the influence of viscosity on the flow coefficient can generally be ignored. Moreover, for gas ρ t＞＞ ρ 0 ρ t＞＞ ρ， Then according to Formula (8):

When measuring the airflow under the non-calibration state, it can be directly calculated with equation (9). but ρ For the density of the measured gas under working conditions, it is inconvenient to use in practice. For this reason, the fluid density and its state can be corrected separately, that is, the density of the measured fluid is corrected in the calibration state first, and then the state is corrected. The final correction formula is:

Where: p0 - absolute pressure under calibration state; P - absolute pressure under working condition; T0 - absolute temperature under calibration state; T - absolute temperature under working condition; ρ′- The density of the measured gas in the calibration state.

### Flow coefficient correction

#### Correlation between flow coefficient and rotor shape

It can be seen from Formula (4) that the flow coefficient is also an important parameter that affects the measurement results. It varies with the shape of the rotor. Although the rotor shape is designed by the manufacturer according to the instrument structure and flow measurement range, which is not considered by the user, the user should understand the relationship between the rotor shape and the accuracy of the measured value.

In general, when measuring the same fluid, the higher the height of the rotor of which shape in the conical tube is, the smaller the flow coefficient of the flowmeter using this rotor is, and the higher the measurement accuracy is. According to this feature, you can choose a rotor flowmeter that is more suitable for your own needs.

#### Correlation between flow coefficient and Reynolds number

When the rotor and structure of the flowmeter are fixed, the flow coefficient is mainly affected by the Reynolds number Re. When the Reynolds number Re is small, the flow coefficient changes with the Reynolds number Re, and it is necessary to correct the flow coefficient (see Equation 7); When the Reynolds number reaches a certain value Remin (critical Reynolds number), the flow coefficient is basically stable, which can be regarded as a constant, and no correction calculation on the flow coefficient is required. It is difficult to find a general theoretical formula to describe the relationship between the flow coefficient and Reynolds number for different flowmeters.

Due to the diversity of fluids and the complexity of the environment, there are many difficulties in the correction of the flow coefficient. If a very accurate measurement is required, the user can let the manufacturer calibrate the flowmeter scale with actual fluid, so that the true value under the working environment can be obtained directly without any correction.

## Model selection and installation technology analysis

### Type of rotameter

The different materials of tapered pipes can be roughly divided into three categories. Among them, the glass tube rotameter is simple in structure, low in cost, easy to be made into an anti-corrosion instrument, and has the advantages of high transparency, intuitive reading, not easy to crack, lightweight, long service life, convenient installation, and connection, etc.The plastic tube rotameter has the characteristics of small volume, light weight, cone tube not easy to break, corrosion resistance, etc.

Metal tube float flowmeter can measure liquid and gas flow, especially suitable for medium measurement with low flow rate and small flow. It can provide instantaneous flow and cumulative flow display, or realize flow indication, integration, recording, control, alarm, and other functions by outputting standard signals.

### Model Selection Analysis

To ensure the accuracy of measurement data, users should select flow meters according to the installation environment, physical and chemical characteristics of the fluid, and other factors.(1) If the fluid is medium and small flow, the pressure is less than 1MPa, the temperature is less than 100 ℃, it is transparent, non-toxic, has no danger of combustion and explosion, and has no corrosion and adhesion to the glass, the glass tube rotameter can generally be used.

(2) In the pipeline environment with relatively small space and weak supporting gravity, the fluid is medium and small flow, low pressure, and low temperature, so the plastic tube rotameter can be selected.

(3) If the fluid is medium and small flow, easy to vaporize (or condense), toxic, flammable and explosive, free of magnetic substances, fibers, and wear substances, and non-corrosive to stainless steel, ordinary metal tube rotameter can be selected; If the fluid is corrosive, anti-corrosion metal tube rotameter shall be used; If the fluid is easy to crystallize or vaporize or has a high viscosity, the metal tube rotameter with jacket and heat tracing or cooling interface shall be selected.

In high-temperature or cold, high-pressure, and toxic environments, a metal tube rotameter with a remote information transmission function shall be selected.

(4) If the fluid pressure is unstable, especially for gas measurement, the rotor flowmeter with a damping structure shall be selected.

### Technical requirements for installation

Correct installation is a necessary condition for normal operation and accurate measurement of the flowmeter. Generally, the following requirements shall be followed:(1) The rotameter must be installed vertically. The fluid flows through the flowmeter from bottom to top, and the verticality is better than 2 °.

(2) The inlet shall have a straight pipe section more than 5 times the pipe diameter, and the outlet shall have a 250mm straight pipe section.

(3) Pipe support shall be installed at the proper installation position.

(4) Bypass pipeline and bypass valve shall be installed beside the flowmeter, and a one-way valve shall be installed downstream.

(5) If the measuring fluid is a dirty medium or contains solid impurities, a filter, and a regular cleaning device must be installed at the inlet.

(6) If the measuring fluid contains ferromagnetic substances, a magnetic filter shall be installed.

(7) The flowmeter powered by liquid crystal or lithium battery shall avoid direct sunlight and high-temperature environment (≥ 65 ℃) as far as possible.

(8) The working pressure of the measured gas shall not be less than 5 times the pressure loss of the flowmeter.

### Summary

The structure of the rotameter is simple and the principle is not complex. However, due to the correlation between flow measurement characteristics and fluid properties, as well as the various physical properties of the fluid, the application of flow measurement technology becomes very complex. Not only the viscosity of fluids is different, but also the compressibility and thermal expansion of gas fluids make fluid measurement more difficult. Therefore, this article is just a summary of the author's experience and technical analysis. For more in-depth research, we expect many fluid measurement researchers to provide more valuable insights.