For any flow measurement, it must include two parts: one is the flow measurement itself; the other is its error tolerance. Otherwise it is incomplete. Therefore, for any kind of flow meter, it must understand its error characteristics.
The so-called error characteristic is the relationship between the flowmeter's error value and the flow measurement value. To discuss the error characteristic, it is to discuss and study the trend of measurement error value changing with the change of flow measurement value.
The measurement error value E of the positive displacement flowmeter can be expressed by the ratio of the difference between the indicated value and the true value to the indicated value. Suppose: V is the fluid volume true value through the flowmeter; I is the flowmeter indication value, then the error value E can be expressed as E= (2-5)
Substituting the relationship (2-3) between the fluid volume V and the indicated value I yields:
E=1- (2-6)
From Formula 2-6, the error characteristics of the volumetric flowmeter are only related to the internal measurement volume v and the instrument gear ratio constant a. In other words, from the point of view of the measurement principle, the measurement error of the volumetric flowmeter is only related to the geometry of the flowmeter. Regardless of the nature of the fluid and the value of the flow rate, we call this error characteristic an ideal volumetric flowmeter. Error characteristics. Drawing a curve is a horizontal line parallel to the horizontal axis, as shown by curve 1 in Figure 2-6.
However, when we calibrate the positive displacement flowmeter and draw the actual error characteristic curve, it is closer to the curve 2 form. When the flow rate is small, the error value is sharply tilted in the negative direction; as the flow rate increases, the error value gradually moves from the negative direction to the positive direction and stabilizes at a certain position. The error curve is parallel to the horizontal axis. As the flow rate continues to increase, the error value will again shift in the negative direction. The actual error characteristic curve shows this change trend because there is an inevitable leakage phenomenon in the positive displacement flowmeter. The so-called leakage flow, that is, the fluid flows directly from the inlet to the outlet through the gap between the rotating part and the housing and is not metered. The following will discuss the relationship of error characteristics that takes into account the leakage flow phenomenon.
Assume that the fluid leakage rate per unit time is denoted by g; the flow rate through the flowmeter is qv; the total volume of fluid passing through the flowmeter is V; the volume of the total leakage flow during this period is V. This strain V can be expressed as * V= g (2-7)
Therefore, when there is a leakage flow, when the rotor discharges N measurement fluid volumes, the volume of fluid actually passing through the flowmeter is V = Nv + V (2-8)
Substituting Equations 2-2, 2-7 into Equation 2-8 yields:
V= v+ g (2-9)
Formula (2-9) can be organized into:
V= (2-10)
Substituting equation (2-10) into the error definition formula (2-5) yields:
E=1- (2-11)
Analytical Equation 2-11 shows that since the volumetric volume v and the gear ratio constant a are all constant values, the relationship between the error E and the flow rate is affected by the leakage flow g per unit time.
If it is assumed that the leakage flow g of the positive displacement flowmeter is a constant value, the variation trend of the error curve can be discussed using Equation (2-11).
When the flow rate is very small, in the extreme case qr = g, then the brackets in equation (2-11) are 0, and the error value E tends to negative infinity.
As the flow qv increases, the value in parentheses in Equation (2-11) gradually increases, and the error value E also gradually increases in the positive direction.
When the flow rate continues to increase, reaching g is very small compared to qv, ie when g/qv is close to 0, Equation (2-11) is converted to Equation (2-6), and the flowmeter error curve tends to the ideal error curve.
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