## 5 Conclusions  
For an online vibrating tube densitometer, we carried out theoretical research and the derivation of fitting equations; built a number of experimental devices; and selected two kinds of densitometers, the straight-tube-type and curved-tube-type at (750-1400) kg/m\({}^{3}\), (15-45) \({}^{\circ}\)C, and (0-25) bar, to assess densitometer metrological performance. The main conclusions are as follows:  
* A set of online vibrating tube liquid densitometer experimental devices were built based on a quantity and value transfer system. The whole device consists of a desktop densitometer, multi-temperature thermostatic stirring system, walk-in thermostat, blowing system, and frequency acquisition system. The experimental research on five densitometers can be carried out at the same time under different temperatures and densities, and the device evaluates an accuracy of \(U=0.08\) kg/m\({}^{3}\), \(k=2\);
* This device solves the problem of the traceability of online vibrating tube liquid densitometers, and can carry out the assessments of quantity and value transfer at (750-1400) kg/m\({}^{3}\), (15-45) \({}^{\circ}\)C, and (0-25) bar and the accuracy grade \(\geq\pm 0.1\) kg/m\({}^{3}\) of online vibrating tube liquid densitometer, and it is proved that this device has the ability to assess quantity and value transfer, as in the previous experiments;
* We selected straight-tube-type and elbow-type densitometers, at (15-45) \({}^{\circ}\)C, and selected five kinds of liquids to carry out online vibrating tube densitometer metrological experiments. We concluded that different density vibration tube frequencies increased with density and decreased with the increase in temperature. Using the frequency and density values obtained from the experiments, we calculated the K coefficient of the theoretical equations and determined the fitted density difference. The fitting errors of the two densitometers are basically within the nominal error, which indicates that the device has a good degree of differentiation and reasonableness. The fitting errors of the two densitometers at (15-45) \({}^{\circ}\)C are not a linear result in a uniform direction (positive or negative), and the factors contributing to this result still need to be determined by further research;
* From the (0-25) bar carried out the online vibrating tube densitometer pressure-frequency experiments, it is concluded that the vibration frequency increases with the increase in pressure in the vibrating tube. The pressure in the pipe and the interaction of the coefficients of the vibrating tube at both ends of the equivalent elasticity coefficient of the corrugated pipe, \(K\), deviate from the pressure and the elasticity coefficient of the \(K\) change rule. This still needs to be studied further. The trend of change in the curved-type density meter by the pressure is more obvious;
* The experimental device will be used to carry out more experiments and tests in the later stage. It will assess the pressure and viscosity concerning the vibration frequency, combined with the fluid Reynolds number, inlet effect, and other factors to explore the influence of the velocity profile on fitting coefficients. At the same time, a set of  
Figure 16: Vibration frequency vs. pressure for straight-tube densitometer. standard density values of liquids under a wide range of temperatures and pressures will be assessed with the test device, because the standard density of the current test values at different pressures is only a theoretical calculation of the value;
* Through the experiment, the rationality and scientific value of the device were verified, and the change rule of vibration frequency with the temperature and pressure of online vibrating tube densitometers was studied, which has certain significance for the use of an online vibrating tube densitometer and its subsequent applications. Conceptualization, Y.S. and D.X. ; methodology, Y.S. ; validation, Y.S. and D.X. ; formal analysis, D.X. ; investigation, D.X. ; resources, D.X., W.C. and J.M.