**1. Introduction**

Fluid flow rate measurements are one of the most complex measurements that are carried out in engineering practice. These measurements, due to the need to maintain a very narrow uncertainty band, usually require the use of sophisticated, precise measuring equipment and the use of appropriate rigorous measurement procedures [1–3].

Liquid flow rate measurements in closed conduits or open channels of small size, for instance up to 1–2 m of diameter, are usually carried out using standard measuring devices such as measuring orifice plates, nozzles, Venturi tubes, measuring weirs, electromagnetic and ultrasound flow meters, calibrated bends, and others. Such devices are usually installed in properly prepared measuring sections of conduits or channels and provide a relatively easy and fairly accurate method of measuring the flow rate.

The situation is definitely more complicated when the liquid flow rate is to be measured in large-size conduits with a diameter of several meters or more. Measurements of the flow rate in this type of structure, usually used in hydropower, are very difficult and expensive, especially when it is necessary to ensure the lowest possible uncertainty of measurement results.

According to international standards [4–6], a few primary methods for flow rate measurement can be used in hydropower plants:


It can be concluded that the first four methods on the above list belong to the group of traditional methods, while the acoustic method is relatively new and has been recently the object of numerous research activities oriented on its improvement and validation [9,10]. This method has not yet reached proper acceptance among the specialists. Standard [4] suggests conditional use of this method, i.e., in case of mutual agreement between interested parties. Its basic advantage is that it can be used for continuous flow rate measurement and monitoring. Such a feature is impossible or extremely hard to achieve using other primary methods of measuring absolute flow rate.

The volumetric gauging method and tracer method are those which are less frequently used in hydropower engineering. The first method is characterized by a very limited application, mainly to hydropower plants with artificial reservoirs, especially in pumped-storage plants. The second one requires very long measuring segments of flow conduits and special conditions facilitating the mixing process of the injected markers (e.g., the use of turbulizers).

The velocity-area method and the pressure-time method are primary methods that are the most commonly used for measuring the flow rate in the pipelines of hydraulic turbines [3,11–13]. It is also worth noting that the velocity-area method using propeller current meters, very popular in the past, nowadays is being replaced by the pressure-time method in hydropower plants equipped with pipelines longer than 10–20 m. One of the main reasons for this is the much lower cost of preparing and performing flow measurements using the pressure-time method and the use of computer techniques in recent years, which facilitate measurements and give the possibility for getting higher accuracy of results obtained with this method.

For low and very low head power plants, particularly with short intakes of hydraulic turbines, (with no penstocks) the situation is different. Up to now, generally only the velocity-area methods, especially current meter method, are basically available in such kind of plants. Flow rate measurements with this method are still quite expensive and alternatives are being sought. One such alternative is the acoustic scintillation technique, under development [14,15].

Relative (index) methods are also used to measure the flow rate in hydropower plants. For example, the Winter–Kennedy method and the methods utilizing non-standardized pressure difference devices, non-standardized overflows (weirs), some simple variants of the acoustic method or local velocity measurement, which can be used for determining the relative value of the flow rate, or even the physical value, provided that calibration has been done on site by comparing with the results of measurements using the primary method [16–18].

As is the case concerning every measurement technique, obtaining the appropriate measurement precision is of the utmost importance. This is absolutely necessary wherever there are low uncertainty requirements, e.g., in the case of performance tests of hydraulic machines. The measurement conditions occurring in the flow systems of these machines require experience and knowledge about the flow phenomena prevailing in these systems, and also force the search for additional, unconventional techniques to ensure sufficiently low measuring uncertainty.

The bases of the analysis presented in the paper are measurement examples of flow rate through a high-head reversible hydraulic machine. Measurements were conducted using the volumetric gauging method and the pressure-time method, recommended (as mentioned earlier) by international standards [4–6] as the primary methods for discharge measurements used for performance tests (warranty, acceptance) of hydraulic turbines, pump turbines, and storage pumps. However, there are some restrictions on applicability as in the case of the pressure-time method, but work is continuously ongoing to expand and update these standards (A. Adamkowski, one of the authors of this work is a member of the PTC 18 Committee that is currently developing a revision to the ASME Performance Test Code PTC 18-2011 "Hydraulic Turbines and Pump Turbines").

The simultaneous application of the pressure-time method and the volumetric gauging method to measure discharge through the tested hydrounit with reversible Francis turbine opened the possibility of their peer verification, which was the main goal of the work.

As part of this task, the suitability of the pressure-time method for measuring flow rate in the pump mode of operation was tested. The use of this method in such conditions is not recommended by standards [4–6], therefore the obtained results are of particular importance for the development of this method.

The tests were performed ensuring a low level of measurement uncertainty. It required a number of procedures, some of which are innovative solutions, such as:


Moreover, in order to reliably estimate the measurement uncertainty of the applied methods, a procedure that takes into account general requirements concerning uncertainty assessment gathered in [19] has been proposed. This task is an attempt to systematize the problem of estimating measurement errors with the use of the analyzed methods.

Comparison concerning results obtained using chosen flow measurement methods, which is an example quite rarely seen in the literature concerning this subject, provides a unique source of knowledge about the features of the methods and the possibilities of their practical use.
