An Innovative Approach to Applying the Pressure-Time Method to Measure Flow

Flow measurement using the pressure-time (Gibson) method typically involves mounting instrumentation on the outside of the penstock. In the case of a plant where the penstock is embedded in concrete, an innovative approach that involved installing instrumentation inside the penstock provided results with an acceptable degree of accuracy.

By Adam T. Adamkowski, Janusz Kubiak Szyszka, Fernando Z. Sierra-Espinosa, Gustavo Urquiza Beltrán, Waldemar Janicki, and Jose Manuel Fernandez

Comision Federal de Electricidad (CFE) in Mexico owns 14 large hydroelectric facilities. These facilities contain 60 turbine-generator units ranging in size from 50 to 350 mw. Many of these units have operated for more than 20 years, and efficiency likely decreased due to normal wear (such as abrasion or cavitation-erosion). To assess the efficiency of its generating units and to determine any work needed, CFE decided in early 2004 to undertake a research project.

CFE contracted with the University of Morelos to perform this research. The program involved computing the efficiency of a total of 13 units based on in situ measurements. To establish the methodology for measuring unit efficiency, researchers performed evaluations on one 180-mw and one 160-mw Francis turbine. These and the other 11 units were chosen because they presented signs of low efficiency and possibly needed rehabilitation.

The research described in this article relates to the 180-mw Francis unit. Efficiency measurement was unique for this unit because the penstock is embedded in concrete. This meant that traditional use of the pressure-time (Gibson) method was not possible. Instead, researchers developed an innovative approach that involved installing flow measurement instrumentation inside the penstock. This method provided results with an acceptable degree of accuracy and revealed that efficiency of this unit had not dropped significantly.

Establishing the flow measurement method

The first step in measuring efficiency of this unit was choosing a method to measure discharge, based on the penstock configuration (see Figure 1 on page 44). One important consideration was the fact that this penstock is fully embedded in concrete, with no access to the penstock wall from outside. In addition, this penstock was 6.5 meters in diameter. This large diameter was a key factor in deciding which method to apply because the significant momentum of the water in this pipe could wash away any instrumentation.

Figure 1: To measure turbine efficiency, pressure transducers were mounted at locations 1, 2, and 3 on the penstock leading to this 180-mw Francis unit. Because the penstock is embedded in concrete, the transducers at location 1 had to be mounted on the inside, using a manhole for access.
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There are several methods to measure absolute water flow rate in hydro plants. These include the current meter, pressure-time (Gibson), tracer, and ultrasonic methods. The first three are traditional methods; the ultrasonic method is a newer one that is still being developed and tested. The ultrasonic method is being applied more frequently at hydro plants because it allows for continuous monitoring of the flow rate. However, the basic flow measurement methods used for efficiency tests of hydraulic machines are the current meter and Gibson methods. The current meter method has frequently been applied at hydro facilities. Another possibility for continuous measurement of the discharge is the non-absolute Winter-Kennedy method.

Pressure measurements taken outside the penstock at location 2 (see Figure 1 on page 44) were performed using a similar collector to that used in location 1, but external access allowed the collector to be placed on the outside of the penstock. The impulse pipes carried the pressure signals from the specially prepared static holes.
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After an analysis of the options, researchers decided to apply the Gibson method for this situation. The Gibson method has been used more recently in power plants with medium and high heads, primarily because of the lower costs of using this method. This lower cost is related to the development of computer techniques that make measurement easier, with a greater degree of accuracy.

The Gibson method uses the water hammer phenomenon (hydraulic transients) in a pipeline to determine the flow rate. In essence, the method involves measuring a variation in static pressure difference that occurs between two cross-sections of the pipeline as a result of a change in momentum over a certain period of time. This phenomenon is induced when water flow rate in the pipeline is time-controlled using a cut-off device (the wicket gates). The flow rate is determined by integrating, within the time interval, the measured change in pressure caused by the inertia effect.

Traditionally, the Gibson method requires that pressure transducers be installed outside the penstock. However, access to this penstock from outside location 1 is not possible (see Figure 1). To overcome this problem, researchers decided to install all needed instrumentation inside the penstock, using a manhole for access. To protect the transducer from the water stream for the time required to conduct the test (about two days), it was placed in a hermetic capsule designed by one of the authors.1 The capsule body was clamped to a steel base that was welded to the inner wall of the penstock floor and connected with a manifold that gathered the pressure from four holes (or taps) at location 1. The capsule also contains a vent valve to allow air to be purged from the impulse pipes and collector, which avoids effects on the pressure measurements caused by air compressibility. The cable connecting the transducers with the computer data acquisition system that took the readings was protected using steel pipe fastened to the interior wall of the penstock. This steel pipe, with the cable inside, came out through a small sealed hole, machined in the manhole for this purpose.

At location 1, pressure measurements were obtained through four 4-millimeter-diameter static holes in steel plates that were welded to the inner wall of the penstock. Four plates were placed 90 degrees apart around the circumference of the penstock (see Figure 2). These hydro-dynamically designed plates were 60 centimeters long by 6 centimeters wide by 1.4 centimeter thick. The extremes of the plates were rimmed and chamfered to avoid pressure fluctuations in the static holes associated with stream line perturbations due to possible boundary layer separation. The perturbations may influence the pressure measurements, especially for a large flow rate. The four plates and the collector, located in the penstock floor, were connected through flexible impulse pipes made of copper, 1 millimeter in thickness and 9.5 millimeters in diameter. The pipes receive the hydraulic impulses from stream pressure and transmit them through the manifold to the pressure transducer.2

Figure 2: Within the circumference of the penstock, the four manifolds with the pressure transducers installed were located 90 degrees apart. A nearby collector gathered data from the four transducers and transmitted it to the control room.
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The pressure measurements were taken at location 2, before the cutoff valve, and location 3, behind the cutoff valve (see Figure 1). These measurements, needed for the Gibson method and to determine the net head, respectively, were taken in the traditional manner, using instrumentation placed outside the penstock. The instrumentation consisted of a pressure collector with static holes drilled directly in the pipe wall.

For the Winter-Kennedy method, two additional pressure measuring points were prepared in steel plates similar to those used at location 1. These plates were placed in opposite locations of a cross-section of the spiral case, where the penstock ends and connects with the turbine. In this case, the pressure difference is due to the curved trajectory of the water flow in the spiral case. As part of the efficiency measurement project, CFE wanted a permanent method to conduct flow measurements, using an option such as the Winter-Kennedy method. Contrary to the Gibson method, the Winter-Kennedy method allows flow measurement permanently, but to be applicable it relies on previous flow measurements taken through an absolute method. In this respect, it depends on the Gibson or any other of the absolute methods mentioned above.

The Gibson method is based on Newton’s second law of motion, applied to the retarded mass of the liquid in the pipe as flow is interrupted (water hammer) during a short time period.3 The inertia forces are represented by a rise (peak) in the pressure difference between locations 1 and 2 (see Figure 1 on page 44). This pressure difference allows for calculation of the flow rate through its time integration over the period when the wicket gates cut off the water flow, using the following equation.

Equation 1:

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  • Q0 is the flow rate;
  • r is the density of fluid;
  • C is a geometric factor that considers any change in penstock cross section between locations 1 and 2;
  • tk is the instant at which the wicket gate has closed completely;
  • t0 is the instant at which the wicket gate starts to close;
  • Dp(t) is the static pressure difference between locations 1 and 2;
  • Dpd(t) represents the dynamic pressure difference between locations 1 and 2;
  • Dpf (t) is the friction losses along the penstock between locations 1 and 2; and
  • Q1 accounts for leakage through the turbine guide vanes of the wicket gate in the closed position.

Using the Winter—Kennedy method, a close relationship between the static pressure difference measured in the spiral case and the flow rate applies.

Equation 2:

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  • Q is the flow rate;
  • k is a constant that must be experimentally determined (using the Gibson method in this case);2
  • Dpwk is the static pressure difference; and
  • n has a theoretical value of 0.5 and must be determined experimentally.

The flow rate obtained from the Gibson method can be used to determine the values of k and n.

Performing the measurements

To perform the tests, instrumentation was prepared to measure the headwater and tailwater levels, active power of the generator, wicket gate opening, absolute pressure in location 1 and relative pressure in location 2 (for the Gibson method), relative pressure at location 3 (to calculate the net head), and the pressure difference between the two points in the spiral case (for the Winter-Kennedy method). Each pressure transducer converted the pressure impulses into an analogical signal, which traveled to the control room.

Once the instruments were installed, the leakage test started. For this purpose, the gate at the tailwater and the cutoff (butterfly) turbine valve were opened, but the turbine wicket gate and the headgate were kept fully closed. Using a bypass valve at the dam, personnel began filling the penstock with water, until the water level reached location 1. Personnel then closed the bypass valve and began recording pressure in location 3 and tailwater level. The water level in the penstock began to decrease because of leakage through the gaps of the wicket gate. This test lasted one night, with a period of six to seven hours before the tests began for the Gibson method.

The Gibson test begins and ends with the turbine running at maximum power. The intervals between these extremes decreases as maximum power is reached because the maximum efficiency of hydro turbines nearly corresponds with the maximum power generated. Thirteen tests were conducted in about four hours. Each test lasted just a few minutes, including: at least four minutes to adjust turbine conditions and stabilize flow, about two minutes for measurement during steady-state conditions of turbine operation, about two minutes for pressure to rise due to closing of the wicket gate, and a run of stabilized pressure required by the Gibson method. The staff at the national electric grid control office were aware of and authorized the tests, because of the power fluctuation they would cause in the grid.

After the tests, there was no opportunity to dewater the penstock and remove the measuring instrumentation because of the cost resulting from lost generation. The pressure signal from location 1 may last for a few days. Typically, the capsules containing the instrumentation is lost within a year, destroyed by the water stream.


The flow rate was calculated for 13 pressure measurements associated with specific turbine loads. As mentioned before, the turbine was connected to the grid during the measurements, even when eliciting water hammer (when no electricity was generated). Figure 3 shows a pressure difference plot between locations 1 and 2 during this period. A peak pressure difference of about 200 kilopascals (kPa) is detected during wicket gate closure, which lasted about six seconds for the higher load tested (maximum discharge). The pressure difference then drops to about zero kPa and oscillates with small amplitude before stabilizing in ten more seconds. Special filters included in the signal analyzer produced recordings with very clean signals. A computer program called GIBSON-ADAM was used to process the signal information.4 Using this program, the friction losses and dynamic pressures are taken into account as quadratic functions of flow rate.

Figure 3: These results from one test using the Gibson method show that a rise in pressure difference between locations 1 and 2 of about 200 kilopascals (kPa) was detected during wicket gate closure (to elicit a water hammer effect) and lasted about six seconds. The pressure then dropped back to about 1,200 kPa, indicating the momentum wave subsided.
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The leakage through the wicket gate was calculated at 0.86 cms, which represents 0.45 percent of the water flow rate for an output of 180 mw.

Once the flow rate was obtained, researchers used conventional formulae to compute efficiency of the turbine and the turbine-generator unit. The measurements taken for various turbine loads also served to identify the flow rate that would result in higher efficiency. The flow rate was plotted against the power, which was measured using the electrical generator output during each test. The range of power tested included conditions that exceeded the nominal output of the unit. A quasi-linear relationship with water flow rate was obtained, against which researchers plotted the resulting efficiency for 105 meters of head. A maximum efficiency of 91.5 percent (see Figure 4) corresponds to a flow rate of 191 cms, computed in the mode that also accounts for the electric generator performance. Computed based on mechanical efficiency alone, an efficiency of 93.8 percent (see Figure 5) corresponds with turbine power of 182 mw and the same flow rate.

Figure 4: For this 180-mw unit, peak efficiency was calculated at 91.5 percent (in the mode accounting for performance of the generator). This corresponds to a flow rate of 191 cubic meters per second and capacity of about 182 mw.
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Figure 5: Measuring only mechanical efficiency, peak efficiency of this 180-mw turbine was 93.8 percent at a flow rate of 191 cubic meters per second and capacity of about 182 mw.
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The uncertainty for these efficiency computations was about ±1.6 percent. As mentioned above, the flow rate results obtained with the Gibson were used to compute the values of constants k and n in Equation 2, in order to determine the flow rate by means of the Winter-Kennedy method.

Visual inspection performed during installation of the instrumentation confirmed the good condition of the turbine runner.7

Lessons learned

The Gibson method has been successfully applied to determine the flow rate at different loads in a turbine. To apply this method, the most important parts of the instrumentation are not commercially available. For instance, the plates for static pressure detection were built at the plant. Also, the manifold with tight housing for the pressure transducer was specially designed and produced.

A maximum hydraulic turbine efficiency of 93.8 percent was obtained for 105 meters of head and 187 cms flow rate. After 20 years of operation, the unit’s efficiency is considered to still be high compared to the design value of 95 percent. The difference is less than 1.6 percent, which is within the range of uncertainty of the method. This result suggests that no modification of the operating conditions or any main part of the hydraulic turbine is necessary.

Experiences of researchers applying the Gibson method to the other 12 units included in the project have demonstrated the potential of the method. There have been some variants in these units. For example, in cases where the penstock is not a straight pipeline, special attention is required because computation of constant C in Equation 1 is affected by bends, contractions, expansions, or Y-shaped bifurcations. The case of Y-shaped bifurcations was studied to try to define the effects of flow phenomena induced in the region where the flow bifurcates, such as boundary layer separation.5 This topic still requires more investigation of the velocity profile and subsequent quantification of the accuracy of results because the flow separation is a local phenomenon with unique characteristics for each specific case.6

What is left as a result of this work is a complete Winter-Kennedy system, which is ready to be used to measure the water flow rate permanently. s

Drs. Adamkowski and Janicki may be reached at Institute of Fluid Flow Machinery, Polish Academy of Sciences, Fiszera 14, Gdansk, Pomorskie, PL-80952 Poland; (48) 58-3411271; E-mail: or wjanicki@ Drs. Kubiak, Sierra, and Urquiza may be reached at University of Morelos, Ave. Universidad 1001, Col. Chamilpa, Cuernavaca, Morelos 62210 Mexico; (52) 777-3297000 (Kubiak), (52) 777-3297084 (Sierra), or (52) 777-3297084 (Urquiza); E-mail:,, or Mr. Fernandez may be reached at Comision Federal de Electricidad, Don Manuelito No. 11, Col. Olivar de los Padres, D.F. 01780 Mexico; (52) 55-54904063; E-mail:


1 Adamkowski, A., Flow Measurement in Closed Pipes Using the Gibson Method. Theoretical and Analytical Approach, Technical Report, Institute for Fluid Machinery, Polish Academy of Sciences, Gdansk, Poland, 1996 (in Polish).

2 Guide for Field Measurement of Vibrations and Pulsations in Hydraulic Machines (Turbines, Storage Pumps and Pump-Turbines), IEC Publication 60994, International Electrotechnical Commission, 1991.

3 Gibson, N.R., “The Gibson Method and Apparatus for Measuring the Flow of Water in Closed Conduits, Proceedings of the American Society of Mechanical Engineers, American Society of Mechanical Engineers Power Division, 1923, pages 343-392.

4 Adamkowski, Adam, and L. Kwapisz, “Determination of the Integral Range for the Gibson Method,” Proceedings of the International Conference Hydroforum 2000, Instytut Maszyn Przeplywowych PAN, Gdansk, Poland, 2000, pages 287-298.

5 Sierra, Fernando Z., et al, “Boundary Layer Separation in Large Diameter Pipe Bifurcations and Its Influence in Flow Rate Measurement Using Gibson Method,” Ingeniería Hidráulica en México, Accepted for publication, 2008 (in Spanish).

6 Sierra-Espinosa, Fernando Z., C.J. Bates, and T. O’Doherty, “Turbulent Flow in a 90-degree Pipe Junction: Part 2. Reverse Flow at the Branch Exit,” Computers & Fluids, Volume 29, 2000, pages 215-233.

7 Adamkowski, Adam, B. Gustavo Urquiza, Waldemar Janicki, and Janusz Kubiak, Flow Measurement Results and Efficiency Computation of Unit 5 in Hydropower Station La Angostura, report No. 66P/DM/CIICAp, November 2004 (in Spanish).

Adam Adamkowski, PhD, is researcher and associate professor with the Institute of Fluid Flow Machinery at the Polish Academy of Sciences. Janusz Kubiak, PhD, Fernando Sierra, PhD, and Gustavo Urquiza, PhD, are researchers and professors at the University of Morelos in Mexico. Waldemar Janicki, PhD, is a research assistant with the Institute of Fluid Flow Machinery. Jose Fernandez is manager of hydroelectricity with Comision Federal de Electricidad in Mexico.

This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.


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