IB Physics Extended Essay

Transcription

1 IB Physics Extended Essay Author: Remo Reuben Candidate number: Word count of essay: 3955 Word count of abstract: 270 The effects of working fluid dynamic viscosity on the efficiency of a hydroelectric reaction turbine Research Question: Approach: How does the dynamic viscosity of a working fluid affect the efficiency of a hydroelectric reaction turbine? A combination of an experimental and data-based approach is taken. Working fluids of different dynamic viscosities are used to create a potential difference across a resistor in series with the generator. This potential difference is used to calculate the electrical power generated. This will be compared to the maximum power that can theoretically be produced. The dynamic viscosities of the working fluids are obtained from secondary sources whose reliability is scrutinized. 0

2 Abstract The aim of this essay is to answer the question: How does the dynamic viscosity of a working fluid affect the efficiency of a hydroelectric reaction turbine? This research question was investigated by using a small hydroelectric generator with a reaction turbine. The working fluids used in this experiment were aqueous sucrose solutions. Their dynamic viscosities were varied by carefully altering their concentrations. The efficiency of the hydroelectric system could not be directly measured. Instead, the fluid s flow rate, and the potential difference across a resistor in series with the generator were measured experimentally. These values were used to calculate the reaction turbine s efficiency. The working fluid dynamic viscosity and hydroelectric efficiency were found to have an exponential decay power relationship. For the particular reaction turbine used in this experiment, the mathematical formula relating the working fluid dynamic viscosity and hydroelectric efficiency was:. This particular power function is judged to be linked to the intrinsic geometry of the reaction turbine used in this experiment. However, the exponential decay trend between the investigation s two variables is explained in this paper using Bernoulli s equation and Newton s third law. Overall, this investigation establishes that the relationship between the dynamic viscosity of a working fluid and the efficiency of a hydroelectric reaction turbine is an exponential decay power function. This conclusion can be beneficial in designing hydroelectric power systems where altering the working fluid s dynamic viscosity can be considered. It will probably be most economically viable and practical to apply in pumped storage systems where the volume of working fluid is relatively small compared to that of river and tidal hydroelectric systems. 1

3 Table of contents: 1. Scope of work Background information and literature Obtaining data for working fluid viscosities Making the hydroelectric generator Experimental variables Hypothesis Major equipment used Experimental procedure overview Constants, potential difference & temperature data collection Data analysis for η (dynamic viscosity) 5% absolute uncertainty Data analysis for working fluid density Data analysis for working fluid (flow rate) Data analysis for average (potential difference) Data analysis for (efficiency) Analysed data table and scatter plot Data table of averaged analysed values Averaged analysed values scatter plot and best-fit line Conclusion Evaluation Bibliography Appendix

4 Introduction Scope of work: The objective of this essay is to investigate the research question: How does the dynamic viscosity of a working fluid affect the efficiency of a hydroelectric reaction turbine? Hydroelectricity is one of the most widely used forms of producing renewable energy. Hydropower currently accounts for 6.3% of global energy production and its renewable aspect has made it the recipient of large amounts of investment 1. Therefore, any improvements in the efficiency of hydroelectric systems can be commercially as well as scientifically significant. Dynamic viscosity is one of the most important factors determining the rate of flow of a fluid. Investigating the effects of different working fluids dynamic viscosities on the efficiency of electrical power output could provide some valuable insights. While it may not be practically feasible to change the dynamic viscosity of the working fluid in very large hydroelectric systems because of the large volumes of fluid used, conclusions from this investigation into the effects of viscosity on power generated can be useful in smaller pumped storage systems. Background information and literature: Dynamic viscosity is a measure of a fluid s internal friction 2. The coefficient of viscosity (η), which is used as the independent variable in this experiment, is defined as the ratio between the shear stress and strain rate of a given fluid. Sheer stress is the force applied to deform the liquid while the strain rate is the rate at which it deforms. Therefore, if more shear stress is needed to deform a fluid, its dynamic viscosity will be relatively higher. In a hydroelectric power generation system, the theoretical power generated is given by the equation: power (W) density of working fluid (kgm -3 ) flow rate of working fluid (m 3 s -1 ) acceleration due to gravity ( ms -1 ) head, or change in height the working fluid undergoes (m) 1 U.S. Energy Information Administration 2 Giancoli, Douglas 2

5 scalar value for the efficiency of the system In this experiment, the hydroelectric generator will be set up as shown above in figure 1. The electrical power generated will be measured experimentally by recording the potential difference across a resistor in series with the generator. The potential difference and the resistance are used to calculate the electrical power output using the equation: potential difference (V) resistance (Ω) Therefore, the two equations for power in this experiment can be combined to provide a formula for efficiency: Hydroelectric efficiency equation Poiseuille s equation establishes the relationship between a fluid s viscosity and its flow rate within a pipe. Poiseuille s equation states that: flow rate of working fluid (m 3 s -1 ) 3

6 radius of pipe (m) pressure at h 1 (Pa) pressure at h 2 (Pa) dynamic viscosity of working fluid (Pas) length of pipe The working fluid will flow through the pipe of known radius as shown in figure 1. Poiseuille s equation can be used to explain trends in the efficiency of the hydroelectric generator related to changes in flow rate. The water turbine used in this experiment is a Francis turbine, which is a reaction turbine. Reaction turbines gain kinetic energy by reducing the working fluid s pressure 3. Because of Newton s Third Law, this loss of the working fluid s pressure while going through the turbine blades causes a reaction force on the blades, increasing their kinetic energy. Therefore, the power output of a hydroelectric system using a reaction turbine is proportional to the pressure differential across the turbine. To explain trends in the efficiency of the hydroelectric system when the working fluids viscosities are changed, the effects of working fluid dynamic viscosity on pressure differential across the turbine can be explored. Experimental setup and data collection description Obtaining data for working fluid viscosities: Due to a lack of access to viscometers, the values for the working fluid viscosities were obtained from secondary sources. The working fluids used in this experiment are aqueous sucrose solutions. The main advantage of using sucrose solutions is that their dynamic viscosities range from 3 to 60 times the viscosity of distilled water depending on the concentration of sucrose present. This is a wide range of values that will enable sufficient data to be collected and analysed. Additionally, the use of sucrose solutions does not pose any health and safety hazards. The source from which the following table of values was obtained is an online publication of the 16 th edition Kaye and Laby engineering textbook 4. The online publisher is National Physical Laboratory, the UK s national measurement standards laboratory. Therefore, the data obtained for the working fluid viscosities is very reliable. However, this data was also cross-referenced with other 3 Encyclopaedia Britannica 4 National Physical Laboratory 4

7 secondary sources 5,6 to make sure it is accurate. The data for the 55% aqueous sucrose solution was obtained from an online publication of ISCOTABLES, a reliable engineering textbook. Aqueous solution sucrose % (by mass) Table 1 Dynamic viscosity (Pas) Dynamic viscosity absolute uncertainty All of the above dynamic viscosity values are only relevant at 20 C (293K). Therefore, it is important to control the ambient temperature the experiment is carried out under. This is crucial since the dynamic viscosities of most fluids are very temperature dependant. The data displayed above will be reliable not just because of the secondary sources, but also because of the reliable methods through which viscosity is measured. Most laboratory viscometers function by timing the descent of a liquid in a tube of controlled radius, and multiplying it by a constant intrinsic of the viscometer. This makes use of Poiseuille s equation, and gives very accurate viscosity measurements. Making the hydroelectric generator: 5 The Korean Physical Society 6 Lane, Les 5

8 The hydroelectric generator was made from a mini vacuum cleaner. The Francis reaction turbine is contained within the grey casing shown in figure 2. As a vacuum cleaner, the DC motor would power the turbine, taking in air and debris. However as a generator, the working fluid enters through the inflow and spins the Francis turbine before exiting with a reduced pressure through the outflow. As the Francis turbine spins, the DC motor s rotor rotates, generating a DC current because of electromagnetic induction. The DC motor s terminals were soldered to crocodile clips for ease of connection to the voltage sensors that will be used in this experiment. Since Francis turbines function by reducing the working fluid s pressure, pressure should not be lost from within the generator. The generator s casing was therefore sealed with silicone sealant, and the generator inflow s connection with the pipe was secured with a hose clip. These measures ensured the hydroelectric generator is airtight for greatest efficiency. To check the precision of the generator s power output, a test run was undertaken with the working fluid source as a domestic water tap. The tap was turned on so that the flow rate was relatively constant, and potential difference readings across a 150Ω resistor in series with the generator were observed (as in figure 4, pg. 10). The potential difference observed was around 0.900V with fluctuations of only 0.002V. These fluctuations can be accounted for by the turbulent and irregular flow of the water from the tap. However, this extremely small level of fluctuation shows that the generator will enable the collection of precise and reliable data. Experimental variables: Independent variable: The dynamic viscosities of the working fluids. This is measured in Pas, and was obtained from secondary sources. The dynamic viscosities used in this experiment range from Pas to Pas. Dependent variable: The efficiency of the hydroelectric reaction turbine. This is the ratio of power experimentally generated to the maximum power it is theoretically possible to produce. It is a scalar quantity with no units. The efficiency is not measured directly, but is instead calculated by measuring the potential difference across a resistor in series with the generator. As explained in the introduction (pg. 3), this can be used to calculate the power experimentally produced, and the efficiency of the hydroelectric turbine. 6

9 Controlled Variables Temperature Average head Pipe length Pipe diameter Hydroelectric turbine Table 2 Dynamic viscosity is extremely temperature dependent. The temperature should be maintained at 20 C (293K) since the dynamic viscosity values obtained for the working fluids are only valid at this temperature. The height of the fluid will inevitably decrease as it empties from its storage container. Therefore, the average head of the liquid should be kept constant for all trials. The pipe length can be kept constant by using the same pipe for all experimental trials. The pipe diameter can be kept constant by using the same pipe for all trials. The same turbine should be used for all trials of this experiment since even small changes to its turbine blade angles can cause noticeable differences in electrical output. Hypothesis: The relationship between the dynamic viscosity of the working fluid and the efficiency of the hydroelectric reaction turbine will be linear with a slope of zero. That is, the efficiency should remain constant regardless of the dynamic viscosity of the working fluid. According to Poiseuille s equation, viscosity only affects the flow rate of the fluid. Therefore, if the working fluid has a high viscosity, the power generated should be low because the flow rate will be low too. Nevertheless, the efficiency should stay the same because the decrease in flow rate 7

10 is accounted for by the hydroelectric efficiency equation (pg. 3). This equation shows that the decrease in the potential difference (V) due to a higher fluid viscosity corresponds to a decrease in the flow rate (Q), keeping the efficiency constant. It is important to note that a higher viscosity does not result in higher frictional forces with the pipe. Viscosity only deals with a fluid s cohesion, or internal friction. Adhesion is the factor that causes external friction. However, the working fluids adhesion in this experiment will be controlled because all of the fluids are aqueous solutions. Therefore, it can be said that the efficiency will not vary with the dynamic viscosity. Major equipment used: Pipe Valve (to stop fluid flow between trials) Hydroelectric turbine and generator Vernier voltage sensor (Order Code DVP-BTA) Vernier temperature sensor (Order Code TMP-BTA) Experimental procedure overview: The range of viscosity values investigated in this experiment is Pas. Three trials were taken for each increment of viscosity. First, an aqueous 60% sucrose solution was made by adding 1.8kg sucrose to 1.2kg distilled H 2 O. It is a 60% sucrose solution because 1.8kg, or 60% of the total 3.0kg mass of the solution is constituted of sugar. To subsequently obtain the 55%, 50%, 40%, and 30% sucrose solutions needed in this experiment, new batches of solution were not made. Instead, after each trial, the sucrose solutions were diluted with distilled H 2 O to lower the concentration of sucrose present. After each sucrose solution was made, its density was measured as this is one of the variables that determine the amount of power a hydroelectric turbine generates. The mass ( ) of distilled H 2 O to be added to dilute the sucrose solutions to the required sucrose percentage can be given by the equation: Sample calculation: 8

11 50g of water should be added to the 55% sucrose solution described on the previous page to make it a 50% solution. Some random errors are probable while diluting the sucrose solutions. This is one of the limitations that will have to be taken into account in this experimental procedure. For example, a 66% sucrose solution has a dynamic viscosity of Pas while only a small change of concentration to 55% halves the viscosity to Pas. Therefore, any small errors here will make a dramatic change on the readings. However, small random errors made in preparing the solutions of lower concentrations will not have such significant effects. To account for this, a percentage uncertainty rather than a fixed uncertainty should be used for viscosity data. To collect data, the apparatus was set up as shown in figure 3 below. 9

12 The transparent container holding the working fluid at the top of the head will be referred to from now on as the reservoir vessel. A portion of the reservoir vessel which holds ± 0.8cm 3 was marked using a permanent marker on the vessel s outer wall. This is represented in orange in figure 3 above. For the rest of the experiment, the data analysed will be that of the fluid which originates from this 1dm 3 portion of the reservoir vessel. It is important to note that h 1 in this experiment is the average height from which the working fluid descends to reach the generator. That is, in this experiment it will be located halfway between the 1dm 3 markers on the reservoir vessel. The temperature probe records the fluid s temperature throughout the trials to make sure it is controlled at 20 C (293K) as much as possible. However, there will be some limitations here that need to be accounted for in uncertainty calculations since the temperature cannot be controlled perfectly with the equipment available. The valve is used to stop the working fluid flowing between trials. The valve s internal diameter is marginally smaller than that of the pipe. However, this is considered negligible in the calculations used in this report since the length of the valve is miniscule compared to that of the entire pipe. Data collection starts when the valve is opened, allowing the working fluid to flow towards the generator. This experiment is conducted with working fluids of six different viscosities. For each working fluid, three trials are taken to minimize random errors. The DC motor, now used as a generator will produce a DC current because of its commutator. The electrical power produced is calculated by first measuring the potential difference across a resister placed in series with the generator. This circuit along with the Vernier voltage sensor used is illustrated in figure 4: The voltage sensor measures and records two readings of potential difference per second and sends them to a linked computer. The voltage sensor s limit of reading is 0.001V. To identify which data sets record the potential difference produced by working fluid originally within the 10

13 reservoir vessel s 1dm 3 markings (because only this fluid has a controlled initial average height of h 1 as shown in figure 3), a video camera was used to capture the voltage-time data table displayed on the computer monitor as the sensor collected data. Sonic cues that could be picked up by the camera were given as the fluid crossed both the upper and lower 1dm 3 marks. Later, these sonic cues can be picked up on the video footage of the sensor data. This allows one to identify which data sets correspond to the average height (h 1 ) between the 1dm 3 markers. This will also enable the calculation of flow rate. The use of sonic cues to identify data sets is shown on pg. 15. This gives rise to another uncertainty that needs to be reflected in calculations and data collection. The sonic cues are given by the person conducting the experiment based on human judgement of the working fluid s menisci passing the 1dm 3 marks. Therefore, human reaction times and parallax errors can come into play here. Constants, potential difference & temperature data collection: Constants Resistor Resistance (±0.1Ω) Head (±0.02m) 1.79 Length of Pipe (±0.01m) 1.89 Radius of Pipe (±0.005m) Working fluid volume (±0.8cm 3 ) Resistor resistance has an uncertainty of ±0.1 Ω because this was the limit of reading of the digital voltmeter. Head has an uncertainty of ±0.02 m even though the measuring tape s limit of reading was 0.001m to account for parallax errors. Length of Pipe has an uncertainty of ±0.01 m even though the measuring tape s limit of reading was 0.001m to account for errors caused by the pipe s bending. Radius of pipe has an uncertainty of ±0.005 m because this was half the limit of reading of the ruler used. Working fluid volume has an uncertainty of ±0.8 cm 3 because this is the tolerance of the class B volumetric flask used. Table 3 11

14 Fluid dynamic viscosity (±5%Pas) Fluid sample mass (±1g) Fluid sample vol. (±0.3cm 3 ) Fluid dynamic viscosity uncertainties are ±5% to allow for random errors caused by fluctuations in the ambient temperature, and possible human errors while making the sucrose solutions. Fluid sample mass has an uncertainty of ±1g because this was the limit of reading of the digital weighing scale. Fluid sample volume has an uncertainty of ±0.3cm 3 because this was the limit of reading of the class B volumetric flask used to take the measurements. The following graphs show a sample of the potential difference and temperature data collected from the Vernier sensors. These graphs plot the data collected for trial 2 with working fluid dynamic viscosity = Pas: Table 4 The Logger Pro software used to generate the above graph uses larger point protectors for every sixth point. 12

15 Potential difference has an uncertainty of ±0.005V even though the digital sensor s limit of reading is smaller. This is because the sensor s readings continuously fluctuate by 0.005V. The uncertainty of ±0.005V accounts for these fluctuations. Reading s for Time have an uncertainty of ±0.5s because the digital sensor took 2 readings every second. This is therefore the limit of reading of time for this sensor. Temperature has an uncertainty of ±0.1 C because this is the digital temperature sensor s limit of reading Reading s for Time have an uncertainty of ±0.5s because the digital temperature sensor took 2 readings every second. This is therefore the limit of reading of time for this sensor. Data analysis and processing This section displays how the raw data collected was processed and analysed. Following are sample calculations for each variable. A data table of calculated values will be displayed after all the sample calculations. Data analysis for η (dynamic viscosity) 5% absolute uncertainty: The following calculation is shown for on pg. 12 (table 4). Pas. The raw data from secondary sources is Pas (1 significant figure) 13

16 To make the absolute uncertainty value s decimal places agree with that of the recorded value, the recorded value has to be rounded. Pas Data analysis for working fluid density: The following sample calculation is for 12). Pas. The raw data can be found in table 4 (pg. gcm -3 kgm -3 (3 significant figures) The absolute uncertainty is the relative uncertainty multiplied by the calculated value: (1 significant figure) kgm -3 Data analysis for working fluid (flow rate): Using the camera, the time-range where the cm 3 of working fluid whose average head = 1.79m flowed through the generator was identified (using sonic cues as explained in pg. 11). This time is then used to calculate as shown below for Pas trial 1: The time is found to range from 23.0 to 11.5s in this trial. cm 3 s -1 m 3 s -1 (3 significant figures) 14

17 cm 3 s -1 (1 significant figure) m 3 s -1 (6 decimal places to match with abs. unc.) Data analysis for average (potential difference): The mean potential difference within the time ranges (obtained from the camera data) is taken. A sample calculation from Pas trial 1 to demonstrate this analysis follows: As mentioned in the previous sample calculation, the time ranges from 23.0 to 11.5s in this trial. The yellow highlighted area of the scatter plot shows the data sets within the sonic cues where the working fluid s average height = h 1 as shown in figure 3 (pg. 9). This represents the appropriate time range where the mean potential difference is taken. V (3 decimal places) 15

18 Data analysis for (efficiency): The following sample calculation is for Pas trial 1. calculated mean potential difference (V) resistance of resistor in series with generator ( Ω) calculated density of working fluid (kgm -3 ) calculated flow rate of working fluid (m 3 s -1 ) acceleration due to gravity ( ms -2 ) average change in working fluid height ( m) (2 significant figures) (1 significant figure) 16

19 Trial Analysed data table and scatter plot: The following table of values displays the analysed data processed based on the sample calculations shown in this section. Fluid η (±5%Pas) Fluid η abs. unc. Fluid ρ (kgm -3 ) Fluid ρ abs. unc. (m 3 s -1 ) absolute Uncertainty Mean (±0.0 05V) Efficiency Effncy. absolute uncertainty Table 5 17

20 The following scatter plot displays the Fluid η and Efficiency data from table 5 above. The data sets in graph 3 show that the efficiency and dynamic viscosity do not have a linear relationship. The efficiency decreases as the dynamic viscosity increases. Therefore, the experimental data collected does not support my hypothesis. To further investigate this relationship, the average values of efficiency at each increment of fluid dynamic viscosity are taken. Sample calculations for average values can be found on pg

21 Data table of averaged analysed values: Avg. Fluid η (±5%Pas) Avg. Fluid η abs. unc. Average efficiency Avg. effncy. absolute uncertainty ln(η) ln(η) abs. unc. ln(efficiency) ln(eff.) abs. unc Table 6 Sample Calculations for natural log values and their uncertainties: The following sample calculation is for ln(η) when Pas. (4 significant figures) (1 significant figure) 19

22 Averaged analysed values scatter plot and best-fit line: Graph 4 displays the Avg. Fluid η and Avg. efficiency data from table 6. Vernier Logger Pro was used to generate an inverse function best-fit line. However, this is not an appropriate best-fit line because it does not go through most of the data sets error bars. Instead, a power function bestfit line is tried: 20

23 This power relationship best-fit line is appropriate for the data analysed displayed above since it goes through the error bars of most of the data sets. The calculations made to determine this bestfit line are demonstrated below: First, a natural log plot is made: Correlation: The best fit line for the natural log plot is next determined: (2 significant figures) (1 decimal place) This linear function is now used to obtain the power best-fit line for graph5: 21

24 Conclusion and Evaluation Conclusion: As the dynamic viscosity of a working fluid increases, the efficiency of the hydroelectric reaction turbine decreases. The two variables have a power relationship. Efficiency is proportional to dynamic viscosity raised to When the dynamic viscosity was Pas, the average efficiency was When the dynamic viscosity was increased to and Pas, the efficiency decreased to and respectively. These exemplar data sets display the power relationship dynamic viscosity and the efficiency of the hydroelectric reaction turbine. This correlation can also be determined from the best-fit line of graph 5 (Avg. dynamic viscosity vs. Avg. efficiency). The best fit line has a curved, exponential decay shape, and went through most of the data sets error bars. This function s equation was derived as. Therefore this equation conclusively demonstrates that efficiency and fluid dynamic viscosity in this experiment have a power relationship. The data collected does not support my original hypothesis since efficiency and dynamic viscosity do not have a linear relationship. The hypothesis was inaccurate because it only focused on the working fluid s flow through the pipe (using Poiseuille s equation) with the assumption that it would be the same as that through the reaction turbine. However, the reaction turbine had a lower efficiency for fluids of higher dynamic viscosities. This is because of the way a reaction turbine gains kinetic energy from the working fluids passed through it. The working fluid loses pressure as it is made to flow through a smaller space towards the centre of the reaction turbine s radial blades 7. According to Bernoulli s equation, fluid flowing through a smaller space will travel with a higher velocity and lose pressure 8. Because of Newton s Third Law, this loss of the working fluid s pressure while going through the turbine causes a reaction force on the blades, increasing 7 Encyclopaedia Britannica 8 Giancoli Image Source: Cink-Hydro-Energy 22

25 their kinetic energy 9. Therefore, the efficiency of a hydroelectric system using a reaction turbine is proportional to the pressure differential across the turbine. Viscosity can be understood as a measure of a fluid s internal friction, or cohesion. Fluids with higher viscosity will resist changes in pressure more because they have high internal frictional forces. Working fluids with higher viscosities cause lower efficiencies because they resist the changes in pressure within the turbine to a higher extent compared to less viscous fluids. Therefore, the pressure differential across a reaction turbine for more viscous fluids will be lower, thereby lowering efficiency. The efficiency of the hydroelectric system decreases as the dynamic viscosity of the working fluid increases. The efficiency of the hydroelectric system is proportional to. This particular function is observed as the relationship between the two variables because of the intrinsic geometry of the reaction turbine blades used in this experiment. Evaluation: The data collected in this experiment was precise. This can be said because the differences between the efficiency values calculated for each increment of viscosity were very small. This can be seen in graph 3 (pg. 18) where the data sets are closely clustered for each viscosity increment. The data obtained from the secondary sources and the data experimentally collected were reasonably accurate. This can be justified by the fact that the best fit line for graph 5 went through five out of the 6 data sets plotted. Additionally, the correlation coefficient for the linear best-fit line of graph 6 was a high There were no systematic errors in this experiment because the Vernier voltage sensor was frequently calibrated between trials. Systematic human errors could have been made while measuring constants like the head. However, these measurements were taken carefully with appropriate measurement uncertainties determined. Random errors relating to the dynamic viscosities of the working fluids could have caused the most significant inaccuracies in this experiment. However, the percentage uncertainty for dynamic viscosity was appropriate since it aptly compensated for any of these random errors (as explained on pg. 9). Some other minor human errors could have been caused when determining by sight when the working fluids crossed the 1dm 3 markings in the reservoir vessel. Yet, the three trials taken at each increment of dynamic viscosity significantly reduced the effects of any of these random errors. No anomalous data was collected in this experiment. 9 Tesla Turbines 23

26 To improve the experimental procedure, certain steps can be taken to improve the precision of the data collected. Instead of using a camera to record the data table of sensor values presented on the computer screen, a stop watch should be used to measure the time taken for 1dm 3 of working fluid to flow through the hydroelectric turbine. This is because the camera records time only to the limit of reading of the Vernier sensors, which was 0.5s. A stop watch will be more precise because it will have a limit of reading of at least 0.01s. Having more precise time readings will be beneficial because they are used to determine flow rate, which is a crucial variable in the hydroelectric efficiency expression. The range of viscosity increments in this experiment ( Pas) was appropriate for collecting data. The three data collection repetitions for each increment of viscosity helped reduce random errors. To further reduce the effects of any possible random errors in the viscosity data, two separate batches of sucrose solutions should be made. This will ensure that random errors caused by the incorrect dilution of the solutions will be minimised. It will be interesting to expand from this experiment to investigate the efficiency of different turbine blade geometries when working fluid viscosities are changed. Such an experiment could provide some useful conclusion as this experiment revolved around only one turbine. Bibliography: U.S. Energy Information Administration. "International Energy Annual 2006." International Energy Data and Analysis. U.S. Department of Energy, Dec Web. 04 Dec < Giancoli, Douglas. "Fluids." Physics Principles With Applications. 5th ed. Upper Saddle River: Prentice Hall, Print. "Turbine." Encyclopaedia Britannica. 15th ed Print. National Physical Laboratory. "Viscosities " Viscosities National Physical Laboratory, Web. 04 Dec < 24

27 Cha, Seoncheol, Sung Hyun Kim, and Doseok Kim. Viscosity of Sucrose Aqueous Solutions Measured by Using Fluorescence Correlation Spectroscopy. The Korean Physical Society. The Korean Physical Society, 4 Apr Web. 04 Dec < Lane, Les. "Table - Sucrose Solutions, Composition, Viscosity, Density." Les Lane's Home Page. Les Lane. Web. 04 Dec < "Francis Turbine." CINK Hydro-Energy K.s. CINK Hydro Energy, Web. 04 Dec < "Reaction Turbine Information." Tesla Turbine. Tesla Turbine, 02 Nov Web. 22 Jan < 25