INTERAMERICAN UNIVERSITY OF BAYAMON PUERTO RICO Hydroelectric Design Dr. Eduardo G. Pérez Díaz Erik T. Rosado González 5/14/2012 Hydroelectric design project for fluid class.
TABLE OF CONTENTS TABLE OF CONTENTS... 1 TABLE OF FIGURE... 2 TABLE OF DATA... 2 ABSTRACT... 3 OBJECTIVE AND INTRODUCTION... 4 Objective... 4 Introduction... 4 THEORY... 5 Hydroelectricity... 5 Mass flow... 6 Reynolds number... 6 EQUIPMENT DESCRIPTION AND ESPECIFICATION... 11 Description... 11 Specifications... 12 RESULTS... 13 DISCUSSION... 13 CONCLUSION... 14 Bibliography... 15 APPENDIX... 16 Appendix A-1 Hydroelectricity... 16 Appendix A-2 Reynolds number (Re)... 16 Appendix B-1 Design Data... 17 Appendix C-1 (Triangle Solver)... 20 Fluid Hydroelectric Design Page 1
TABLE OF FIGURE Figure 1 Hydroelectricity... 5 Figure 2 Moody Diagram... 8 Figure 3 Generator and Turbine... 11 Figure 4 Triangle Solver (Microsoft Mathematics)... 20 TABLE OF DATA Table 1 Design Specifications for 11MW Hydro Turbine... 12 Table 2 Results for H 50m... 13 Table 3 Design Results for 18 MW Hydroelectric... 17 Fluid Hydroelectric Design Page 2
ABSTRACT This report deals with the design of a hydroelectric plant with a net capacity of 18MW. In the design we took into account losses by height, turbines, inlets and pipes, according to their material. We also calculated the distance and height of the pipes using Excel "software", (for more information check appendix B-1). Moreover, calculating the flow rate and pipe diameter we found several models that meet the desired design and produce the 18 MW of net power using 2 turbines of 11MW each with an efficiency of 85%. Fluid Hydroelectric Design Page 3
OBJECTIVE AND INTRODUCTION Objective The objective of this design (Hydroelectricity, for more information check appendix A-1) is to create several models that meet the requirements set and choose the best model considering the design, cost and maintenance. Moreover, to use the theory and equations available for the design of a hydroelectric. Introduction This design requires a turbine capable of producing 18 MW with an efficiency of85%. The method used to produce this energy is the force of falling water (potential energy). For this design we must consider the following factors: pipes, heights, velocity, density, pipe diameter, materials and losses, among other factors, for this design. Fluid Hydroelectric Design Page 4
THEORY Figure 1 Hydroelectricity [1] Hydroelectricity is the term referring to electricity generated by hydropower; the production of electrical power through the use of the gravitational force of falling or flowing water. It is the most widely used form of renewable energy, accounting for 16 percent of global electricity consumption, and 3,427 terawatt-hours of electricity production in 2010, which continues the rapid rate of increase experienced between 2003 and 2009, for more information check appendix A-1. [1] In physics and engineering, in particular fluid dynamics and hydrometry, the Volumetric Flow Rate, (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes through a given surface per unit time. The SI unit is m3 s-1 (cubic meters per second). In US Customary Units and British Imperial Units, volumetric flow rate is often expressed as ft3/s (cubic feet per second). It is usually represented by the symbol Q. [2] Volumetric flow rate should not be confused with volumetric flux, as defined by Darcy's law and represented by the symbol q, with units of m3/(m2 s), that is, m s-1. The integration of a flux over an area gives the volumetric flow rate. [2] Fundamentally, the volume flow rate is defined as: Where: Q = volumetric flow rate, ΔV = change in volume flowing through the area, Δt = time interval of volumetric flow. Equation 1 Fluid Hydroelectric Design Page 5
Volumetric flow rate can also be defined by: Where: v = velocity field of the substance elements flowing, A = cross-sectional vector area/surface. Mass flow, also known as mass transfer and bulk flow, is the movement of material matter. In physics, mass flow occurs in open systems and is often measured as occurring when moving across a certain boundary characterized by its cross-sectional area and a flow rate. In engineering and biology it may also be a flow of fluids in a tube or vessel of a certain diameter. A bulk transfer of particles of matter in a characterised type of flow is also known as bulk flow. [2] Where: = density, V = velocity, A = area, Q = volume flow. Equation 2 Reynolds number (for more information about Reynolds number check appendix A-2) can be defined for a number of different situations where a fluid is in relative motion to a surface. These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension. This dimension is a matter of convention for example a radius or diameter is equally valid for spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such non-newtonian fluids, special rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels. [3] Equation 3 Fluid Hydroelectric Design Page 6
Where: v = is the mean velocity of the object relative to the fluid (SI units: m/s) L = is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter when dealing with river systems) (m) µ= is the dynamic viscosity of the fluid (Pa s or N s/m² or kg/(m s)) = is the kinematic viscosity ({\bold \nu} = \mu /{\rho}) (m²/s) ρ = is the density of the fluid (kg/m³) Flow in pipe For flow in a pipe or tube, the Reynolds number is generally defined as: Equation 4 Pipe friction Where: = is the hydraulic diameter of the pipe; its characteristic travelled length, {L}, (m). Q = is the volumetric flow rate (m3/s). A = is the pipe cross-sectional area (m²). is the mean velocity of the object relative to the fluid (SI units: m/s). µ = is the dynamic viscosity of the fluid (Pa s or N s/m² or kg/(m s)). υ = is the kinematic viscosity (m²/s). ρ = is the density of the fluid (kg/m³). Pressure drops seen for fully developed flow of fluids through pipes can be predicted using the Moody diagram (figure 2) which plots the Darcy Weisbach friction factor against Reynolds number and relative roughness. The diagram clearly shows the laminar, transition, and turbulent flow regimes as Reynolds number increases. The nature of pipe flow is strongly dependent on whether the flow is laminar or turbulent. Fluid Hydroelectric Design Page 7
Figure 2 Moody Diagram Incompressible flow equation In most flows of liquids, and of gases at low Mach number, the mass density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. For this reason the fluid in such flows can be considered to be incompressible and these flows can be described as incompressible flow. Bernoulli performed his experiments on liquids and his equation in its original form is valid only for incompressible flow. A common form of Bernoulli's equation, valid at any arbitrary point along a streamline where gravity is constant, is: Equation 5 Where: is the fluid flow speed at a point on a streamline, is the acceleration due to gravity, is the elevation of the point above a reference plane, with the positive z-direction pointing upward so in the direction opposite to the gravitational acceleration, is the pressure at the chosen point, and is the density of the fluid at all points in the fluid. Fluid Hydroelectric Design Page 8
For conservative force fields, Bernoulli's equation can be generalized as: Equation 6 where Ψ is the force potential at the point considered on the streamline. E.g. for the Earth's gravity Ψ = gz. The following two assumptions must be met for this Bernoulli equation to apply: the flow must be incompressible even though pressure varies, the density must remain constant along a streamline; friction by viscous forces has to be negligible. By multiplying with the fluid density \rho, equation (5) can be rewritten as: or: Equation 7 Where: is dynamic pressure, Equation 8 is the piezometric head or hydraulic head (the sum of the elevation z and the pressure head) and is the total pressure (the sum of the static pressure p and dynamic pressure q). The constant in the Bernoulli equation can be normalised. A common approach is in terms of total head or energy head H:, Equation 9 Fluid Hydroelectric Design Page 9
The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached. In liquids when the pressure becomes too low cavitation occurs. The above equations use a linear relationship between flow speed squared and pressure. At higher flow speeds in gases, or for sound waves in liquid, the changes in mass density become significant so that the assumption of constant density is invalid. Fluid Hydroelectric Design Page 10
EQUIPMENT DESCRIPTION AND ESPECIFICATION Description Conventional (dams) Figure 3 Generator and Turbine Most hydroelectric power comes from the potential energy of dammed water driving a water turbine and generator. The power extracted from the water depends on the volume and on the difference in height between the source and the water's outflow. This height difference is called the head. The amount of potential energy in water is proportional to the head. A large pipe (the "penstock") delivers water to the turbine. Pumped-storage This method produces electricity to supply high peak demands by moving water between reservoirs at different elevations. At times of low electrical demand, excess generation capacity is used to pump water into the higher reservoir. When there is higher demand, water is released back into the lower reservoir through a turbine. Pumped-storage schemes currently provide the most commercially important means of large-scale grid energy storage and improve the daily capacity factor of the generation system. Fluid Hydroelectric Design Page 11
Specifications Table 1 Design Specifications for 11MW Hydro Turbine Constant Values Loss on Pipe Pipe Dimensions (m) Pipe Dimension (ft) Units Convertions Codo Dimensions Density (ρ) 1000 K (in) 0.04 Z (actual) 370.096203 H(ft) 330 ft 1 Z (elbow) 36.92014 Viscosity (µ) 1.00E-03 K (elbow) 0 X (actual) 365.76 L(ft) 1200 m 0.3048 X (elbow) 36.576 ɛ 4.50E-05 Y (actual) 100.584 Y (elbow) 5.0292 Gravity (g) 9.81 Z (ideal) 369.2013852 Radio 50 Power (KW) 11000 X (ideal) 365.76 C 36.92014 % (elbow) 10% Y (ideal) 50.292 α 0.756299 Nth 85.00% Z (right) 332.2812467 S 37.81496 Wa (KW) 18000 X (right) 329.184 We (KW) 21176.4706 Y (right) 45.2628 per unit 10588.2353 Y (design) 50.292 unit (aprox) 11000 Fluid Hydroelectric Design Page 12
RESULTS Table 2 Results for H 50m Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.025 0.14 0.000321 1.62403 227364.2 0.017695461 6.288363 0.00537711 44.85219 51.28036 0.025 0.15 0.0003 1.414711 212206.6 0.017690979 4.452577 0.00408034 44.85219 49.41086 0.03 0.13 0.000346 2.260189 293824.5 0.017423666 12.9152 0.01041479 37.37683 50.56281 0.03 0.135 0.000333 2.095868 282942.1 0.017397449 10.67813 0.00895548 37.37683 48.2878 0.035 0.125 0.00036 2.852057 356507.1 0.017240875 21.16319 0.01658354 32.03728 53.63164 0.035 0.13 0.000346 2.636887 342795.3 0.017199112 17.35247 0.01417568 32.03728 49.75831 0.04 0.13 0.000346 3.013585 391766 0.017022397 22.43158 0.01851517 28.03262 50.94559 0.04 0.135 0.000333 2.79449 377256.2 0.016979919 18.52775 0.01592085 28.03262 46.97431 0.045 0.13 0.000346 3.390283 440736.8 0.016879353 28.1514 0.02343327 24.91788 53.67854 0.045 0.135 0.000333 3.143801 424413.2 0.016830764 23.2432 0.02014982 24.91788 48.68498 0.05 0.135 0.000333 3.493113 471570.2 0.016707194 28.48463 0.02487632 22.4261 51.55751 0.05 0.14 0.000321 3.24806 454728.4 0.016659657 23.68109 0.02150845 22.4261 46.66641 0.055 0.139 0.000324 3.624459 503799.8 0.016560948 29.52381 0.02678227 20.38736 50.60751 0.055 0.14 0.000321 3.572866 500201.2 0.016551032 28.46729 0.02602522 20.38736 49.53131 0.06 0.142 0.000317 3.788652 537988.5 0.016437328 31.34208 0.02926377 18.68841 50.79136 0.06 0.143 0.000315 3.735849 534226.4 0.016427324 30.24301 0.02845375 18.68841 49.67122 0.065 0.145 0.00031 3.936293 570762.6 0.016323959 32.90395 0.031589 17.25084 50.97611 0.065 0.15 0.0003 3.678248 551737.1 0.01627587 27.69176 0.02758309 17.25084 45.65976 0.07 0.145 0.00031 4.239085 614667.4 0.016250333 37.98868 0.03663577 16.01864 54.95985 0.07 0.15 0.0003 3.96119 594178.5 0.016199262 31.96472 0.03198985 16.01864 48.81509 Note: For more information about design data table, check appendix B-1. DISCUSSION In the design of a hydroelectric plant that produces 18 MW of power with an efficiency of 85% in the turbine and with a maximum drop of 50 292 (m) we find the following: 1. If we increase the flow rate (Q), diameter (D) and velocity (V) also increase. 2. If we increase the diameter and maintain a constant flow, losses are reduced significantly. 3. If we increase the diameter and maintain a constant flow, velocity decreases considerably. As part of the design, we designed in the pipe a straight tube of 332.2812467 (m) long and an elbow with a length of 36.92014 (m), and a radius of 50 (m), for a total of 370.096203 (m) long. With this data we can calculate the friction losses in the tube, taking into account the entire stretch. Fluid Hydroelectric Design Page 13
CONCLUSION In my design of a hydroelectric plant that produces an output of 18 MW with an efficiency of 85% in the turbine and with a flow rate from.025 to.07, velocity of 1.62403 m/s to 3.96119 m/s were found several designs to choose from. It is recommended to choose a design medium in speed since having a very high velocity causes erosion in the material. These particles could damage the turbine increasing maintenance cost and shortening the lifetime of the materials and equipment used. It is also recommended to use the materials (turbines, tubes) that can meet the parameters used in this design; otherwise it will not meet its primary objective to create 18MW of power. Fluid Hydroelectric Design Page 14
Bibliography [1] W. contributors, "Hydroelectricity," 2012. [Online]. Available: http://en.wikipedia.org/w/index.php?title=hydroelectricity&oldid=490319594. [Accessed 2012]. [2] V. f. rate, "Wikipedia contributors," 2012. [Online]. Available: http://en.wikipedia.org/w/index.php?title=volumetric_flow_rate&oldid=488916750. [Accessed 2012]. [3] W. contributors, "Reynolds number," 2012. [Online]. Available: http://en.wikipedia.org/w/index.php?title=reynolds_number&oldid=489815209. [Accessed 2012]. Fluid Hydroelectric Design Page 15
APPENDIX Appendix A-1 Hydroelectricity Hydroelectricity is the term referring to electricity generated by hydropower; the production of electrical power through the use of the gravitational force of falling or flowing water. It is the most widely used form of renewable energy, accounting for 16 percent of global electricity consumption, and 3,427 terawatt-hours of electricity production in 2010, which continues the rapid rate of increase experienced between 2003 and 2009. [1] Hydropower is produced in 150 countries, with the Asia-Pacific region generating 32 percent of global hydropower in 2010. China is the largest hydroelectricity producer, with 721 terawatthours of production in 2010, representing around 17 percent of domestic electricity use. There are now three hydroelectricity plants larger than 10 GW: the Three Gorges Dam in China, Itaipu Dam in Brazil, and Guri Dam in Venezuela. [1] The cost of hydroelectricity is relatively low, making it a competitive source of renewable electricity. The average cost of electricity from a hydro plant larger than 10 megawatts is 3 to 5 U.S. cents per kilowatt-hour. Hydro is also a flexible source of electricity since plants can be ramped up and down very quickly to adapt to changing energy demands. However, damming interrupts the flow of rivers and can harm local ecosystems, and building large dams and reservoirs often involves displacing people and wildlife. Once a hydroelectric complex is constructed, the project produces no direct waste, and has a considerably lower output level of the greenhouse gas carbon dioxide (CO2) than fossil fuel powered energy plants. [1] Appendix A-2 Reynolds number (Re) In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. [3] The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number is named after Osborne Reynolds (1842 1912), who popularized its use in 1883. [3] Reynolds numbers frequently arise when performing dimensional analysis of fluid dynamics problems, and as such can be used to determine dynamic similitude between different experimental cases. [3] They are also used to characterize different flow regimes, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion; turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities. [3] Fluid Hydroelectric Design Page 16
Appendix B-1 Design Data Table 3 Design Results for 18 MW Hydroelectric Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.025 0.100 4.50E-04 3.183 3.18E+05 1.80E-02 34.343 0.021 44.852 79.732 0.025 0.110 4.09E-04 2.631 2.89E+05 1.78E-02 21.182 0.014 44.852 66.401 0.025 0.120 3.75E-04 2.210 2.65E+05 1.78E-02 13.648 0.010 44.852 58.759 0.025 0.130 3.46E-04 1.883 2.45E+05 1.77E-02 9.121 0.007 44.852 54.162 0.025 0.140 3.21E-04 1.624 2.27E+05 1.77E-02 6.288 0.005 44.852 51.280 0.025 0.150 3.00E-04 1.415 2.12E+05 1.77E-02 4.453 0.004 44.852 49.411 0.025 0.160 2.81E-04 1.243 1.99E+05 1.77E-02 3.227 0.003 44.852 48.161 0.025 0.170 2.65E-04 1.101 1.87E+05 1.77E-02 2.386 0.002 44.852 47.303 0.025 0.180 2.50E-04 0.982 1.77E+05 1.78E-02 1.797 0.002 44.852 46.700 0.025 0.190 2.37E-04 0.882 1.68E+05 1.78E-02 1.374 0.002 44.852 46.268 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.030 0.100 4.50E-04 3.820 3.82E+05 1.77E-02 48.839 0.030 37.377 86.989 0.030 0.115 3.91E-04 2.888 3.32E+05 1.75E-02 24.006 0.017 37.377 61.825 0.030 0.120 3.75E-04 2.653 3.18E+05 1.75E-02 19.351 0.014 37.377 57.101 0.030 0.125 3.60E-04 2.445 3.06E+05 1.75E-02 15.743 0.012 37.377 53.436 0.030 0.130 3.46E-04 2.260 2.94E+05 1.74E-02 12.915 0.010 37.377 50.563 0.030 0.135 3.33E-04 2.096 2.83E+05 1.74E-02 10.678 0.009 37.377 48.288 0.030 0.140 3.21E-04 1.949 2.73E+05 1.74E-02 8.892 0.008 37.377 46.470 0.030 0.145 3.10E-04 1.817 2.63E+05 1.74E-02 7.455 0.007 37.377 45.007 0.030 0.150 3.00E-04 1.698 2.55E+05 1.74E-02 6.289 0.006 37.377 43.818 0.030 0.155 2.90E-04 1.590 2.46E+05 1.73E-02 5.336 0.005 37.377 42.847 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.035 0.110 4.09E-04 3.683 4.05E+05 1.74E-02 40.504 0.028 32.037 73.260 0.035 0.115 3.91E-04 3.370 3.88E+05 1.73E-02 32.308 0.023 32.037 64.947 0.035 0.120 3.75E-04 3.095 3.71E+05 1.73E-02 26.029 0.020 32.037 58.574 0.035 0.125 3.60E-04 2.852 3.57E+05 1.72E-02 21.163 0.017 32.037 53.632 0.035 0.130 3.46E-04 2.637 3.43E+05 1.72E-02 17.352 0.014 32.037 49.758 0.035 0.135 3.33E-04 2.445 3.30E+05 1.72E-02 14.339 0.012 32.037 46.693 0.035 0.140 3.21E-04 2.274 3.18E+05 1.71E-02 11.935 0.011 32.037 44.246 0.035 0.145 3.10E-04 2.120 3.07E+05 1.71E-02 10.000 0.009 32.037 42.276 0.035 0.150 3.00E-04 1.981 2.97E+05 1.71E-02 8.432 0.008 32.037 40.677 0.035 0.155 2.90E-04 1.855 2.88E+05 1.71E-02 7.151 0.007 32.037 39.370 Fluid Hydroelectric Design Page 17
Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.040 0.100 4.50E-04 5.093 5.09E+05 1.74E-02 85.366 0.053 28.033 114.773 0.040 0.105 4.29E-04 4.619 4.85E+05 1.74E-02 66.519 0.044 28.033 95.683 0.040 0.110 4.09E-04 4.209 4.63E+05 1.73E-02 52.458 0.036 28.033 81.430 0.040 0.115 3.91E-04 3.851 4.43E+05 1.72E-02 41.824 0.030 28.033 70.642 0.040 0.120 3.75E-04 3.537 4.24E+05 1.71E-02 33.679 0.026 28.033 62.375 0.040 0.125 3.60E-04 3.259 4.07E+05 1.71E-02 27.370 0.022 28.033 55.966 0.040 0.130 3.46E-04 3.014 3.92E+05 1.70E-02 22.432 0.019 28.033 50.946 0.040 0.135 3.33E-04 2.794 3.77E+05 1.70E-02 18.528 0.016 28.033 46.974 0.040 0.140 3.21E-04 2.598 3.64E+05 1.69E-02 15.414 0.014 28.033 43.805 0.040 0.145 3.10E-04 2.422 3.51E+05 1.69E-02 12.910 0.012 28.033 41.254 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.045 0.110 4.09E-04 4.735 5.21E+05 1.71E-02 65.940 0.046 24.918 92.046 0.045 0.115 3.91E-04 4.332 4.98E+05 1.71E-02 52.551 0.038 24.918 78.463 0.045 0.120 3.75E-04 3.979 4.77E+05 1.70E-02 42.300 0.032 24.918 68.057 0.045 0.125 3.60E-04 3.667 4.58E+05 1.69E-02 34.363 0.027 24.918 59.994 0.045 0.130 3.46E-04 3.390 4.41E+05 1.69E-02 28.151 0.023 24.918 53.679 0.045 0.135 3.33E-04 3.144 4.24E+05 1.68E-02 23.243 0.020 24.918 48.685 0.045 0.140 3.21E-04 2.923 4.09E+05 1.68E-02 19.330 0.017 24.918 44.701 0.045 0.145 3.10E-04 2.725 3.95E+05 1.68E-02 16.184 0.015 24.918 41.495 0.045 0.150 3.00E-04 2.546 3.82E+05 1.67E-02 13.634 0.013 24.918 38.896 0.045 0.155 2.90E-04 2.385 3.70E+05 1.67E-02 11.554 0.012 24.918 36.773 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.050 0.110 4.09E-04 5.261 5.79E+05 1.71E-02 80.946 0.056 22.426 104.840 0.050 0.115 3.91E-04 4.814 5.54E+05 1.70E-02 64.488 0.047 22.426 88.142 0.050 0.120 3.75E-04 4.421 5.31E+05 1.69E-02 51.891 0.040 22.426 75.354 0.050 0.125 3.60E-04 4.074 5.09E+05 1.68E-02 42.140 0.034 22.426 65.446 0.050 0.130 3.46E-04 3.767 4.90E+05 1.68E-02 34.511 0.029 22.426 57.689 0.050 0.135 3.33E-04 3.493 4.72E+05 1.67E-02 28.485 0.025 22.426 51.558 0.050 0.140 3.21E-04 3.248 4.55E+05 1.67E-02 23.681 0.022 22.426 46.666 0.050 0.145 3.10E-04 3.028 4.39E+05 1.66E-02 19.820 0.019 22.426 42.732 0.050 0.150 3.00E-04 2.829 4.24E+05 1.66E-02 16.693 0.016 22.426 39.543 0.050 0.155 2.90E-04 2.650 4.11E+05 1.65E-02 14.142 0.014 22.426 36.940 Fluid Hydroelectric Design Page 18
Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.055 0.135 3.33E-04 3.842 5.19E+05 1.66E-02 34.251 0.030 20.387 55.421 0.055 0.136 3.31E-04 3.786 5.15E+05 1.66E-02 32.989 0.029 20.387 54.136 0.055 0.137 3.28E-04 3.731 5.11E+05 1.66E-02 31.782 0.028 20.387 52.907 0.055 0.138 3.26E-04 3.677 5.07E+05 1.66E-02 30.628 0.028 20.387 51.732 0.055 0.139 3.24E-04 3.624 5.04E+05 1.66E-02 29.524 0.027 20.387 50.608 0.055 0.140 3.21E-04 3.573 5.00E+05 1.66E-02 28.467 0.026 20.387 49.531 0.055 0.141 3.19E-04 3.522 4.97E+05 1.65E-02 27.456 0.025 20.387 48.501 0.055 0.142 3.17E-04 3.473 4.93E+05 1.65E-02 26.488 0.025 20.387 47.514 0.055 0.143 3.15E-04 3.425 4.90E+05 1.65E-02 25.560 0.024 20.387 46.569 0.055 0.144 3.13E-04 3.377 4.86E+05 1.65E-02 24.671 0.023 20.387 45.663 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.060 0.140 3.21E-04 3.898 5.46E+05 1.65E-02 33.688 0.031 18.688 53.182 0.060 0.141 3.20E-04 3.870 5.44E+05 1.65E-02 33.082 0.031 18.688 52.565 0.060 0.142 3.17E-04 3.789 5.38E+05 1.64E-02 31.342 0.029 18.688 50.791 0.060 0.143 3.15E-04 3.736 5.34E+05 1.64E-02 30.243 0.028 18.688 49.671 0.060 0.144 3.13E-04 3.684 5.31E+05 1.64E-02 29.190 0.028 18.688 48.598 0.060 0.145 3.10E-04 3.634 5.27E+05 1.64E-02 28.181 0.027 18.688 47.569 0.060 0.146 3.08E-04 3.584 5.23E+05 1.64E-02 27.213 0.026 18.688 46.583 0.060 0.147 3.06E-04 3.535 5.20E+05 1.64E-02 26.286 0.025 18.688 45.636 0.060 0.148 3.04E-04 3.488 5.16E+05 1.64E-02 25.396 0.025 18.688 44.729 0.060 0.149 3.02E-04 3.441 5.13E+05 1.64E-02 24.542 0.024 18.688 43.858 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.065 0.130 3.46E-04 4.897 6.37E+05 1.65E-02 57.423 0.049 17.251 75.945 0.065 0.135 3.33E-04 4.541 6.13E+05 1.64E-02 47.359 0.042 17.251 65.703 0.065 0.140 3.21E-04 4.222 5.91E+05 1.64E-02 39.343 0.036 17.251 57.539 0.065 0.145 3.10E-04 3.936 5.71E+05 1.63E-02 32.904 0.032 17.251 50.976 0.065 0.150 3.00E-04 3.678 5.52E+05 1.63E-02 27.692 0.028 17.251 45.660 0.065 0.155 2.90E-04 3.445 5.34E+05 1.62E-02 23.442 0.024 17.251 41.322 0.065 0.160 2.81E-04 3.233 5.17E+05 1.62E-02 19.953 0.021 17.251 37.758 0.065 0.165 2.73E-04 3.040 5.02E+05 1.62E-02 17.071 0.019 17.251 34.812 0.065 0.170 2.65E-04 2.864 4.87E+05 1.61E-02 14.676 0.017 17.251 32.362 0.065 0.175 2.57E-04 2.702 4.73E+05 1.61E-02 12.675 0.015 17.251 30.313 Fluid Hydroelectric Design Page 19
Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 0.070 0.130 3.46E-04 5.274 6.86E+05 1.64E-02 66.337 0.057 16.019 83.830 0.070 0.135 3.33E-04 4.890 6.60E+05 1.64E-02 54.700 0.049 16.019 71.986 0.070 0.140 3.21E-04 4.547 6.37E+05 1.63E-02 45.432 0.042 16.019 62.546 0.070 0.145 3.10E-04 4.239 6.15E+05 1.63E-02 37.989 0.037 16.019 54.960 0.070 0.150 3.00E-04 3.961 5.94E+05 1.62E-02 31.965 0.032 16.019 48.815 0.070 0.155 2.90E-04 3.710 5.75E+05 1.62E-02 27.054 0.028 16.019 43.802 0.070 0.160 2.81E-04 3.482 5.57E+05 1.61E-02 23.023 0.025 16.019 39.684 0.070 0.165 2.73E-04 3.274 5.40E+05 1.61E-02 19.694 0.022 16.019 36.281 0.070 0.170 2.65E-04 3.084 5.24E+05 1.60E-02 16.928 0.019 16.019 33.451 0.070 0.175 2.57E-04 2.910 5.09E+05 1.60E-02 14.617 0.017 16.019 31.084 Appendix C-1 (Triangle Solver) Figure 4 Triangle Solver (Microsoft Mathematics) Fluid Hydroelectric Design Page 20