# Hydroelectric Design

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1 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.

2 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 Description Specifications RESULTS DISCUSSION CONCLUSION Bibliography APPENDIX Appendix A-1 Hydroelectricity Appendix A-2 Reynolds number (Re) Appendix B-1 Design Data Appendix C-1 (Triangle Solver) Fluid Hydroelectric Design Page 1

3 TABLE OF FIGURE Figure 1 Hydroelectricity... 5 Figure 2 Moody Diagram... 8 Figure 3 Generator and Turbine Figure 4 Triangle Solver (Microsoft Mathematics) TABLE OF DATA Table 1 Design Specifications for 11MW Hydro Turbine Table 2 Results for H 50m Table 3 Design Results for 18 MW Hydroelectric Fluid Hydroelectric Design Page 2

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 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) H(ft) 330 ft 1 Z (elbow) Viscosity (µ) 1.00E-03 K (elbow) 0 X (actual) L(ft) 1200 m X (elbow) ɛ 4.50E-05 Y (actual) Y (elbow) Gravity (g) 9.81 Z (ideal) Radio 50 Power (KW) X (ideal) C % (elbow) 10% Y (ideal) α Nth 85.00% Z (right) S Wa (KW) X (right) We (KW) Y (right) per unit Y (design) unit (aprox) Fluid Hydroelectric Design Page 12

14 RESULTS Table 2 Results for H 50m Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H 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 (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 (m) long and an elbow with a length of (m), and a radius of 50 (m), for a total of (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

15 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 m/s to 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

16 Bibliography [1] W. contributors, "Hydroelectricity," [Online]. Available: [Accessed 2012]. [2] V. f. rate, "Wikipedia contributors," [Online]. Available: [Accessed 2012]. [3] W. contributors, "Reynolds number," [Online]. Available: [Accessed 2012]. Fluid Hydroelectric Design Page 15

17 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 [1] Hydropower is produced in 150 countries, with the Asia-Pacific region generating 32 percent of global hydropower in 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 ( ), who popularized its use in [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

18 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 E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Fluid Hydroelectric Design Page 17

19 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Fluid Hydroelectric Design Page 18

20 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Fluid Hydroelectric Design Page 19

21 Q D(m) ɛ/d V(m/s) Re f Hf Hm Ht H E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Appendix C-1 (Triangle Solver) Figure 4 Triangle Solver (Microsoft Mathematics) Fluid Hydroelectric Design Page 20

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