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An Introduction to Wave and Tidal Energy Renewable Energy in (and above) the Oceans Frank R. Leslie, BSEE, MS Space Technology 5/25/2002, Rev. 1.7 [email protected]; (321) 768-6629

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An Introduction to Wave and Tidal Energy

Renewable Energy in (and above) the Oceans

Frank R. Leslie,

BSEE, MS Space Technology

5/25/2002, Rev. 1.7

[email protected]; (321) 768-6629

“It is pleasant, when the sea is high and the winds are dashing the waves about, to watch from shore the struggles of another.”

Lucretius, 99-55 B.C.

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Overview of Ocean Energy

  • Ocean energy is replenished by the sun and through tidal influences of the moon and sun gravitational forces

  • Near-surface winds induce wave action and cause wind-blown currents at about 3% of the wind speed

  • Tides cause strong currents into and out of coastal basins and rivers

  • Ocean surface heating by some 70% of the incoming sunlight adds to the surface water thermal energy, causing expansion and flow

  • Wind energy is stronger over the ocean due to less drag, although technically, only seabreezes are from ocean energy

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What’s renewable energy?

  • Renewable energy systems transform incoming solar energy and its alternate forms (wind and river flow, etc.), usually without pollution-causing combustion

  • This energy is “renewed” by the sun and is “sustainable”

  • Renewable energy is sustainable indefinitely, unlike long-stored, depleting energy from fossil fuels

  • Renewable energy from wind, solar, and water power emits no pollution or carbon dioxide

  • Renewable energy is “nonpolluting” since no combustion occurs (although the building of the components does in making steel, etc., for conversion machines does pollute during manufacture)

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Renewable Energy (Continued)

  • Fuel combustion produces “greenhouse gases” that are believed to lead to climate change (global warming), thus combustion of biomass is not as desirable as other forms

  • Biomass combustion is also renewable, but emits CO2 and pollutants

    • Biomass can be heated with water under pressure to create synthetic fuel gas; but burning biomass creates pollution and CO2

  • Nonrenewable energy comes from fossil fuels and nuclear radioactivity (process of fossilization still occurring but trivial)

    • Nuclear energy is not renewable, but sometimes is treated as though it were because of the long depletion period

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The eventual declineof fossil fuels

  • Millions of years of incoming solar energy were captured in the form of coal, oil, and natural gas; current usage thus exceeds the rate of original production

  • Coal may last 250 to 400 years; estimates vary greatly; not as useful for transportation due to losses in converting to liquid “synfuel”

  • We can conserve energy by reducing loads and through increased efficiency in generating, transmitting, and using energy

  • Efficiency and conservation will delay an energy crisis, but will not prevent it

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Available Energy

  • Potential Energy: PE = mh

  • Kinetic Energy: KE = ½ mv2 or ½ mu2

  • Wave energy is proportional to wave length times wave height squared (LH2)per wave length per unit of crest length

    • A four-foot (1.2 m), ten-second wave striking a coast expends more than 35, 000 HP per mile of coast [Kotch, p. 247]

  • Maximum Tidal Energy, E = 2HQ x 353/(778 x 3413)= 266 x 10-6 HQ kWh/yr, where H is the tidal range (ft)and Q is the tidal flow (lbs of seawater)

  • E = 2 HQ ft-lb/lunar day (2 tides)or E = 416 x 10-4 HV kWh, where V is cubic feet of flow

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  • Cost of installation, operation, removal and restoration

  • Compare cost/watt & cost/watt-hour vs. other sources

  • Relative total costs compared to other sources

  • Externality costs aren’t included in most assessments

  • Cost of money (inflation) must be included (2 to 5%/year)

  • Life of energy plant varies and treated as linear depreciation to zero

  • Tax incentives or credits offset the hidden subsidies to fossil fuel and nuclear industry

  • Environmental Impact Statements (EIS) require early funding to justify permitting

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Ocean Energy

  • The tidal forces and thermal storage of the ocean provide a major energy source

  • Wave action adds to the extractable surface energy

  • Major ocean currents (like the Gulf Stream) may be exploited to extract energy with underwater rotors (turbines)

  • The oceans are the World’s largest solar collectors (71% of surface)

  • Thermal differences between surface and deep waters can drive heat engines

  • Over or in proximity to the ocean surface, the wind moves at higher speeds over water than over land roughness

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Wave Energy

  • Energy of interchanging potential and kinetic energy in the wave

  • Cycloidal motion of wave particles carries energy forward without much current

  • Typical periodicities are one to thirty seconds, thus there are low-energy periods between high-energy points

  • In 1799, Girard & son of Paris proposed using wave power for powering pumps and saws

  • California coast could generate 7 to 17 MW per mile [Smith, p. 91]

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Ocean Energy: Wave Energy

  • Wave energy potential varies greatly worldwide

Figures in kW/m

Source: Wave Energy paper. IMechE, 1991 and European Directory of Renewable Energy (Suppliers and Services) 1991

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Concepts of Wave Energy Conversion

  • Change of water level by tide or wave can move or raise a float, producing linear motion from sinusoidal motion

  • Water current can turn a turbine to yield rotational mechanical energy to drive a pump or generator

    • Slow rotation speed of approximately one revolution per second to one revolution per minute less likely to harm marine life

    • Turbine reduces energy downstream and could protect shoreline

  • Archimedes Wave Swing is a Dutch device [Smith, p. 91]

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Salter “Ducks”

  • Scottish physicist Prof. Stephen Salter invented “Nodding Duck” energy converter in 1970

  • Salter “ducks” rock up and down as the wave passes beneath it. This oscillating mechanical energy is converted to electrical energy

  • Destroyed by storm

  • A floating two-tank version drives hydraulic rams that send pressurized oil to a hydraulic motor that drives a generator, and a cable conducts electricity to shore

Ref.: TidalPower.html©1996 Ramage

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Fluid-Driven Wave Turbines

  • Waves can be funneled and channeled into a rising chute to charge a reservoir over a weir or through a swing-gate

    • Water passes through waterwheel or turbine back to the ocean

    • Algerian V-channel [Kotch, p.228]

  • Wave forces require an extremely strong structure and mechanism to preclude damage

  • The Ocean Power Delivery wave energy converter Pelamis has articulated sections that stream from an anchor towards the shore

    • Waves passing overhead produce hydraulic pressure in rams between sections

    • This pressure drives hydraulic motors that spin generators, and power is conducted to shore by cable

    • 750 kW produced by a group 150m long and 3.5m diameter 020402

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Fluid-Driven Wave Turbines

  • Davis Hydraulic Turbines since 1981

    • Most tests done in Canada

    • 4 kW turbine tested in Gulf Stream

  • Blue Energy of Canada developing two 250 kW turbines for British Columbia

  • Also proposed Brothers Island tidal fence in San Francisco Bay, California 1000 ft long by 80 ft deep to produce 15 – 25 MW

  • Australian Port Kembla (south of Sydney) to produce 500 kW 020402

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Air-Driven Wave Turbines (Con’t)

  • A floating buoy can compress trapped air similar to a whistle buoy

  • The oscillating water column (OWC) in a long pipe under the buoy will lag behind the buoy motion due to inertia of the water column

  • The compressed air spins a turbine/alternator to generate electricity at $0.09/kWh

The Japanese “Mighty Whale” has an air channel to capture wave energy. Width is 30m and length is 50 m. There are two 30 kW and one50 kW turbine/generators 020402

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Air-Driven Wave Turbines

  • British invention uses an air-driven Wells turbine with symmetrical blades

  • Incoming waves pressurize air within a heavy concrete box, and trapped air rushes upward through pipe connecting the turbine

  • A Wavegen™, wave-driven, air compressor or oscillating water column (OWC) spins a two-way Wells turbine to produce electricity

  • Wells turbine is spun to starting speed by external electrical power and spins the same direction regardless of air flow direction

  • Energy estimated at 65 megawatts per mile

Photo by Wavegen 020402

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Ocean Energy: Tidal Energy

  • Tides are produced by gravitational forces of the moon and sun and the Earth’s rotation

  • Existing and possible sites:

    • France: 1966 La Rance river estuary 240 MW station

      • Tidal ranges of 8.5 m to 13.5 m; 10 reversible turbines

    • England: Severn River

    • Canada: Passamaquoddy in the Bay of Fundy (1935 attempt failed)

    • California: high potential along the northern coast

  • Environmental, economic, and esthetic aspects have delayed implementation

  • Power is asynchronous with load cycle

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Tidal Energy

  • Tidal mills were used in the Tenth and Eleventh Centuries in England, France, and elsewhere

  • Millpond water was trapped at high tide by a gate (Difficult working hours for the miller; Why?)

    • Rhode Island, USA, 18th Century, 20-ton wheel 11 ft in diameter and 26 ft wide

    • Hamburg, Germany, 1880 “mill” pumped sewage

    • Slade’s Mill in Chelsea, MA founded 1734, 100HP, operated until ~1980

    • Deben estuary, Woodbridge, Suffolk, England has been operating since 1170 (reminiscent of “the old family axe”; only had three new handles and two new heads!)

    • Tidal mills were common in USA north of Cape Cod, where a 3 m range exists [Redfield, 1980]

    • Brooklyn NY had tidal mill in 1636 [?]

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Tidal Energy (continued)

  • Potential energy = S integral from 0 to 2H (ρgz dz),

    where S is basin area, H is tidal amplitude, ρ is water density, and g is gravitational constant yielding 2 S ρ gH2

  • Mean power is 2 S ρ gH2/tidal period; semidiurnal better

  • Tidal Pool Arrangements

    • Single-pool empties on ebb tide

    • Single-pool fills on flood tide

    • Single-pool fills and empties through turbine

    • Two-pool ebb- and flood-tide system; two ebbs per day; alternating pool use

    • Two-pool one-way system (high and low pools) (turbine located between pools)

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Tidal Water Turbines

  • Current flow converted to rotary motion by tidal current

  • Turbines placed across Rance River, France

  • Large Savonius rotors (J. S. Savonius, 1932?) placed across channel to rotate at slow speed but creating high torque (large current meter)

  • Horizontal rotors proposed for Gulf Stream placement off Miami, Florida

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Tidal Flow: Rance River, France

  • 240 MW plant with 24, 10 MW turbines operated since 1966

  • Average head is 28 ft

  • Area is approximately 8.5 square miles

  • Flow approx, 6.64 billion cubic feet

  • Maximum theoretical energy is 7734 million kWh/year; 6% extracted

  • Storage pumping contributes 1.7% to energy level

  • At neap tides, generates 80,000 kWh/day; at equinoctial spring tide, 1,450,000 kWh/day (18:1 ratio!); average ~500 million kWh/year

  • Produces electricity cheaper than oil, coal, or nuclear plants in France

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Tidal Flow: Passamaquoddy, Lower Bay of Fundy, New Brunswick, Canada

  • Proposed to be located between Maine (USA) and New Brunswick

  • Average head is 18.1 ft

  • Flow is approximately 70 billion cubic feet per tidal cycle

  • Area is approximately 142 square miles

  • About 3.5 % of theoretical maximum would be extracted

  • Two-pool approach greatly lower maximum theoretical energy

  • International Commission studied it 1956 through 1961 and found project uneconomic then

  • Deferred until economic conditions change

[Ref.: Harder]

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Other Tidal Flow Plants under Study Brunswick, Canada

  • Annapolis River, Nova Scotia: straight-flow turbines; demonstration plant was to be completed in 1983; 20 MW; tides 29 to 15 feet; Tidal Power Corp.; ~$74M

  • Experimental site at Kislaya Guba on Barents Sea

    • French 400 kW unit operated since 1968

    • Plant floated into place and sunk: dikes added to close gaps

  • Sea of Okhotsk (former Sov. Union) under study in 1980

  • White Sea, Russia: 1 MW, 1969

  • Murmansk, Russia: 0.4 MW

  • Kiansghsia in China

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Other Tidal Flow Plants under Study Brunswick, Canada(continued)

  • Severn River, Great Britain: range of 47 feet (14.5 m) calculated output of 2.4 MWh annually. Proposed at $15B, but not economic.

  • Chansey Islands:20 miles off Saint Malo, France; 34 billion kWh per year; not economic; environmental problems; project shelved in 1980

  • San Jose, Argentina: potential of 75 billion kWh/year; tidal range of 20 feet (6m)

  • China built several plants in the 1950s

  • Korean potential sites (Garolim Bay)

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Hydraulic Pressure Absorbers Brunswick, Canada

  • Large synthetic rubber bags filled with water could be placed offshore where large waves pass overhead

    • Also respond to tides

    • A connecting pipe conducts hydraulic pressure to a positive displacement motor that spins a generator

    • The motor can turn a generator to make electricity that varies sinusoidally with the pressure

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Ocean Thermal Energy: Brunswick, CanadaOTEC (Ocean Thermal Electric Conversion)

  • French Physicist Jacque D’Arsonval proposed in 1881

  • Georges Claude built Matanzos Bay, Cuba 22 kW plant in 1930 [Smith, p.94]

  • Keahole Point, Hawaii has the US 50 kW research OTEC barge system

  • OTEC requires some 36 to 40°F temperature difference between the surface and deep waters to extract energy

  • Open-cycle plants vaporize warm water and condense it using the cold sea water, yielding potable water and electricity from turbines-driven alternators

  • Closed-cycle units evaporate ammonia at 78°F to drive a turbine and an alternator

  • Hybrid cycle uses open-cycle steam to vaporize closed-cycle ammonia

  • China also has experimented with OTEC


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Wind Energy Equations Brunswick, Canada(also applies to water turbines)

  • Assume a “tube” of air the diameter, D, of the rotor

    • A = π D2/4

  • A length, L, of air moves through the turbine in t seconds

    • L = u·t, where u is the wind speed

  • The tube volume is V = A·L = A·u·t

  • Air density, ρ, is 1.225 kg/m3 (water density ~1000 kg/m3)

  • Mass, m = ρ·V = ρ·A·u·t, where V is volume

  • Kinetic energy = KE = ½ mu2

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Wind Energy Equations Brunswick, Canada(continued)

  • Substituting ρ·A·u·t for mass, and A = π D2/4 , KE = ½·π/4·ρ·D2·u3·t

  • Theoretical power, Pt = ½·π/4·ρ·D2·u3·t/t = 0.3927·ρa·D2·u3, ρ (rho) is the density, D is the diameter swept by the rotor blades, and u is the speed parallel to the rotor axis

  • Betz Law shows 59.3% of power can be extracted

  • Pe = Pt·59.3%·ήr·ήt·ήg, where Pe is the extracted power, ήr is rotor efficiency, ήt is transmission efficiency, and ήg is generator efficiency

  • For example, 59.3%·90%·98%·80% = 42% extraction of theoretical power

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Generic Trades in Energy Brunswick, Canada

  • Energy trade-offs required to make rational decisions

  • PV is expensive ($4 to 5 per watt for hardware + $5 per watt for shipping and installation = $10 per watt) compared to wind energy ($1.5 per watt for hardware + $5 per watt for installation = $6 per watt total)

  • Are Compact Fluorescent Lamps (CFLs) always better to use than incandescent?

Ref.: windfarm/index.asp?i=2


Photo of FPL’s Cape Canaveral Plant by F. Leslie, 2001

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Energy Storage Brunswick, Canada

  • Renewable energy is often intermittent, and storage allows alignment with time of use.

  • Compressed air, flywheels, weight-shifting (pumped water storage at Niagara Falls)

  • Batteries are traditional for small systems and electric vehicles; first cars (1908) were electric

  • Hydrogen can be made by electrolysis

  • Energy is best stored as a financial credit through “net metering”

    • Net metering requires a utility to bill at the same rate for buying or selling energy details.solar_electric.html

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Energy Brunswick, CanadaTransmission

  • Electricity and hydrogen are energy carriers, not natural fuels

  • Electric transmission lines lose energy in heat (~2% to 5%); trades loss vs. cost

  • Line flow directional analysis can show where new energy plants are required to reduce energy transmission

  • Hydrogen is made by electrolysis of water, cracking of natural gas, or from bacterial action (lab experiment level)

  • Oil and gas pipelines carry storable energy

    • Pipelines (36” or larger) can transport hydrogen without appreciable energy loss due to low density and viscosity

    • More efficient than 500 kV transmission line and is out of view

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Legal aspects and other complications Brunswick, Canada

  • PURPA: Public Utility Regulatory Policy Act of 1978. Utility purchase from and sale of power to qualified facilities; avoided costs offsetting basis of purchases

  • Energy Policy Act of 1992 leads to deregulation

  • “NIMBYs” rally to shrilly insist “Not In My Backyard”!

  • Investment taxes and subsidies favor fossil and nuclear power

  • High initial cost dissuades potential users; future is uncertain

  • Lack of uniform state-level net metering hinders offsetting costs

  • Environmental Impact Statements (EIS) require extensive and expensive research and trade studies

  • Numerous “public interest” advocacy groups are well-funded and ready to sue to stop projects

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Conclusion Brunswick, Canada

  • Renewable energy offers a long-term approach to the World’s energy needs

  • Economics drives the energy selection process and short-term (first cost) thinking leads to disregard of long-term, overall cost

  • Wave and tidal energy are more expensive than wind and solar energy, the present leaders

  • Increasing oil, gas, and coal prices will ensure that the transition to renewable energy occurs

  • Offshore and shoreline wind energy plants offer a logical approach to part of future energy supplies

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References: Books, etc. Brunswick, Canada

  • General:

    • Sørensen, Bent. Renewable Energy, Second Edition. San Diego: Academic Press, 2000, 911 pp. ISBN 0-12-656152-4.

    • Henry, J. Glenn and Gary W. Heinke. Environmental Science and Engineering. Englewood Cliffs: Prentice-Hall, 728pp., 1989. 0-13-283177-5, TD146.H45, 620.8-dc19

    • Brower, Michael. Cool Energy. Cambridge MA: The MIT Press, 1992. 0-262-02349-0, TJ807.9.U6B76, 333.79’4’0973.

    • Di Lavore, Philip. Energy: Insights from Physics. NY: John Wiley & Sons, 414pp., 1984. 0-471-89683-7l, TJ163.2.D54, 621.042.

    • Bowditch, Nathaniel. American Practical Navigator. Washington:USGPO, H.O. Pub. No. 9.

    • Harder, Edwin L. Fundamentals of Energy Production. NY: John Wiley & Sons, 368pp., 1982. 0-471-08356-9, TJ163.9.H37, 333.79. Tidal Energy, pp. 111-129.

  • Wind:

    • Patel, Mukund R. Wind and Solar Power Systems. Boca Raton: CRC Press, 1999, 351 pp. ISBN 0-8493-1605-7, TK1541.P38 1999, 621.31’2136

    • Gipe, Paul. Wind Energy for Home & Business. White River Junction, VT: Chelsea Green Pub. Co., 1993. 0-930031-64-4, TJ820.G57, 621.4’5

    • Johnson, Gary L, Wind Energy Systems. Englewood Cliffs NJ: Prentice-Hall, Inc. TK 1541.J64 1985. 621.4’5; 0-13-957754-8.

  • Waves:

  • Smith, Douglas J. “Big Plans for Ocean Power Hinges on Funding and Additional R&D”. Power Engineering, Nov. 2001, p. 91.

  • Kotch, William J., Rear Admiral, USN, Retired. Weather for the Mariner. Annapolis: Naval Institute Press, 1983. 551.5, QC994.K64, Chap. 11, Wind, Waves, and Swell.

  • Solar:

    • Duffie, John and William A. Beckman. Solar Engineering of Thermal Processes. NY: John Wiley & Sons, Inc., 920 pp., 1991.

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References: Internet Brunswick, Canada

  • General:


    • Federal Energy Regulatory Commission



    • http://mailto:[email protected]

    • Site devoted to the decline of energy and effects upon population

  • Tidal:





  • Waves:







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References: Internet Brunswick, Canada

  • Thermal:


    • on OTEC systems

  • Wind:

    • http:[email protected] Wind Energy elist

    • http:[email protected] Wind energy home powersite elist


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Units and Constants Brunswick, Canada

  • Units:

    • Power in watts (joules/second)

    • Energy (power x time) in watt-hours

  • Constants:

    • 1 m = 0.3048 ft exactly by definition

    • 1 mile = 1.609 km; 1m/s = 2.204 mi/h (mph)

    • 1 mile2 = 27878400 ft2 = 2589988.11 m2

    • 1 ft2 = 0.09290304 m2; 1 m2 = 10.76391042 ft2

    • 1 ft3 = 28.32 L = 7.34 gallon = 0.02832 m3; 1 m3 = 264.17 US gallons

    • 1 m3/s = 15850.32 US gallons/minute

    • g = 32.2 ft/s2 = 9.81 m/s2; 1 kg = 2.2 pounds

    • Air density, ρ (rho), is 1.225 kg/m3 or 0.0158 pounds/ft3 at 20ºC at sea level

    • Solar Constant: 1368 W/m2 exoatmospheric or 342 W/m2 surface (80 to 240 W/m2)

    • 1 HP = 550 ft-lbs/s = 42.42 BTU/min = = 746 W (J/s)

    • 1 BTU = 252 cal = 0.293 Wh = 1.055 kJ

    • 1 atmosphere = 14.696 psi = 33.9 ft water = 101.325 kPa = 76 cm Hg =1013.25 mbar

    • 1 boe (42- gallon barrel of oil equivalent) = 1700 kWh

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Energy Equations Brunswick, Canada

  • Electricity:

    • E=IR; P=I2 R; P=E2/R, where R is resistance in ohms, E is volts, I is current in amperes, and P is power in watts

    • Energy = P t, where t is time in hours

  • Turbines:

    • Pa = ½ ρ A2 u3, where ρ (rho) is the fluid density, A = rotor area in m2, and u is wind speed in m/s

    • P = R ρ T, where P = pressure (Nm-2 = Pascal)

    • Torque, T = P/ω, in Nm/rad, where P = mechanical power in watts, ω is angular velocity in rad/sec

  • Pumps:

    • Pm = gQmh/ήp W, where g=9.81 N/kg, Qm is mass capacity in kg/s, h is head in m, and ήp is pump mechanical efficiency

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