Max, et al.,
Is "two thirds limit to the power " related to the Betz Limit of 59.3% of available power in the wind power domain? Frank Leslie -----Original Message----- From: Max Enfield [mailto:[EMAIL PROTECTED] Sent: Wednesday, February 02, 2005 1:01 AM To: [email protected] Subject: Re: [microhydro] Confused about potential energy. ReadFamily wrote: > > I was thinking about the pumped water storage idea and then started to think about the energy in the system. > > If there is a full tank at the top and an empty tank at the bottom then the potential energy in the system is mgh (mass of water x gravitational constant x height difference). > > So if you let the water flow from top tank to bottom tank through a simple pipe then the potential energy is gone. (assuming bottom tank is at height 0). > > Now put the water back into the top tank and this time put a turbine in the pipe. The water flows from the top tank to the bottom tank and power is generated by the turbine and extracted from the system. But the difference in potential energy in the system is the same. All the water from the top is now in the bottom. Where did the energy that was extracted from the system by the turbine come from? > > I'm sure that the answer is somewhere in the statement in the first case where the water flows through a simple pipe. The potential energy in the system has changed - so where did the energy go? I dont know. > > Dominic Read > Georgia, USA. Yes the difference in potential energy is the same. In the first case where the water flows unimpeded down the pipe most of the potential energy is lost as friction in the pipe (eventually to be dissipated as heat) with some being used to provide the kinetic energy for the water to move. In the second case, the turbine impedes the flow of water and so less energy is lost as friction or needed for kinetic energy. However the water must flow for the turbine to work and so some of the potential energy is still consumed as friction or converted to kinetic energy. In the best case the turbine is able to extract up to two thirds of the potential energy. I have expressed the view several times to this group that hydraulics is intuitively obvious only to a gifted few - so don't be put off if at first you find the ideas somewhat alien. The two thirds limit to the power that can be extracted can be proved rigorously, based on the fact that both the frictional loss and the kinetic energy are proportional to the square of the water velocity. Regards, Max Enfield Planetary Power Does your company feature in the microhydro business directory at http://microhydropower.net/directory ? If not, please register free of charge and be exposed to the microhydro community world wide! NOTE: The advertisements in this email are added by Yahoogroups who provides us with free email group services. The microhydro-group does not endorse products or support the advertisements in any way. More information on micro hydropower at http://microhydropower.net To unsubscribe: send empty message to [EMAIL PROTECTED] ---------------------------------------------------------------------------- -- Yahoo! Groups Links a.. To visit your group on the web, go to: http://groups.yahoo.com/group/microhydro/ b.. To unsubscribe from this group, send an email to: [EMAIL PROTECTED] c.. Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service. [Non-text portions of this message have been removed] ------------------------ Yahoo! Groups Sponsor --------------------~--> Has someone you know been affected by illness or disease? Network for Good is THE place to support health awareness efforts! http://us.click.yahoo.com/RzSHvD/UOnJAA/79vVAA/FGYolB/TM --------------------------------------------------------------------~-> Does your company feature in the microhydro business directory at http://microhydropower.net/directory ? If not, please register free of charge and be exposed to the microhydro community world wide! NOTE: The advertisements in this email are added by Yahoogroups who provides us with free email group services. The microhydro-group does not endorse products or support the advertisements in any way. More information on micro hydropower at http://microhydropower.net To unsubscribe: send empty message to [EMAIL PROTECTED] Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/microhydro/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
