# Energy calculations for steam turbine

I am a civil engineering undergraduate. I have an interest in Biotropic Design and sustainable energy and am working on a new conceptual design. I would like to know what analytics may be done to prove the efficiency of the system in a proof of concept for local government. I don't know how to calculate any of the results that I will likely be asked such as:

1. What volumetric size is the system likely to occupy?
2. What is the estimated power output?
3. How much is it going to cost to run?
4. How much water will it need to run?
5. What pressure needs to be maintained to keep the system free of condensation before the turbine?

Add any other questions you think you'd ask if you were expected to spend £5 million on building a new powerstation for your city and answer it with the necessary equations to back up a positive attitude towards getting the job done.

The system works on the principle of negative pressure as opposed to energy intensive positive pressure.

There are two tanks in a closed system. Tank A is the wet tank and Tank B is the dry tank. A contains water at nominal room temperature but this may vary depending on weather conditions and may decrease to no less than 278K. Tank B temperature is unknown.

Between A & B is a turbine that unrestrained operates at an estimated 99.9% efficiency {take this as fact}. I would like to calculate energy output at 50% efficiency under load producing 1GW minimum.

Tank A pressure is 3psi.

You can choose the minimum size tank to maintain that will maintain negative pressure maximum of 10psi for 24 hour period. The maximum size is immaterial as it will tie up with another system for another purpose that is kept in negative pressure for permanent operation at a maximum of 8psi.

A proof of concept research system has already been made and works. It uses a Tesla turbine. The Tesla design is being improved but there are patent design modifications I cannot reveal with that aspect. Tank A measures 348K and system depressurised to 25 inches of mercury (ultimately 28.5inches). Tank B is easily 278K, if not lower. The turbine output is estimated at 1kW. It is a closed system. Eventually it will be designed to extract thermal energy from naturally heated water. That water may be up to 380K.

The idea is to get water to boil at 272K and keep a constant supply available. The incoming water will have a minimum temperature of 278K.

I don't know anything about any equations relating to this question.

1. How can I calculate the amount energy extracted with all the above information?
2. What equipment would I need to measure energy and power?

If there is anything else you think should be added to the list, do edit and suggest rather than comment. I would like this question to become a permanent example for reference.

(no, this is not a university exam question.) Cold Steam Research

The energy that is available to use in any pressure/temperature combination steam is easily determined from a steam table. Steam can be passed through a turbine at theoretically any pressure/temperature as long as the exhaust of the turbine is at a lower pressure than the inlet. This is the basic steam cycle from Thermo 1.

The issues will become how you keep the exhaust pressure that low, and also how you get rid of the exhaust steam. Condensing the steam back to water so it can be pumped either out or back to the source tank will require cooling it, so you will need a cooling medium below the steam temperature.

As to your questions, number one would be you telling the local government how it is actually supposed to work. If there is a patent then the patent describes the process, and you cannot maintain it as a secret. There is almost no chance of anyone other than a sucker giving you money for a process when you won't tell them how it is supposed to work.

As to how big, how much energy, etc, that is all based on the output of a kg of water, and then scaled based on how much work your input energy will provide.

Costs will be a function of all the design inputs. If I understand what you are trying to do, I suggest that getting water to boil at 272K will be several orders of magnitude more difficult than getting it to boil at 348K. Getting water to boil at that low a pressure will require almost a perfect vacuum, which is difficult to achieve at scale. And then we need an even more perfect vacuum at an even lower temperature to exhaust the steam from the turbine.

• Thanks, Scott. Would you be so kind as to provide me with these steam tables in your answer? Commented Feb 2, 2020 at 15:55
• this one seems to be fine. tlv.com/global/US/calculator/steam-table-pressure.html Commented Feb 2, 2020 at 19:30
• "would be you telling the local government how it is actually supposed to work?" YES. Commented Feb 26, 2020 at 2:52
• "If there is a patent..." There is none. Yet. Commented Feb 26, 2020 at 2:53