# Steam turbine maths

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1. Oct 21, 2014

### pixelpuffin

im designing a steam turbine and boiler for a solar energy project but i cant figure out the math and have had trouble looking it up
the only thing that is definite about the turbine (other than that its a tesla turbine) is that the thermal wattage is 5,855 watts or 1,434.72 calories per second (because its solar its actually a range but i plan to optimize the system for the average and later install a thermal buffer)
i need to determine
inlet and outlet area
inlet and outlet steam velocity
inlet and outlet steam pressure
inlet and outlet steam temperature

my goal is to get ~ 60% efficiency at average operating conditions and >20% efficiency at the high and low ends of its operation
it would be nice if it operated at 60 hertz or 3,600 rpm though thats not important

using the ideal gas law i get P*1/T*2.16*1/1,000=p so i can calculate the density with pressure and temperature

from there im pretty much lost, mainly because i cant find any way to calculate the ratio between thermal drop off and pressure drop off

does anybody know how to at least estimate this
i have some coding knowledge so if theres a differential equation i have no trouble solving it

2. Oct 22, 2014

### jack action

The steam turbines are dictated by the Rankine cycle (they are 12 pages for that lesson in the previous link). To help you familiarize with the concept, there are plenty of examples on the web to help you understand how to make the estimation you are looking for.

Keywords: Rankine cycle.

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