# Connection between corrected mass flow and pressure ratio in the Turbine (G) Block

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Gero on 31 Jul 2023
Answered: Yifeng Tang on 7 Aug 2023
Hello,
I was trying to find the equation that describes the connection between corrected mass flow and pressure ratio in the Turbine (G) Block in Simscape if I use the analytical parametrization of the turbine map. Could you please give me the equation the turbine map is based on if the performance parameterization specification is set to "Analytical"?
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Gero on 7 Aug 2023
it works with stodola's ellipse. The correlation is:
m_corr = sqrt(m_corr_Design^2/(1-pi_Design^2))*(1-(pi)^2)
Tank you for tip it was very helpfull.
Yifeng Tang on 7 Aug 2023
Hi Gero,
I can confirm with you that the equation you shared is indeed the one implemented in the Turbine (G) block, with some modification for numerical stability (e.g. avoiding dividing by zero) and a multiplier for nozzle opening fraction. I'll reach out to the Documentation team and ask for an update.
I'll summarize this conversation and put into the answer section.

Yifeng Tang on 7 Aug 2023
Summary from the discussion in the Comments section.
While the formulation isn't given in the Documentation page of the Turbine (G) block, there is an example of a steam turbine that provides some hints. In this example: https://www.mathworks.com/help/releases/R2023a/simscape/ug/rankine-cycle-steam-turbine.html , the turbine is modeled using Simscape language as a custom block and the source code is visible. It's in two-phase domain, but the analytical form, Stodola's ellipse relation accordingly to the notes in the turbine block, is the same as in Turbine (G). The stodola's ellipse correlation is (credit: Gero): m_corr = sqrt(m_corr_Design^2/(1-pi_Design^2))*(1-(pi)^2).
In Turbine (G), the same equation is implemented, with some modification for numerical stability (e.g. avoiding dividing by zero) and a multiplier for nozzle opening fraction.

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