(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have been asked to calculate a range of values relating to a Gas Turbine engine, and while I have been able to find the majority of the values I am almost certain that the Thermal Efficiency value of 1.64% I have come up with is incorrect.

This relies on Shaft power, fuel mass flow rate, and the Lower Calorific Value in the formula shown below.

LCV = 42,000 kJ/kg (Given value)

Fuel mass flow rate = 0.00821256 kg/sec (Calculated)

Shaft power = 5.66 kW (Calculated, but not confident of this result)

N = 3040 rpm (Given value)

F (brake load)= 50 N (Given Value)

2. Relevant equations

The formula for Thermal Efficiency that I have is: [tex]\eta[/tex]_{thermal}= [tex]\dot{W}[/tex]_{Shaft}/([tex]\dot{m}[/tex]_{fuel}[tex]\times[/tex] Lower Calorific Value)

The formula for Shaft Power (in kW) I have is: [tex]\dot{W}[/tex]_{Shaft}= (F * N) / 26850

(Not sure where 26850 comes from, I was given this equation. If someone can explain where that number comes from I would be very grateful.)

The mass flow rate of fuel I worked out as follows:

2 litres of fuel used in 207 seconds (Given values) = 9.6618E^{-3}l/sec

0.0096618 [tex]\div[/tex] 1000 = 9.6618E^{-6}m^{3}/sec

Relative density of fuel = 0.85 (Given value)

Mass flow rate = 9.6618E^{-6}[tex]\times[/tex] 850 = 0.00821256 kg/sec

There are a whole range of other values (Temps/Pressures/C_{p(g)}/C_{p(a)}/Gamma_{a}/Gamma_{g}etc) which I haven't included as I don't believe them to be relevant.

If necessary I will add these as requests.

Thanks

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# Homework Help: Calculating Gas Turbine Shaft Power

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