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Homework Help: Calculating Gas Turbine Shaft Power

  1. Dec 31, 2008 #1


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    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 m3/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/Cp(g)/Cp(a)/Gammaa/Gammag etc) which I haven't included as I don't believe them to be relevant.

    If necessary I will add these as requests.

  2. jcsd
  3. Jan 1, 2009 #2
    Your turbine speed is in RPM and your fuel flow is in kg/sec, so you have to get Wf in kg/min.
    I have an example of this but it isn’t in metric but your formulas appear to be correct. The number 26850 probably comes from correcting for units.
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