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An adiabatic gas turbine expands air at 1300 kPa and 500◦C to 100 kPa and 127◦C. Air enters the turbine through a 0.2-m2 opening with an average velocity of 40 m/s, and exhausts through a 1-m2 opening. Determine (a) the mass flow rate of air through the turbine (b) the power produced by the turbine

Respuesta :

Given:

Pressure, [tex]P_{1}[/tex] = 1300 kPa

Temperature,  [tex]T_{1}[/tex] = [tex]500^{\circ}[/tex]

[tex]P_{2}[/tex] = 100 kPa

[tex]T_{2} = 127^{\circ}[/tex]  

velocity, v = 40 m/s

A = 1[tex]m^{2}[/tex]

Solution:

For air propertiess at

[tex]P_{1}[/tex] = 1300 kPa

[tex]T_{1}[/tex] = [tex]500^{\circ}[/tex]

[tex]h_{1}[/tex] = 793kJ/K

[tex]v_{1}[/tex] = [tex]0.172\frac{m^{3}}{kg}[/tex]

and also at

[tex]P_{2}[/tex] = 100 kPa

[tex]T_{2} = 127^{\circ}[/tex]  

[tex]h_{2}[/tex] = 401 KJ/K

[tex]v_{2}[/tex] =  [tex]1.15\frac{m^{3}}{kg}[/tex]

a) Mass flow rate is given by:

[tex]m' = \frac{Av}{v_{1}}[/tex]

Now,

[tex]m = \frac{0.2\times 40}{0.172}[/tex] = 46.51 kg/s

b) for the power produced by turbine, [tex]P = m'(h_{1} - h_{2})[/tex]

[tex]P = 46.51\times(793 - 401)[/tex] = 18.231 MW

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