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1 Consider a steam turbine operating at steady-state. There is one inlet and one

ID: 1861820 • Letter: 1

Question

1

Consider a steam turbine operating at steady-state. There is one inlet and one outlet, and adiabatic conditions may be assumed. Apply the first law for a control-volume to determine the power output. Inlet conditions are 125 bars, 450 degree C, and average flow speed of 100 m/s. The inlet is area 100 cm2 at a height of 2 m above the datum. The exit quality is 90% at 1 bar and average flow speed of 50 m/s, at a height of 50 cm above the datum. Determine the following: the mass flow rate in kg/s the change in specific enthalpy in kJ/kg the change in kinetic energy per unit mass in kJ/kg the change in potential energy per unit mass in kJ/kg the shaft work in kJ/kg the exit area in cm2 the power output of the turbine in kW the ( plusminus ) percent power output due to changes in enthalpy the ( plusminus ) percent power output due to changes in kinetic energy the ( plusminus ) percent power output due to changes in potential energy

Explanation / Answer

At Inlet P = 12500 KPa and T = 450 Deg

v1 = 0.02299 m^3/Kg

h1 = 3199.78 KJ/Kg

these values are from steam tables

Density at inlet(p1) = 1/v1 = 1/0.02299 = 43.497 Kg/m^3

At exit P= 100Kpa and x =0.9

vf = 0.001043 and vg= 1.694

v2 = (1-x)*vf + x*vg = 1.5247 m^3/Kg

Density at exit(p2) = 1/v2 = 0.656 Kg/m^3

hf = 417.44 and hg = 2675.46

h2 = (1-x)*hf + x*hg = 2449.658 KJ/Kg

a)Mass flow Rate = p1*V1*A1 = 43.497*100*100*10^-4 = 43.497 Kg/s

b) Change in specific enthalpy = h1-h2 = 3199.78 - 2449.658 = 750.12 KJ/Kg

c) Change in KE = V1^2 - V2^2 = (100^2 - 50^2) = 7.5 KJ/Kg

d) Change in PE = g(Z1-Z2) = 9.8*(2-0.5) = 0.0147 KJ/Kg

e) shaft work = Change in specific enthalpy + Change in KE + Change in PE

Shaft Work = 750.12 + 7.5 + 0.0147 = 757.637 KJ/Kg

f) mass flow is constant

p2*V2*A2 = 43.497

0.656*50*A2 = 3.497

A2 = 1066.375 cm^2

g)Percent Power Due to enthalpy = (Change in specific enthalpy/Shaft Work)*100 = (750.12/757.637)*100 = 99 percent

h)Percent Power Due to KE = (7.5/757.637)*100 = 0.989%

i)Percent Power Due to PE = (0.0147/757.637)*100 = 0.0019%