- #1
Northbysouth
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Homework Statement
Air expands through a turbine from 8 bar, 960 K to 1 bar, 450 K. The inlet velocity is small compared to the exit velocity of 90 m/s, The turbine operates at a steady state and develops a power output of 2500 kW. Heat transfer between the turbine and it's surroundings and potential energy effects are negligible. Modeling air as an ideal gas, calculate the mass flow rate of air, in kg/s, and the exit area, in m2
Homework Equations
m' = ρvA
ρ = p/RT
du = dQ - dw
h = u + pv
1Q2+m'i(hi+v2i/2 + gzi) = m'e(he + ve2/2 + gze)
p1 = 800,000 Pa
T1 = 960 K
v1 = 0m/s
p2 = 100,000 Pa
T = 450 K
v2 = 90 m/s
The Attempt at a Solution
Using du = dQ - dw I know that
dw = -2500 kW
I also have:
m'i(hi) = m'e(he + v2e/2)
To calculate enthalpy
h = pv
hi = 2500 kW
he = 2500 kW + (100,000 Pa)(90 m/s)
he = 11500000 W
With this information I should then be able to plug it into the large equation (The 1st law of thermodynamics I believe) and hence get mi
But when I do this I get mi = 0.2777 kg/s which isn't right. My TA said the answer is round about 4 kg/s.
Help is appreciated. Thank you