Given Sleam at 1500 psia 1000 degree F and 2 fts enters a t

Given : Sleam at 1500 psia, 1000 degree F and 2 ft/s enters a turbine operating at steady stata, 22% of the entering mass flow is extracted through port 2 at 160 pala, 450 degree F and 10 ft/s. The rest exits as a two phase mixture with a quality of 85%, velocity of 150 ft/s and pressure of 1 pais at port 3. The turbine develops a power output of 9 times 10^8 BTU Find: determine the mass flow rate of steam entering the turbine.

Solution

Solution:

v1 = 2 ft/s

v2 = 10ft/s

v3 = 150 ft/s

W= 9 x 10^8 btu/h = 250000 btu/s

here we can use

Steady energy equation

which states engery entering is equal to energy coming out

(enthalpy + KE + PE + Heat)inlet = (enthalpy + KE + PE + Work)outlet

Using steam table

enthaply at 1500 psi 1000F

h1=2720.5 kJ/kg = 2578.53 btu/kg

similarly enthalpy at

150 psi & 450F

h2=2778 kJ/kg= 2633.03 btu/kg

at port 3 pressure is 1 psi with quality x =0.85

h = 151.5 + 0.85 x (2415.9)

= 2205.01 kJ/kg = 2089 btu/kg

using steady energy equation at all ports & taking massflow as m , 0.22m & 0.78 m at 1,2& 3 ports respectively

h1 + KE1= h2 + KE2 + h3 + KE3 + W

m(2578.53) + 0.5 x m (2)^2 = 0.22m(2633.03) + 0.5x0.22m(10)^2 + 0.78m(2089) + 0.5(0.78)(150)^2 - 250 x 10^3

on solving we get m equal to

m = 29.71 kg/s