This includes sketches symbolic equations and solution steps

This includes sketches, symbolic equations and solution steps. Place a box around each numeric answer and don\'t forget units. Given: Steam at 1500 psia, 1000 degreeF and 2 ft/s enters a turbine operating at steady state. 22% of the entering mass flow is extracted through port 2 at 160 psia, 450 degreeF 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 psia at port 3. The turbine develops a power output of 9 degree 10^8 BTU/hr. Find: Determine the mass flow rate of steam entering the turbine

Solution

Given Data:

W= 9 x 10^8 btu/hr = 25 x 10^4 btu/s

v1 = 2 ft/s

v2 = 10 ft/s

v3 = 150 ft/s

From Steady flow energy equation:

(enthalpy + KE + PE + Q) = (enthalpy + KE + PE + W)

from steam tables

enthalpy at 1500 psia & 1000F

h1=2578.53 btu/kg

similarly

enthalpy at 160 psia & 450F

h2 = 2633.03 btu/kg

enthalpy at 3rd outlet with quality 0.85 & 1 psia is

h3 = 2089 btu/kg

taking mass flow m at inlet & 0.22m at second port & remaining that is 0.78m at port 3 & PE as zero

m(2578.53) + 0.5 x 0.22m(2)^2 = 0.22m(2633.03) + 0.5x0.22m(10)^2 + 0.78m(2089) + 0.5x0.78m(150)^2 - 25 x 10^4

m= 29.71 kg