How to find throat area at the nozzle in single stage turbine? | GATE AE | Propulsion




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Q : In a single-stage turbine designed on free vortex theory the following particulars are given : Mass flow through turbine – 18 kg/s; Inlet total head temperature – 1000 K; Inlet total head pressure – 4 kgf/cm2. The gas leaves the stage in an axial direction. Assuming that all the nozzle loss amounts to 4 per cent of the isentropic heat drop across the nozzle, find the total throat area of the nozzle. Assume a mean specific heat at constant pressure of 0·274 throughout the cycle.

Given data,

m =18 kg/s

Tt = 1000 K

Pt = 4 kgf/cm2

cp= 0·274

Solution:

R = 29.27 kgf m/kg°K

γ = 1.4

g = 9.81 m/s2

J = 427 kgf.m/kcal

Nozzle throat area, A = m/(ρU )…(1)

Perfect gas equation, ρ = P/(RT )…(2)

 Isentropic relation,

 P/Pt = (2/(γ+1))γ/(γ-1)

 T/Tt = (P/Pt )(γ-1)/γ = 2/(γ+1)

P = 4×(2/(1.4+1))^(1.4/(1.4-1)) = 2.168 kgf/cm2

 T=1000×2/(1.4+1) = 858 K

From eqn.(2)

ρ = (2.168×104)/(29.27×858) = 0.863 m3/kg

Throat velocity,

 U =√(2gJcp (Tt-T ))

 = √(2×9.81×427×0.274(1000-858) )

 = 572 m/s

From eqn.(1)

A = 18/(0.863×572) = 364 cm2

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