Answer to Question #204946 in Mechanical Engineering for Gowtham Jampala

Question

In a steam nozzle steam expands from 15 bar to 5 bar with initial temperature of 300°C and mass flow of 1 kg/s. Determine the throat and exit areas considering (i) expansion to be frictionless and, (ii) friction loss of 8% throughout the nozzle. 

Answer 1

Initial pressure(p₁) = 15 bar

Initial Temperature(T₁)= 300°C

Exit pressure(p2) = 5 bar

Nozzle efficiency (nozzle) = 100%

mass flow of steam (v₁)= 1kg/s

Discharge mass flow (v₂) = ?

From steam table, For 15 bar, 300°C, h₁ = 2943 kJ/kg s₁ = 6.926 kJ/kg.K

From steam table, For 5 bar,

hf₂ = 439.3 kJ/kg ; hfg₂ = 2244.1 kJ/kg;

sf₂ = 1.3 61 kJ/kg K ; sfg₂ = 5.937 kJ/kgK.

Since $s_1=s_2,$

s₁ = sf2 + x₂sfg₂

6.926 = 1.361 + x₂(5.937)

x₂ =0 .9373

We know that,

h₂ = hf2+x2hfg2

h₂ = 439.3+(0.9373)2244.1

h₂ = 2542KJ/Kg

Exit velocity (v₂) = Rt[(2000(2943) 2542) + 50²] = 896.91kg/s.