Question 5.3: Steam is expanded in a set of nozzles from 10 bar and 200ºC ...

Steam pressure at the entry to the steam nozzles,

p_{1}  =    10 bar, 200ºC

Steam exit pressure,                p_{1}    =  5 bar

We know that,                            \frac{ p_{2} }{ p_{1} }  =   (\frac{2}{n  +  1})^{\frac{n}{n  –  1}}    =   [\frac{2}{(13  +  1)}] ^{\frac{1.3}{0.3}}

=  (\frac{2}{2.3})^{4.333}      = 0.5457

∴                                            p_{2}  =  p_{1}    ×   0.5457    =    10   ×   0.5457  \simeq   5.5  bar

Since throat pressure ( p_{2} ) is greater than the exit pressure, the nozzle used is convergent-divergent nozzle. The minimum area will be at throat, where the pressure is 5.5 bar.

From Mollier chart,                        h_{1}    –   h_{2}  \simeq    120    kJ / kg 

Specific volume,                                 v \simeq   0.345 m³/kg

Velocity at the throat,                      C_{2}  =  44.72  \sqrt{120} = 489.88  m/s 

Throat area,                                    A_{2}  =  \frac{\dot{m}v}{C_{2}}  =  \frac{3  ×   0.345}{489.88}   =  0.0021 m².