Question

Steam at 10 bar and 330°C is fed to an adiabatic turbine at a mass flow rate of m = 5 kg/s. The output stream is saturated steam at 1.1 bar. The inlet steam flows

through a 15 cm diameter pipe and the exit steam discharges through a 20 cm diameter pipe.

a) Calculate the velocity of the input and output streams in m/s.

b) The power generated by the turbine in kW

Answer 1

Given:

The steam is at Pi = 10 bar and temperature = 330 0C

And outlet pressure Pf = 1.1 bar

di = 15 cm do = 20 cm

a.)

As we know from the equation of continuity the outlet and inlet folw rates ar same so:

  

And   

The density of steam at 10 bar is taken as 5.147 kg/m3

So from the above equation V1 = 5.497 km/s

  

The density of steam at 11 bar is taken as 5.638 kg/m3

so the V2 = 2.822 km/s

So the velocity of inlet and outlet is calculated from equation of continuity.

b.)

Pressura 10 bar and temperature 330 0C the values of entropy and enthalpy of steam is calculated from the steam table which are as follow :

Enthalpy h = 3135.5 kj/kg

Entropy S = 7.2585 kJ/kg.K

For pressure 1.1 bar we need to find the Enthalpy value as the entropy value wil be same for that we quality (X) of the stema is calculated from the equation give below:

The values of Sf and Sfg are find out from steam table which are

Sf = 1.3388 kJ/kg.K

Sfg = 5.989 kJ/kg.K

The value of quality is X = 0.988

Enthalpy of mixture is calculated from saturated liquid properties:

hf = 430.7 kj/kg

hfg = 2248.55 kj/kg

  

From the above equation enthalpy at 1.1 bar is 2652.2674 kj/kg

So the power required is calculated as

  

So the power generated by the the turbine is 2416.163 kw. Which is calculated using steam table data and quality data which is calculated using the quality equation.