How Does the Steady Flow Energy Equation Apply to an Adiabatic Steam Turbine?

[AMEY PHADKE]

Homework Statement

The power output of an adiabatic steam turbine is 5 MW and inlet and exit conditions are as under
Given Inlet Pressure 2MPa Temprature 400 DEGREE CELSIUS Velocity 50m/s Elevation 10m
Exit Pressure 15 KPa Temprature 0.9 dry Velocity 180m/s Elevation 6 m
Determine the work done /kg of steam and the mass floe rate in kg/s

Homework Equations

Q-W=m(h2+v2^2/2+gZ2)-m(h1+v1^2/2+gz1) J/s

The Attempt at a Solution

I attempted to solve but can not under stand the meaning of .9 dry & how to find z1 and z2 pl. help

 

[KataKoniK]

Thank you for providing the necessary information to solve this problem. Let's break down the steps to find the work done per kilogram of steam and the mass flow rate:

1. Determine the specific enthalpy at the inlet and exit conditions:
Using steam tables or a steam properties calculator, we can find the specific enthalpy at the given inlet and exit conditions. The specific enthalpy (h) is a measure of the energy of the steam per unit mass and is usually given in units of kJ/kg.

h1 = 3218 kJ/kg (inlet condition)
h2 = 269 kJ/kg (exit condition)

2. Find the change in elevation:
The change in elevation (Δz) is given by the difference in elevation between the inlet and exit conditions. In this case, Δz = 6m - 10m = -4m (since the exit elevation is lower than the inlet elevation).

3. Calculate the change in kinetic energy:
The change in kinetic energy (ΔKE) is given by the difference in velocity between the inlet and exit conditions. In this case, ΔKE = (180 m/s)^2/2 - (50 m/s)^2/2 = 12,250 kJ/kg.

4. Calculate the work done:
Using the first law of thermodynamics, we can calculate the work done per kilogram of steam as follows:

W = Q - m(h2 + ΔKE + gΔz) + m(h1 + ΔKE + gΔz)
where Q is the heat transfer, which is equal to zero in an adiabatic process.

W = -m(h2 - h1) + mΔKE + mgΔz
W = m(h1 - h2) + mΔKE + mgΔz
W = 3218 kJ/kg - 269 kJ/kg + 12,250 kJ/kg + (9.8 m/s^2)(-4m)
W = 14,199 kJ/kg

5. Calculate the mass flow rate:
The power output of the turbine is given as 5 MW, which is equal to 5,000,000 J/s. We can use this information to calculate the mass flow rate (m) as follows:

5,000,000 J/s = m(14,199 kJ/kg)
m = 0