Mass and Energy Analysis for Control Volumes
The
idea
behind the turbine is that a fluid passes through and does
work against the blades which are attached to the shaft.
The shaft then rotates and the turbine produces work.
Hydroelectric power plants use turbines to generate power,
but turbines are also used in aircraft, ships, and many
other large vehicles.
Turbines
are often operational for long periods of time so that
they can be considered as steady-flow devices which
undergo a steady-flow process. During a steady-flow
process the mass, volume, and total energy content remain
constant.
Heat
transfer
from turbines is usually negligible since they are typically well
insulated. Potential energy chances are also negligible.
Problem 5-55 in Thermodynamics:
An Engineering Approach Sixth Edition (SI Units) is
a good example of a typical mass and energy analysis
problem.
The problem states that argon gas enters an adiabatic
turbine steadily at 900 kPa and 450°C with a velocity of
80 m/s and leaves at 150 kPa with a velocity of 150 m/s.
The question wants to know the exit temperature of the
argon if the power output of the turbine is 250 kW. When
we rearrange equation 3 for the work out and remove
potential energy and heat transfer we result in equation
4:
There are two things that we need to find
before we can solve the problem. The first issue is that
we aren’t given the mass flow rate. We can use the ideal
gas law to solve for the specific volume and then find the
mass flow rate using the definition of the mass flow rate.
Using the relationship that the change in
enthalpy for an ideal gas can be expressed as the product
of the specific heat at constant pressure and change in
temperature we can now solve the problem.
For dimensional homogeneity, the change
in kinetic energy needs to be converted to kJ/kg so the
denominator becomes 2000 instead of 2. When you solve the
equation you yield a temperature at the exit of:
