This document discusses energy analysis of steady-flow systems such as turbines, compressors, and nozzles. It provides the definitions and equations for steady-flow mass and energy balances in control volumes. Examples are also given to demonstrate how to use these equations to analyze steady-flow devices and calculate properties like mass flow rate and power. Key concepts covered include the steady-flow assumption of constant properties, the forms of the mass and energy balance equations, and examples of calculations for diffusers, compressors and turbines.

1. Lecture# 10
MASS AND ENERGY ANALYSIS
OF CONTROL VOLUMES
ENERGY ANALYSIS OF STEADY-FLOW SYSTEMS:
• A large number of engineering devices such as turbines,
compressors, and nozzles operate for long periods of time under the
same conditions once the transient start-up period is completed
and steady operation is established, and they are classified as
steady-flow devices.
• Processes involving such devices can be represented reasonably
well by a somewhat idealized process, called the steady-flow
process , which was defined in before as a process during which
a fluid flows through a control volume steadily. That is, the
fluid properties can change from point to point within the
control volume, but at any point, they remain constant during
the entire process. (Remember, steady means no change with
time.)

2. •The fluid properties at an inlet or exit remain constant during a steady
flow process.
•It follows that the mass flow rate of the fluid at an opening must
remain constant during a steady flow process.
•The mass balance for a general steady-flow system was given as:
The mass balance for a single-stream (one-inlet and one-outlet)
steady-flow system was given as:
(2-2)
(2-1)

3. •Where the subscripts 1 and 2 denote the inlet and the exit states,
respectively, ρ is density, V is the average flow velocity in the flow
direction, and A is the cross-sectional area normal to flow direction.
Noting that energy can be transferred by heat, work, and mass
only, the energy balance in Eq. 2-3 for a general steady-flow
system can also be written more explicitly as:
(2-3)
(2-4)

4. Dividing Eq. 2.5 by m gives the energy balance on a unit-mass basis as
(2-5)
(2-6)

5. where q= Q·/m· and w= W·/m· are the heat transfer and
work done per unit mass of the working fluid, respectively.
When the fluid experiences negligible changes in its kinetic
and potential energies (that is, ∆ke ≈ 0, ∆pe ≈ 0), the energy
balance equation is reduced further to

6. SOME STEADY-FLOW ENGINEERING DEVICES
1- Nozzles and Diffusers
. A nozzle is a device that increases the velocity of
a fluid at the expense of pressure.
A diffuser is a device that increases the pressure of a fluid by
slowing it down.

7. FIGURE 9– 1
Nozzles and diffusers are shaped so that they cause large
changes in fluid velocities and thus kinetic energies.

8. EXAMPLE 1:
Air at 10°C and 80 kPa enters the diffuser of a jet engine
steadily with a velocity of 200 m/s. The inlet area of the
diffuser is 0.4 m2. The air leaves the diffuser with a velocity
that is very small compared with the inlet velocity.
Determine (a) the mass flow rate of the air and
(b) the temperature of the air leaving the diffuser.
Solution: Air enters the diffuser of a jet engine steadily
at a specified velocity. The mass flow rate of air and the
temperature at the diffuser exit are to be determined

9. (a) To determine the mass flow rate, we need to find
the specific volume of the air first. This is determined
from the ideal-gas relation at the inlet conditions.

12. 2- Turbines and Compressors
In steam, gas, or hydroelectric power plants, the
device that drives the electric generator is the turbine.
As the fluid passes through the turbine, work is done
against the blades, which are attached to the shaft. As
a result, the shaft rotates, and the turbine produces
work.
Compressors, as well as pumps and fans, are devices
used to increase the pressure of a fluid. Work is
supplied to these devices from an external source
through a rotating shaft. Therefore, compressor
involve work inputs.

13. •A fan increases the pressure of a gas slightly and is
mainly used to mobilize a gas.
• A compressor is capable of compressing the gas to very
high pressures.
•Pumps work very much like compressors except that
they handle liquids instead of gases.
•Note that:
•turbines produce power output whereas
compressors, pumps, and fans require power input.
Heat transfer from turbines is usually negligible (Q = 0)
since they are typically well insulated.

14. EXAMPLE :2
Air at 100 kPa and 280 K is compressed steadily to 600
kPa and 400 K. The mass flow rate of the air is 0.02 kg/s,
and a heat loss of 16 kJ/kg occurs during the process.
Assuming the changes in kinetic and potential energies
are negligible, determine the necessary power input to
the compressor

15. EXAMPLE 3 :
The power output of an adiabatic steam turbine is 5 MW,
and the inlet and the exit conditions of the steam are as
indicated in Fig.
(a) Compare the magnitudes of h, ke, and pe.
(b) Determine the work done per unit mass of the steam
flowing through the turbine.
(c) Calculate the mass flow rate of the steam

16. a) At the inlet, steam is in a superheated vapor state,
and its enthalpy is
P1 = 2 Mpa ,T1= 4000C ,h1 =3248.4 kJ/kg (Table A–6)
At the turbine exit, we obviously have a saturated liquid–vapor
mixture at 15-kPa pressure. The enthalpy at this state is
h2= hf + x2hfg = [225.94 (0.9)(2372.3)] kJ/kg = 2361.01 kJ/kg