VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED...
-
Upload
winfred-dorsey -
Category
Documents
-
view
227 -
download
1
Transcript of VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED...
![Page 1: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/1.jpg)
VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY
AERO ENGINEERING THERMODYNAMICSSEM:III YEAR:II
PREPARED BYMr.B.Narendhiran
DEPARTMENT OF AERONAUTICALASSISTANT PROFESSOR
![Page 2: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/2.jpg)
UNIT-I
![Page 3: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/3.jpg)
Thermodynamic Systems, States and Processes
Objectives are to:• define thermodynamics systems and states of systems• explain how processes affect such systems• apply the above thermodynamic terms and ideas to the laws of
thermodynamics
![Page 4: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/4.jpg)
“Classical” means Equipartition Principle applies: each molecule has average energy ½ kT per in thermal equilibrium.
Internal Energy of a Classical ideal gasInternal Energy of a Classical ideal gas
At room temperature, for most gases:
monatomic gas (He, Ne, Ar, …) 3 translational modes (x, y, z)
kTEK2
3
diatomic molecules (N2, O2, CO, …) 3 translational modes (x, y, z) + 2 rotational modes (wx, wy)
kTEK2
5
pVkTNU2
3
2
3
![Page 5: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/5.jpg)
Internal Energy of a Gas
pVkTNU2
3
2
3
A pressurized gas bottle (V = 0.05 m3), contains helium gas (an ideal monatomic gas) at a pressure p = 1×107 Pa and temperature T = 300 K. What is the internal thermal energy of this gas?
J105.705.0105.1 537 mPa
![Page 6: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/6.jpg)
Changing the Internal Energy
U is a “state” function --- depends uniquely on the state of the system in terms of p, V, T etc.
(e.g. For a classical ideal gas, U = )
WORK done by the system on the environment
Thermal reservoir
HEAT is the transfer of thermal energy into the system from the surroundings
There are two ways to change the internal energy of a system:
Work and Heat are process energies, not state functions.
Wby = -Won
Q
![Page 7: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/7.jpg)
Work Done by An Expanding Gas
The expands slowly enough tomaintain thermodynamic equilibrium.
PAdyFdydW
Increase in volume, dV
PdVdW +dV Positive Work (Work isdone by the gas)
-dV Negative Work (Work isdone on the gas)
![Page 8: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/8.jpg)
A Historical Convention
Energy leaves the systemand goes to the environment.
Energy enters the systemfrom the environment.
+dV Positive Work (Work isdone by the gas)
-dV Negative Work (Work isdone on the gas)
![Page 9: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/9.jpg)
Total Work Done
PdVdW
f
i
V
V
PdVW
To evaluate the integral, we must knowhow the pressure depends (functionally)on the volume.
![Page 10: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/10.jpg)
Pressure as a Function of Volume
f
i
V
V
PdVW
Work is the area underthe curve of a PV-diagram.
Work depends on the pathtaken in “PV space.”
The precise path serves to describe the kind of process that took place.
![Page 11: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/11.jpg)
Different Thermodynamic Paths
The work done depends on the initial and finalstates and the path taken between these states.
![Page 12: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/12.jpg)
Work done by a Gas
Note that the amount of work needed to take the system from one state to another is not unique! It depends on the path taken.
We generally assume quasi-static processes (slow enough that p and T are well defined at all times):
This is just the area under the p-V curve
f
i
V
Vby dVpW
V
p p
V
p
V
dWby = F dx = pA dx = p (A dx)= p dV
Consider a piston with cross-sectional area A filled with gas. For a small displacement dx, the work done by the gas is:
dx
When a gas expands, it does work on its environment
![Page 13: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/13.jpg)
What is Heat?
Q is not a “state” function --- the heat depends on the process, not just on the initial and final states of the system
Sign of Q : Q > 0 system gains thermal energyQ < 0 system loses thermal energy
Up to mid-1800’s heat was considered a substance -- a “caloric fluid” that could be stored in an object and transferred between objects. After 1850, kinetic theory.
A more recent and still common misconception is that heat is the quantity of thermal energy in an object.
The term Heat (Q) is properly used to describe energy in transit, thermal energy transferred into or out of a system from a thermal reservoir …
(like cash transfers into and out of your bank account)
Q U
![Page 14: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/14.jpg)
An Extraordinary Fact
The work done depends on the initial and finalstates and the path taken between these states.
BUT, the quantity Q - W does not dependon the path taken; it depends only on the initial and final states.
Only Q - W has this property. Q, W, Q + W,Q - 2W, etc. do not.
So we give Q - W a name: the internal energy.
![Page 15: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/15.jpg)
-- Heat and work are forms of energy transfer and energy is conserved.
The First Law of Thermodynamics
(FLT)
U = Q + Won
work doneon the system
change intotal internal energy
heat added
to system
or
U = Q - Wby
State Function Process Functions
![Page 16: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/16.jpg)
1st Law of Thermodynamics
• statement of energy conservation for a thermodynamic system• internal energy U is a state variable• W, Q process dependent
system done work : positive
system addedheat : positive
by
to
W
Q
WQU
![Page 17: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/17.jpg)
The First Law of Thermodynamics
bydWdQdE int
What this means: The internal energy of a systemtends to increase if energy is added via heat (Q)and decrease via work (W) done by the system.
ondWdQdE int
. . . and increase via work (W) done on the system.
onby dWdW
![Page 18: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/18.jpg)
Isoprocesses
• apply 1st law of thermodynamics to closed system of an ideal gas
• isoprocess is one in which one of the thermodynamic (state) variables are kept constant
• use pV diagram to visualise process
![Page 19: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/19.jpg)
Isobaric Process• process in which pressure is kept constant
![Page 20: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/20.jpg)
Isochoric Process• process in which volume is kept constant
![Page 21: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/21.jpg)
Isothermal Process• process in which temperature is held constant
![Page 22: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/22.jpg)
Isochoric (constant volume)
Thermodynamic processes of an ideal gas( FLT: U = Q - Wby )
V
p
1
2
pVTNkU
0pdVWby
FLT: UQ Q
Temperature changes
Isobaric (constant pressure)
V
p
1 2
VpTNkU FLT: VpWUQ by 1
VppdVWby
Q
p
Temperature and volume change
![Page 23: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/23.jpg)
Isothermal (constant temperature)
2
1
V
V 1
2by V
VnNkTdVpW
0U
FLT: byWQ
p
V
1
2
( FLT: U = Q - Wby )
V
1p
Q
Thermal Reservoir
T
Volume and pressure change
![Page 24: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/24.jpg)
The First Law Of Thermodynamics
§2-1.The central point of first law
§2-2. Internal energy and total energy
§2-3.The equation of the first law
§2-4.The first law for closed system
§2-5.The first law for open system
§2-6.Application of the energy equation
![Page 25: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/25.jpg)
§2-1.The central point of first law
1.Expression In a cyclic process, the algebraic sum of the
work transfers is proportional to the algebraic sum of the heat transfers.
Energy can be neither created nor destroyed; it can only change forms.
The first law of thermodynamics is simply a statement of energy principle.
![Page 26: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/26.jpg)
§2-1.The central point of first law
2.Central point The energy conservation law is used to
conservation between work and heat.
Perpetual motion machines of the first kind.(PMM1)
Heat: see chapter 1; Work: see chapter 1;
![Page 27: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/27.jpg)
§2-2.Internal Energy
1.Definition:
Internal energy is all kinds of micro-energy in system.
2. Internal energy is property
It include:
a) Kinetic energy of molecule (translational kinetic, vibration, rotational energy)
b) Potential energy
c) Chemical energy
d) Nuclear energy
![Page 28: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/28.jpg)
§2-2.Internal Energy
3.The symbol u: specific internal energy, unit –J/kg, kJ/kg ; U: total internal energy, unit – J, kJ;4.Total energy of system E=Ek+Ep+U Ek=mcf
2/2 Ep=mgz ΔE=ΔEk+ΔEp+ΔU per unit mass: e=ek+ep+u Δe=Δek+Δep+Δu
![Page 29: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/29.jpg)
§2-3. The equation of the first law
1. The equation
( inlet energy of system) – (outlet energy of system) = (the change of the total energy of the system)
Ein-Eout=ΔEsystem
![Page 30: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/30.jpg)
§2-4.The first law in closed system1. The equation
Ein-Eout=ΔEsystem
WQ
![Page 31: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/31.jpg)
§2-4.The first law in closed system
Q-W=ΔEsystem=ΔU
Q=ΔU+W
Per unit mass:
q= Δu+w
dq=du+dw
If the process is reversible, then:
dq=du+pdv
This is the first equation of the first law.
Here q, w, Δu is algebraic.
![Page 32: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/32.jpg)
§2-4.The first law in closed system
The only way of the heat change to mechanical energy is expansion of working fluid.
![Page 33: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/33.jpg)
§2-5. The first law in open system
1. Stead flow
For stead flow, the following conditions are fulfilled:
① The matter of system is flowing steadily, so that the flow rate across any section of the flow has the same value;
② The state of the matter at any point remains constant;
③ Q, W flow remains constant;
![Page 34: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/34.jpg)
§2-5. The first law in open system2. Flow work
Wflow=pfΔs=pV
wflow=pvp
V
![Page 35: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/35.jpg)
§2-5. The first law in open system
3. 技术功 “ Wt” are expansion work and the
change of flow work for open system.
4. 轴功 “ Ws” is “ Wt” and the change of kinetic
and potential energy of fluid for open system.
![Page 36: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/36.jpg)
§2-5. The first law in open system
5. Enthalpy
for flow fluid energy:
+mcf2/2+mgzU+pV
H =U+pV unit: J, kJ
For Per unit mass:
h=u+pv unit: J/kg, kJ/kg
![Page 37: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/37.jpg)
§2-5. The first law in open system6. Energy equation for steady flow open system
U1+p1V1H1, mcf1
2/2, mgz1
U2+p2V2H2 , mcf22/2, mgz2
QW
![Page 38: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/38.jpg)
§2-5. The first law in open system
12
111 2
1mgzcmHQE fin
22
222 2
1mgzcmHWE fsout
0 systemE
0)2
1()
2
1( 2
2221
2111 mgzmcHWmgzcmHQ fsf
![Page 39: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/39.jpg)
§2-5. The first law in open system
sf WzmgcmHQ 2
2
1
0)2
1()
2
1( 2
2221
211 gzchwgzchq fsf
Per unit mass:
sf wzgchq 2
2
1
![Page 40: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/40.jpg)
§2-5. The first law in open system
vdphq
If neglect kinetic energy and potential energy , then:
twhq
If the process is reversible, then:
This is the second equation of the first law.
![Page 41: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/41.jpg)
W
§2-5. The first law in open system7. Energy equation for the open system
Inlet flows Out flows
Q
1
2
… …
i
Open system
1
2
……
j
![Page 42: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/42.jpg)
§2-5. The first law in open systemEnergy equation for the open system
...2
...2
...
)2
1()
2
1( systemjjfjj
n
i
iifi
n
iis EmzgchmzgchWQ
![Page 43: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/43.jpg)
§2-6. Application of The Energy Equation1. Enginea). Turbines energy equation:
Ein-Eout=Esystem=0
Wi=H2-H1
wi=h2-h1
U1+p1V1H1, mcf1
2/2, mgz1
U2+p2V2H2
mcf22/2, mgz2
Q WiQ≈0
=0
=0
![Page 44: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/44.jpg)
§2-6. Application of The Energy Equation
1. Engine
b). Cylinder engine energy equation:
Wt=H2-H1+Q=(U+pV) 2-(U+pV) 1 +Q
Q Wt
H1
H2
Ek1, Ep1≈0
Ek1, Ep1≈0
![Page 45: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/45.jpg)
§2-6. Application of The Energy Equation
2. Compressors
Energy equation:
Wc=- Wt =H2-H1
Wc
H1
H2
Ek1, Ep1≈0
Ek1, Ep1≈0
Q≈0
![Page 46: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/46.jpg)
§2-6. Application of The Energy Equation
3. Mixing chambers
Energy equation:
m1h1 + m2h2 -m3h3=0
Cold water: m1h1
hot water: m2h2
Mixing water: m3h3
![Page 47: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/47.jpg)
§2-6. Application of The Energy Equation
4. Heat exchangers
Energy equation:
m1h1
m 2 h 2
m3h3
m4h4
m5h5
m6h6
(m1h1 + m2h2 + m3h3)-(m4h4 + m5h5 + m6h6)= 0
![Page 48: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/48.jpg)
§2-6. Application of The Energy Equation
5. Throttling valves
Energy equation:
h1 -h2 =0
h1
h2
![Page 49: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/49.jpg)
Unit - II
Air Cycles
![Page 50: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/50.jpg)
OTTO CYCLE
![Page 51: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/51.jpg)
![Page 52: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/52.jpg)
![Page 53: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/53.jpg)
OTTO CYCLE
Efficiency is given by
Efficiency increases with increase in compression ratio and specific heat ratio (γ) and is independent of load, amount of heat added and initial conditions.
1
11
r
![Page 54: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/54.jpg)
![Page 55: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/55.jpg)
r
1 0
2 0.242
3 0.356
4 0.426
5 0.475
6 0.512
7 0.541
8 0.565
9 0.585
10 0.602
16 0.67
20 0.698
50 0.791
CR ↑from 2 to 4, efficiency ↑ is 76%
CR from 4 to 8 efficiency is 32.6
CR from 8 to 16 efficiency 18.6
![Page 56: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/56.jpg)
![Page 57: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/57.jpg)
OTTO CYCLEMean Effective Pressure
It is that constant pressure which, if exerted on the piston for the whole outward stroke, would yield work equal to the work of the cycle. It is given by
21
32
21
VV
Q
VV
Wmep
![Page 58: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/58.jpg)
OTTO CYCLEMean Effective Pressure
We have:
Eq. of state:
To give:
rV
V
VVVV
11
1
1
1
2121
1
101 p
T
m
RMV
r
TMRmp
Q
mep1
1
10
132
![Page 59: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/59.jpg)
OTTO CYCLEMean Effective Pressure
The quantity Q2-3/M is heat added/unit mass equal to Q’, so
r
TRmp
Q
mep1
1
10
1
![Page 60: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/60.jpg)
OTTO CYCLEMean Effective Pressure
Non-dimensionalizing mep with p1 we get
Since:
1011
1
1
TR
mQ
rp
mep
10 vcm
R
![Page 61: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/61.jpg)
OTTO CYCLEMean Effective Pressure
We get
Mep/p1 is a function of heat added, initial temperature, compression ratio and properties of air, namely, cv and γ
11
1
1
11
rTc
Q
p
mep
v
![Page 62: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/62.jpg)
Choice of Q’
We have
For an actual engine:
F=fuel-air ratio, Mf/Ma
Ma=Mass of air,
Qc=fuel calorific value
M
QQ 32
cyclekJinQFM
QMQ
ca
cf
/
32
![Page 63: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/63.jpg)
Choice of Q’
We now get:
Thus:
M
QFMQ ca
rV
VVAnd
V
VV
M
MNow a
11
1
21
1
21
rFQQ c
11
![Page 64: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/64.jpg)
Choice of Q’
For isooctane, FQc at stoichiometric conditions is equal to 2975 kJ/kg, thus
Q’ = 2975(r – 1)/r
At an ambient temperature, T1 of 300K and cv for air is assumed to be 0.718 kJ/kgK, we get a value of Q’/cvT1 = 13.8(r – 1)/r.
Under fuel rich conditions, φ = 1.2, Q’/ cvT1 = 16.6(r – 1)/r.
Under fuel lean conditions, φ = 0.8, Q’/ cvT1 = 11.1(r – 1)/r
![Page 65: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/65.jpg)
OTTO CYCLEMean Effective Pressure
Another parameter, which is of importance, is the quantity mep/p3. This can be obtained from the following expression:
1
11
11
13
rTcQrp
mep
p
mep
v
![Page 66: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/66.jpg)
![Page 67: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/67.jpg)
![Page 68: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/68.jpg)
Diesel CycleThermal Efficiency of cycle is given by
rc is the cut-ff ratio, V3/V2
We can write rc in terms of Q’:
1
111
1c
c
r
r
r
11
1
rTc
Qr
pc
![Page 69: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/69.jpg)
We can write the mep formula for the diesel cycle like that for the Otto cycle in
terms of the η, Q’, γ, cv and T1:
11
1
1
11
rTc
Q
p
mep
v
![Page 70: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/70.jpg)
Diesel CycleWe can write the mep in terms of γ, r and
rc:
The expression for mep/p3 is:
11
11
1
r
rrrr
p
mep cc
rp
mep
p
mep 1
13
![Page 71: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/71.jpg)
DUAL CYCLE
![Page 72: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/72.jpg)
![Page 73: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/73.jpg)
![Page 74: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/74.jpg)
Dual Cycle
The Efficiency is given by
We can use the same expression as before to obtain the mep.
To obtain the mep in terms of the cut-off and pressure ratios we have the following expression
11
111
1cpp
cp
rrr
rr
r
![Page 75: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/75.jpg)
Dual Cycle
For the dual cycle, the expression for mep/p3
is as follows:
11
111
1
r
rrrrrrrr
p
mep cppcp
![Page 76: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/76.jpg)
Dual Cycle
For the dual cycle, the expression for mep/p3
is as follows:
11
111
1
r
rrrrrrrr
p
mep cppcp
3
1
13 p
p
p
mep
p
mep
![Page 77: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/77.jpg)
Dual Cycle
We can write an expression for rp the pressure ratio in terms of the peak pressure which is a known quantity:
We can obtain an expression for rc in terms of Q’ and rp and other known quantities as follows:
rp
prp
1
1
3
![Page 78: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/78.jpg)
Dual Cycle
We can also obtain an expression for rp in terms of Q’ and rc and other known quantities as follows:
111
11
pvc rrTc
Qr
c
vp r
rTcQ
r1
111
![Page 79: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/79.jpg)
![Page 80: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/80.jpg)
![Page 81: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/81.jpg)
First Law of Thermodynamics Review
SIin kJ/kg of units has (work) W wherepower
SIin kJ/kg of units has Q wherefer heat trans of rate
:negligible are changesenergy potential and kinetic
& exists stream fluid 1only if
22
:LawFirst State-Steady22
mWW
mQQ
hhWQ
gzV
hmgzV
hmWQ
ie
ii
iee
e
![Page 82: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/82.jpg)
Vapor Power Cycles
• In these types of cycles, a fluid evaporates and condenses.
• Ideal cycle is the Carnot
• Which processes here would cause problems?
![Page 83: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/83.jpg)
Ideal Rankine Cycle• This cycle follows the idea of the Carnot
cycle but can be practically implemented.1-2 isentropic pump 2-3 constant pressure heat
addition
3-4 isentropic turbine 4-1 constant pressure heat rejection
![Page 84: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/84.jpg)
Ideal Cycle Analysis
• h1=hf@ low pressure (saturated liquid)
• Wpump (ideal)=h2-h1=vf(Phigh-Plow)
– vf=specific volume of saturated liquid at low pressure
• Qin=h3-h2 heat added in boiler (positive value)– Rate of heat transfer = Q*mass flow rate
– Usually either Qin will be specified or else the high temperature and pressure (so you can find h3)
![Page 85: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/85.jpg)
Ideal Cycle Analysis, cont.
• Qout=h4-h1 heat removed from condenser (here h4 and h1 signs have been switched to keep this a positive value)
• Wturbine=h3-h4 turbine work
– Power = work * mass flow rate
• h4@ low pressure and s4=s3
![Page 86: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/86.jpg)
Deviations from Ideal in Real Cycles• Pump is not ideal
• Turbine is not ideal
• There will be a pressure drop across the boiler and condenser
• Subcool the liquid in the condenser to prevent cavitation in the pump. For example, if you subcool it 5°C, that means that the temperauture entering the pump is 5°C below the saturation temperature.
pump
factual
actual
idealpump
PPvWW
W 12
equation pump theof inversean is that thisnote ideal
actualturbine W
W
![Page 87: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/87.jpg)
Reheat Cycle
• Allows us to increase boiler pressure without problems of low quality at turbine exit
![Page 88: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/88.jpg)
Regeneration• Preheats steam entering boiler using a
feedwater heater, improving efficiency– Also deaerates the fluid and reduces large
volume flow rates at turbine exit.
![Page 89: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/89.jpg)
Unit – III
AIR-COMPRESSORS
![Page 90: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/90.jpg)
Reciprocating Compressors Scroll Compressors Screw Compressors Turbo Compressors Roller Type Compressors Vane Type Compressors
![Page 91: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/91.jpg)
Refrigeration Technology
Main Types of Compressors The compressor is the heart of a mechanical refrigeration system.
There is the need for many types of compressors because of the variety of refrigerants and the capacity, location and application of the systems.
Generally, the compressor can be classified into two basic types: positive displacement and roto-dynamic.
Chapter10. Compressors
![Page 92: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/92.jpg)
92
Refrigeration Technology
As shown in Fig.10-1, the positive displacement family includes reciprocating compressors and rotary compressors.
According to the movement of compression components, the rotary compressors can be further classified as scroll, screw, roller-type and vane type.
The roto-dynamic compressor which is also called centrifugal or turbo compressor, is classified as radial flow and axial flow types according to the flow arrangement.
Chapter10. Compressors
Rotary Turbo/Centrifugal
Roto-dynamicPositive Displacement
Reciprocating
compressors
roller-type
vane-type rotary
Scroll Screw
Fig.10-1 .The classification of compressors
![Page 93: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/93.jpg)
93
Refrigeration Technology
10-1.Reciprocating Compressors
Chapter10. Compressors
![Page 94: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/94.jpg)
Refrigeration Technology
1. The Construction of Reciprocating Compressors
Fig.10-2 Cutaway view of small two-cylinder reciprocating compressor[12]
Chapter10. Compressors
Reciprocating compressor compresses the vapor by moving piston in cylinder to change the volume of the compression chamber, as shown in Fig.10-2.
The main elements of a reciprocating compressor include piston, cylinder, valves, connecting rod, crankshaft and casing.
![Page 95: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/95.jpg)
Refrigeration Technology
A wide variety of compressor designs can be used on the separable unit including horizontal, vertical, semi-radial and V-type.
However, the most common design is the horizontal, balanced-opposed compressor because of its stability and reduced vibration.
Chapter10. Compressors
![Page 96: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/96.jpg)
Refrigeration Technology
2. Principle of Operation Fig. 10-3 shows single-acting piston actions in the cylinder of a
reciprocating compressor. The piston is driven by a crank shaft via a connecting rod. At the top of the cylinder are a suction valve and a discharge valve. A reciprocating compressor usually has two, three, four, or six
cylinders in it.
Fig.10-3 The compression cycle [13]
Chapter10. Compressors
![Page 97: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/97.jpg)
97
Refrigeration Technology
Fig.10-4 Principle of operation of a reciprocating compressor
Chapter10. Compressors
2
4
3
Clearance
Discharge volume
Suction intake volume
Total cylinder volume
Piston displacement
volume
pressure
1
The states of the refrigerant in a reciprocating compressor can be expressed by four lines on a PV diagram as shown in Fig.10-4.
![Page 98: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/98.jpg)
Refrigeration Technology
3. Clearance Space and Clearance Fraction In order to prevent the piston from striking the valve plate, a clearance
volume must be allowed at the end of the piston compression stroke.
Manufacturing design tolerances require this to allow for reasonable bearing wear, which would effectively lengthen the stroke.
The space between the bottom and top of the valve assembly adds extra to the clearance volume.
Chapter10. Compressors
![Page 99: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/99.jpg)
99
Refrigeration Technology
The clearance volume will cause the vapor not being completely discharged after compression.
The remaining vapor trapped in the clearance volume will re-expend in the next suction stroke.
As a result, the volume of the vapor sucked in by the compressor in each stroke is less than the volume the piston swept through.
So the compressor volumetric displacement must be greater than the volume of vapor to be drawn in.
Other factors that cause reduction to the compressor capacity are: pressure drop through valves which reduces the amount of vapor sucked
or discharged; vapor leaks around closed valves or between the piston and cylinder; refrigerant evaporating out of oil in the cylinder space; the vapor heated by the cylinder walls, thus, increasing its specific volume.
Chapter10. Compressors
![Page 100: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/100.jpg)
Refrigeration Technology
The performance of reciprocating compressors can be described by volumetric efficiency.
Here we only consider the actual and the clearance volumetric efficiencies. The actual volumetric efficiency is defined as
3
3
,
,va
volume flow rate entering compressor m s
displacement rate of compressor m s
Chapter10. Compressors
![Page 101: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/101.jpg)
Refrigeration Technology
2. Advantages and limitation Scroll compressors can deliver high compression pressure ratio. The pressure ratio is increased by adding spiral wraps to the scroll. Scroll compressors are true rotary motion and can be dynamically
balanced for smooth, vibration-free, quiet operation. They have no inlet or discharge valves to break or make noise and no
associated valve losses. Although scroll compressors continue to expand into larger and
smaller size compressor market, some weak points of scroll compressors could limit this trend.
One of them is that the effect of leakage at the apex of the crescent shaped pokets could become so significant in small size compressors that scoll compressors can not be constructed much smaller.
Chapter10. Compressors
![Page 102: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/102.jpg)
102
Refrigeration Technology
10-3. Screw Compressors
Chapter10. Compressors
![Page 103: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/103.jpg)
Refrigeration Technology
2. Advantages of the screw compressor Screw compressors are reliable and compact. Compressor rotors can be manufactured with very small
clearances at an economic cost. In many applications, the screw compressor offers significant
advantages over reciprocating compressors.
1. Its fewer moving parts mean less maintenance. There is no need to service the items such as compressor valves, packing and piston rings, and the associated downtime for replacement.
2. The absence of reciprocating inertial forces allows the screw compressor to run at high speeds. So, it could be constructed more compact.
Chapter10. Compressors
![Page 104: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/104.jpg)
104
Refrigeration Technology
3. The continuous flow of cooling lubricant allows much higher single-stage compression ratios.
4. The compactness tends to reduce package costs.
5. Low vibration due to reducing or eliminating pulsations by screw technology
6. Higher speeds and compression ratios help to maximize available production horsepower.
A major problem with screw compressors is that the pressure difference between entry and exit creates very large radial and axial forces on the rotors whose magnitude and direction is independent of the direction of rotation.
Chapter10. Compressors
![Page 105: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/105.jpg)
105
Refrigeration Technology
10-4. Turbo Compressors
Chapter10. Compressors
![Page 106: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/106.jpg)
Refrigeration Technology
1. The construction and operation of turbo Compressors
“Turbo compressor” as understood in refrigeration industry usually refers to a centrifugal compressor.
A schematic diagram of the centrifugal compressor is shown in Fig.10-14.
Chapter10. Compressors
Vapor enters axially at the centre wheel 1 and flows through the passage 3 in the impeller 2.
The pressure and absolute velocity of the vapor rises when it passes the impeller because of the centrifugal force.
In the stationary diffuser 4 the flow of vapor is decelerated to further raise the vapor pressure.
The compressed vapor is collected in the scroll or volute 5 and discharged to the delivery pipe 6.
Fig.10-14 Schematic diagram of the centrifugal compressor1-eye, inlet cavity. 2–impeller (wheel). 3-blades (or vanes).4-diffuser. 5-volute (scroll). 6- outlet cavity.
![Page 107: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/107.jpg)
Refrigeration Technology
The major elements of a centrifugal compressor are shown in Fig.10-13.
A turbo compressor consists of a housing and at least one rotor of which the shaft is pivotally supported by the housing, with a free shaft end and with a rotor connected with the other end of the rotor shaft.
Chapter10. Compressors
Fig. 10-13 Two-stage centrifugal compressor1-Second-stage variable inlet guide vane. 2-First-stage impeller.3-Second-stage impeller. 4-Water-cooled motor.5-Base, oil tank, and lubricating oil pump assembly.6-First-stage guide vanes and capacity control.7-Labyrinth seal. 8-Cross-over connection. 9-Guide vane actuator.10-Volute casing. 11-Pressure-lubricated sleeve bearing. The discharge opening is not shown.
![Page 108: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/108.jpg)
108
Refrigeration TechnologyChapter10. Compressors
The free end of the rotor shaft facing away from the rotor projects into a pressure chamber connected with the housing, and is acted upon by a pressurized fluid whose force of pressure compensates for the force of the axial thrust acting on the rotor.
Thus, the starting friction of the compressor is lower and drive motors of lower output target can be utilized.
Fig. 10-13 Two-stage centrifugal compressor1-Second-stage variable inlet guide vane. 2-First-stage impeller.3-Second-stage impeller. 4-Water-cooled motor.5-Base, oil tank, and lubricating oil pump assembly.6-First-stage guide vanes and capacity control.7-Labyrinth seal. 8-Cross-over connection. 9-Guide vane actuator.10-Volute casing. 11-Pressure-lubricated sleeve bearing. The discharge opening is not shown.
![Page 109: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/109.jpg)
Refrigeration Technology
10-5. Roller Type Compressors
Chapter10. Compressors
![Page 110: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/110.jpg)
110
Refrigeration TechnologyChapter10. Compressors
The roller type compressor , which is also called as “blade-type rotary compressor” by some companies, compresses gases by revolving a steel cylindrical roller on an eccentric shaft which is mounted concentrically in a cylinder (Fig.10-15).
Fig.10-15 Roller-type compressor [18]
![Page 111: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/111.jpg)
111
Refrigeration TechnologyChapter10. Compressors
Fig.10-15 Roller-type compressor [18]
Because of the shaft being eccentric, the cylinder roller is eccentric with the cylinder as well.
The cylinder roller touches the cylinder wall at the point of minimum clearance.
As the shaft turns, the roller rolls around the cylinder wall in the direction of shaft rotation, always maintaining contact with the cylinder wall.
![Page 112: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/112.jpg)
112
Refrigeration Technology
wu wei-dong
Chapter10. Compressors
Fig.10-15 Roller-type compressor [18]
With relation to the camshaft, the inside surface of the cylinder roller moves counter to the direction of shaft rotation in the manner of a crankpin bearing.
A spring-loaded blade mounted in a slot in the cylinder wall, bears firmly against the roller at all times.
The blade moves in and out of the cylinder slot to follow the roller as the latter rolls around the cylinder wall.
![Page 113: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/113.jpg)
Refrigeration Technology
Cylinder heads or end-plates are used to close the cylinder at each end and to serve as supports for the camshaft.
Both the roller and blade extend the full length of the cylinder with only working clearance being allowed between these parts and the end-plates.
Suction and discharge ports are located in the cylinder wall near the blade slot, but on opposite sides.
The flow of vapor through both the suction and discharge ports is continuous, except for the instant that the cylinder at the point of contact between the blade and roller on one side and between the roller and cylinder wall on the other side.
Chapter10. Compressors
![Page 114: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/114.jpg)
114
Refrigeration Technology
10-6. Vane Type Compressors
Chapter10. Compressors
![Page 115: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/115.jpg)
Refrigeration Technology
The vane type compressor , which is also called as “sliding vane compressor”or “multi-vane compressor” by some companies, employs a series of rotating vanes or blades which are installed equidistant around the periphery of a slotted rotor (Fig.10-16).
Fig.10-16 vane-type rotary compressor.[19]
Chapter10. Compressors
![Page 116: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/116.jpg)
116
Refrigeration Technology
The rotor shaft is mounted eccentrically in a steel cylinder so that the rotor nearly touches the cylinder wall on one side, the two being separated only by an oil film at this point.
Directly opposite this point the clearance between the rotor and the cylinder wall is maximum.
Heads or end-plates are installed on the ends of the cylinder and to hold the rotor shaft.
Fig.10-16 vane-type rotary compressor.[19]
Chapter10. Compressors
The vanes move back and forth radially in the rotor slots as they follow the contour of the cylinder wall when the rotor is turning.
The vanes are held firmly against the cylinder wall by action of the centrifugal force developed by the rotating rotor.
In some instances, the blades are spring-loaded to obtain a more positive seal against the cylinder wall.
![Page 117: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/117.jpg)
Refrigeration Technology
The suction vapor drawn into the cylinder through suction ports in the cylinder wall is entrapped between adjacent rotating vanes.
The vapor is compressed by the reduction in volume that results as the vanes rotate from the point of maximum rotor clearance to the point of minimum rotor clearance.
The compressed vapor is discharged from the cylinder through ports located in the cylinder wall near the point of minimum rotor clearance.
Chapter10. Compressors
![Page 118: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/118.jpg)
118
Refrigeration Technology
The discharge ports are so located as to allow discharge of the compressed vapor at the desired point which is the design point of the compressor during the compressing process.
Operation of the compressor at compression ratios above or below the design point will result in compression losses and increasing power consumptions.
Current practice limits compression ratios to a maximum of 7 to 1.
Chapter10. Compressors
![Page 119: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/119.jpg)
Unit – IV
![Page 120: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/120.jpg)
Refrigeration &
Air Conditioning
![Page 121: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/121.jpg)
Objectives
• Basic operation of refrigeration and AC systems• Principle components of refrigeration and AC
systems• Thermodynamic principles of refrigeration cycle • Safety considerations
![Page 122: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/122.jpg)
Uses of Systems
• Cooling of food stores and cargo• Cooling of electronic spaces and
equipment– CIC (computers and consoles)– Radio (communications gear)– Radars– ESGN/RLGN– Sonar
• Cooling of magazines• Air conditioning for crew comfort
![Page 123: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/123.jpg)
Definition Review
• Specific heat (cp): Amount of heat required to raise the temperature of 1 lb of substance 1°F (BTU/lb) – how much for water?
• Sensible heat vs Latent heat
• LHV/LHF
• Second Law of Thermodynamics: must expend energy to get process to work
![Page 124: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/124.jpg)
Refrigeration Cycle
• Refrigeration - Cooling of an object and maintenance of its temp below that of surroundings
• Working substance must alternate b/t colder and hotter regions
• Most common: vapor compression– Reverse of power cycle– Heat absorbed in low temp region and
released in high temp region
![Page 125: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/125.jpg)
Generic Refrigeration Cycle
![Page 126: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/126.jpg)
Thermodynamic Cycle
![Page 127: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/127.jpg)
TypicalRefrigeration
Cycle
![Page 128: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/128.jpg)
Components
• Refrigerant • Evaporator/Chiller • Compressor• Condenser• Receiver• Thermostatic
expansion valve (TXV)
![Page 129: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/129.jpg)
Refrigerant• Desirable properties:
– High latent heat of vaporization - max cooling– Non-toxicity (no health hazard)– Desirable saturation temp (for operating pressure)– Chemical stability (non-flammable/non-explosive)– Ease of leak detection– Low cost– Readily available
• Commonly use FREON (R-12, R-114, etc.)
![Page 130: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/130.jpg)
Evaporator/Chiller
• Located in space to be refrigerated
• Cooling coil acts as an indirect heat exchanger
• Absorbs heat from surroundings and vaporizes– Latent Heat of Vaporization– Sensible Heat of surroundings
• Slightly superheated (10°F) - ensures no liquid carryover into compressor
![Page 131: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/131.jpg)
![Page 132: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/132.jpg)
Compressor
• Superheated Vapor:– Enters as low press, low temp vapor– Exits as high press, high temp vapor
• Temp: creates differential (T) promotes heat transfer
• Press: Tsat allows for condensation at warmer temps
• Increase in energy provides the driving force to circulate refrigerant through the system
![Page 133: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/133.jpg)
Condenser
• Refrigerant rejects latent heat to cooling medium
• Latent heat of condensation (LHC)
• Indirect heat exchanger: seawater absorbs the heat and discharges it overboard
![Page 134: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/134.jpg)
Receiver
• Temporary storage space & surge volume for the sub-cooled refrigerant
• Serves as a vapor seal to prevent vapor from entering the expansion valve
![Page 135: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/135.jpg)
Expansion Device
• Thermostatic Expansion Valve (TXV)
• Liquid Freon enters the expansion valve at high pressure and leaves as a low pressure wet vapor (vapor forms as refrigerant enters saturation region)
• Controls:– Pressure reduction– Amount of refrigerant entering evaporator
controls capacity
![Page 136: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/136.jpg)
![Page 137: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/137.jpg)
Air Conditioning
• Purpose: maintain the atmosphere of an enclosed space at a required temp, humidity and purity
• Refrigeration system is at heart of AC system
• Heaters in ventilation system
• Types Used:• Self-contained• Refrigerant circulating• Chill water circulating
![Page 138: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/138.jpg)
AC System Types
• Self-Contained System– Add-on to ships that originally did not have AC
plants– Not located in ventilation system (window unit)
• Refrigerant circulating system– Hot air passed over refrigerant cooling coils
directly
• Chilled water circulating system– Refrigerant cools chill water– Hot air passes over chill water cooling coils
![Page 139: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/139.jpg)
Basic AC System
![Page 140: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/140.jpg)
Safety Precautions
• Phosgene gas hazard– Lethal – Created when refrigerant is exposed to high
temperatures
• Handling procedures– Wear goggles and gloves to avoid eye irritation and
frostbite
• Asphyxiation hazard in non-ventilated spaces (bilges since heavier than air)
• Handling of compressed gas bottles
![Page 141: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/141.jpg)
Unit – V
One Dimensional Compressible flow
![Page 142: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/142.jpg)
5.1 Introduction
Good approximation for practicing gas dynamicists eq. nozzle flow 、 flow through wind tunnel & rocket engines
![Page 143: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/143.jpg)
5.2 Governing Equations
• For a steady,quasi-1D flow
The continuity equation :
222111 AuAu
s
dt
sdv
![Page 144: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/144.jpg)
The momentum equation :
s s
sdpdfdt
vvsdv
)(
)(
2222221
21111 )( 2
1
AuApApdAuAp x
A
A
Automatically balainced
X-dir
Y-dir
![Page 145: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/145.jpg)
The energy equation
s
dvfsdvpdq )(
s
dsvV
edV
et
)
2()]
2([
22
consthu
hu
h 0
22
2
21
1 22
peh
total enthalpy is constant along the flow
Actually, the total enthalpy is constant along a streamline in any adiabatic steady flow
![Page 146: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/146.jpg)
5.3 Area-Velocity Relation0)( uAd
uA
AudAduudA
0 udu
d
d
dPdP
0A
dA
u
dud
u
duM
ua
duu
a
udud 2
2
2
2
∵ adiabatic & inviscid no dissipation mechanism∴
→ isentropic
u
duM
A
dA)1( 2
![Page 147: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/147.jpg)
Important information1. M→0 incompressible flow
Au=const consistent with the familiar continuity eq for incompressible flow
2. 0 M≦ < 1 subsonic flow
an increase in velocity (du , +) is associated with a decrease in area (dA,- ) and vice versa.
3. M>1 supersonic flowan increase in velocity is associated with an increase in area , and vice versa
4. M=1 sonic flow →dA/A=0
a minimum or maximum in the area
![Page 148: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/148.jpg)
![Page 149: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/149.jpg)
A subsonic flow is to be accelerated isentropically from subsonic to supersonic
Supersonic flow is to be decelercted isentropically from supersonic to subsonic
![Page 150: VELTECH Dr.R.R&Dr.S.R TECHNICAL UNIVERSITY AERO ENGINEERING THERMODYNAMICS SEM:IIIYEAR:II PREPARED BY Mr.B.Narendhiran DEPARTMENT OF AERONAUTICAL ASSISTANT.](https://reader037.fdocuments.us/reader037/viewer/2022102622/56649e2d5503460f94b1ce87/html5/thumbnails/150.jpg)
Application of area-velocity relation
1.Rocket engines