SlideShare a Scribd company logo
1 of 22
Download to read offline
ANWESA KAR
M.TECH(THERMAL ENGG.)
1.REYNOLDS NUMBER
 It is the ratio of inertia force to the viscous force.
Where,
Re
VL


 is density
is velocity
L is linear dimension
 is viscosity
Significance-It is used to identify the nature of
flow (Laminar or Turbulent)
V
2.FROUDE NUMBER
 It is the ratio of inertia force to the gravity force
 Where ,
V is the velocity
g is the acceleration due to gravity
L is the characteristics length
Significance-It is used to analyze nature of flow where
free surface is present. e.g. weirs ,channels ,spillways
V
Fr
gL

3.WEBERS NUMBER
 It is the ratio of inertia force to surface tension force.
 Where
V is the velocity
L is the characteristics length
Significance-It is used in analyzing formation of droplet
and in capillary studies.
/
V
We
L 

 is the surface tension
 is the density
4.EULER NUMBER
 It is the ratio of inertia force to pressure force.
 Where
P is the pressure
V is the velocity
Significance-It is used to characterize energy losses in a
flow.
V
Eu
P


 is the density
5.MACH NUMBER
 It is the ratio of inertia force to elastic force.
 Where
V is the velocity of object
C is the speed of sound
Significance-It is used to analyze fluid flow where
compressibility is a important factor.
V
M
C

6.BIOT NUMBER
 It is the ratio of conductive resistance to convective
resistance.
Where
h is the heat transfer coefficient
K is the thermal conductivity
Significance-It is used in the heat transfer calculation
(lumped heat analysis).
chL
Bi
K

cL is the characteristics length(volume of
the body/surface area of contact)
7.FOURIER NUMBER
 It is the ratio of heat conducted through a body to the
heat stored.
 Where,
t is the characteristics time
 Significance-It is used in transient heat analysis.
2
c
t
L

 
 is the thermal diffusivity
cL is the length
8.NUSSELT NUMBER
It is the ratio of convective heat transfer to conductive heat
transfer.
Where
h is the convective heat transfer coefficient
L is the characteristics length
K is the thermal conductivity
Significance-It describe the enhancement of heat transfer
because of convection in comparison to conduction
hL
Nu
K

9.PRANDTL NUMBER
 It is the ratio of momentum diffusivity to heat diffusivity
 Where
K is the thermal conductivity
Significance-Prandtl number is used to describe thermal
boundary layer.
Pr PC
K


 is the dynamic viscosity
PC is the specific heat
10.GRASHOF NUMBER
 It is the ratio of buoyancy force to viscous force.
 Where
g is acceleration due to gravity
Significance-It is used in flow analysis in natural convection.
 is the coefficient of thermal expansion
sT is the surface temperature
T is the fluid temperature far from the surface
 is the kinematic viscosity of fluid
3
2
( )s cg T T L
Gr




11.RAYLEIGH NUMBER
 Rayleigh number is the product of Grashof number
and Prandtl number.
Ra= Gr . Pr
Significance-It is associated with buoyancy driven flow .
Its value is used to characterize laminar to turbulent
transition.
12.STANTON NUMBER
 It is defined as the ratio of heat transferred by convection
to the heat capacity of fluid.
 Where h is the heat transfer coefficient
u is the speed of fluid
Significance-It is used in heat transfer for forced
convection flows.
Re.Pr p
Nu h
St
uC
 
 is the density of fluid
pC is the Specific heat capacity of the fluid
13.PECLET NUMBER
 It is defined as the product of Reynold number and
Prandtl number.
 Where
L is the characteristics length
u is the velocity
Significance-It is used in calculations including
convective heat transfer rate.
Re.Pr
Lu
Pe

 
 is the thermal diffusivity
14.JAKOB NUMBER
 It is the ratio of sensible energy absorbed to latent
energy absorbed during liquid- vapor phase change.
 Where
Significance-It is used in analyzing flow pattern in
process of boiling.
( )P s sat
fg
C T T
Ja
h


PC
s satT T
fgh
is the specific heat capacity
is the temperature difference
Latent heat of vaporization
15.BOND NUMBER
 It is the ratio of buoyancy force to the surface tension
force.
 Where
g is the acceleration due to gravity
Significance-It is used in analyzing the behavior of
bubbles.
1 2( )g
Bo
 



1 2( )  is the difference in density
 is the surface tension
16.SCHIMDT NUMBER
 It is the ratio of momentum diffusivity to mass
diffusivity.
 Where
D is the mass diffusivity
Significance-It is used in fluid flows where simultaneous
mass and momentum diffusion occurs.
Sc
D


 is the kinematic viscosity
17.LEWIS NUMBER
 It is the ratio of thermal diffusivity to the mass diffusivity.
Where
D is the mass diffusivity
K is the thermal conductivity
Significance-It is used to analyze fluid flow with
simultaneous heat and mass transfer by convection.
p
K
Le
D C D


 
 is the thermal diffusivity
pC is the specific heat capacity
18.SOMMERFELD NUMBER
 Sommerfeld number is defined by the following equation
Where
r is the radius of the journal
c is the radial clearance
P is the bearing pressure
Significance-It is used in hydrodynamic lubrication
analysis.
2
. snr
S
c P
 
  
 
 is the dynamic viscosity
sn is the journal speed in r.p.s
19.KNUDSEN NUMBER
 It is the ratio of molecular mean free path to the
characteristics length.
 Where
L is the characteristics length
Significance-It is useful in determining whether
continuum mechanics formulation can be applied or
not in a system.
Kn
L


 is the mean free path
20.SHERWOOD NUMBER
 It is the ratio of convection mass transfer to the
diffusion mass transfer
 Where
K is the mass transfer coefficient
l is the characteristics length
D is the mass diffusivity
Significance-It is used in mass transfer problems.
Kl
Sh
D

Dimensionless number

More Related Content

What's hot

Critical thickness of insulation
Critical thickness of insulationCritical thickness of insulation
Critical thickness of insulationMdNoorruddin
 
Boiling & condensation
Boiling & condensationBoiling & condensation
Boiling & condensationziad zohdy
 
Shell and Tube Heat Exchanger in heat Transfer
Shell and Tube Heat Exchanger in heat TransferShell and Tube Heat Exchanger in heat Transfer
Shell and Tube Heat Exchanger in heat TransferUsman Shah
 
Heat exchangers and types
Heat exchangers and typesHeat exchangers and types
Heat exchangers and typesGopesh Chilveri
 
Overal Heat Transfer Coefficient
Overal Heat Transfer CoefficientOveral Heat Transfer Coefficient
Overal Heat Transfer CoefficientDheirya Joshi
 
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...tmuliya
 
Shell and tube heat exchanger design
Shell and tube heat exchanger designShell and tube heat exchanger design
Shell and tube heat exchanger designhossie
 
Parts of shell and tube heat exchanger
Parts of shell and tube heat exchangerParts of shell and tube heat exchanger
Parts of shell and tube heat exchangerKarnav Rana
 
Types of agitators
Types of agitatorsTypes of agitators
Types of agitatorsKarnav Rana
 
Distillation Column
Distillation ColumnDistillation Column
Distillation ColumnKhalid Nawaz
 
Log mean temperature difference
Log mean temperature differenceLog mean temperature difference
Log mean temperature differenceRupesh Datir
 
heat transfer through fins
heat transfer through finsheat transfer through fins
heat transfer through finsprasantjangir
 

What's hot (20)

Critical thickness of insulation
Critical thickness of insulationCritical thickness of insulation
Critical thickness of insulation
 
Boiling & condensation
Boiling & condensationBoiling & condensation
Boiling & condensation
 
Shell and Tube Heat Exchanger in heat Transfer
Shell and Tube Heat Exchanger in heat TransferShell and Tube Heat Exchanger in heat Transfer
Shell and Tube Heat Exchanger in heat Transfer
 
Heat exchanger design.
Heat exchanger design.Heat exchanger design.
Heat exchanger design.
 
Heat conduction through a plane wall
Heat conduction through a plane wallHeat conduction through a plane wall
Heat conduction through a plane wall
 
Heat exchangers and types
Heat exchangers and typesHeat exchangers and types
Heat exchangers and types
 
Overal Heat Transfer Coefficient
Overal Heat Transfer CoefficientOveral Heat Transfer Coefficient
Overal Heat Transfer Coefficient
 
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...
Lectures on Heat Transfer - Introduction - Applications - Fundamentals - Gove...
 
Batch Reactor
Batch ReactorBatch Reactor
Batch Reactor
 
Shell and tube heat exchanger design
Shell and tube heat exchanger designShell and tube heat exchanger design
Shell and tube heat exchanger design
 
Parts of shell and tube heat exchanger
Parts of shell and tube heat exchangerParts of shell and tube heat exchanger
Parts of shell and tube heat exchanger
 
Types of agitators
Types of agitatorsTypes of agitators
Types of agitators
 
Distillation Column
Distillation ColumnDistillation Column
Distillation Column
 
01 kern's method.
01 kern's method.01 kern's method.
01 kern's method.
 
Log mean temperature difference
Log mean temperature differenceLog mean temperature difference
Log mean temperature difference
 
Interphase mass transfer
Interphase mass transferInterphase mass transfer
Interphase mass transfer
 
heat transfer through fins
heat transfer through finsheat transfer through fins
heat transfer through fins
 
analysis of heat exchanger by LMTD method
analysis of heat exchanger by LMTD methodanalysis of heat exchanger by LMTD method
analysis of heat exchanger by LMTD method
 
Compressor and Types
Compressor and TypesCompressor and Types
Compressor and Types
 
Transport phenomena
Transport phenomenaTransport phenomena
Transport phenomena
 

Similar to Dimensionless number

Dimension less quantities
Dimension less quantitiesDimension less quantities
Dimension less quantitiesSALONI AGARWAL
 
Dimensionless number in chemical engineering
Dimensionless number in chemical engineering Dimensionless number in chemical engineering
Dimensionless number in chemical engineering Hardi Trivedi
 
Dimension less numbers in applied fluid mechanics
Dimension less numbers in applied fluid mechanicsDimension less numbers in applied fluid mechanics
Dimension less numbers in applied fluid mechanicstirath prajapati
 
International Journal of Engineering and Science Invention (IJESI)
International Journal of Engineering and Science Invention (IJESI)International Journal of Engineering and Science Invention (IJESI)
International Journal of Engineering and Science Invention (IJESI)inventionjournals
 
Me 2204 fluid mechanics and machinery
Me 2204 fluid mechanics and machineryMe 2204 fluid mechanics and machinery
Me 2204 fluid mechanics and machineryanish antony
 
Dimensionless numbers
Dimensionless numbersDimensionless numbers
Dimensionless numbersKeerthi Vasan
 
Fundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docx
Fundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docxFundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docx
Fundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docxhanneloremccaffery
 
kuliah-3-fundamental-of-convection3(0).ppt
kuliah-3-fundamental-of-convection3(0).pptkuliah-3-fundamental-of-convection3(0).ppt
kuliah-3-fundamental-of-convection3(0).pptssuser355c2a
 
Etht grp 11(140080125009,10,11,12)
Etht grp 11(140080125009,10,11,12)Etht grp 11(140080125009,10,11,12)
Etht grp 11(140080125009,10,11,12)Yash Dobariya
 
CE6451 FLUID-MECHANICS 2 MARKS.pdf
CE6451 FLUID-MECHANICS 2 MARKS.pdfCE6451 FLUID-MECHANICS 2 MARKS.pdf
CE6451 FLUID-MECHANICS 2 MARKS.pdfROEVER GROUPS
 
9-Viscous flow in ducts.pptx
9-Viscous flow in ducts.pptx9-Viscous flow in ducts.pptx
9-Viscous flow in ducts.pptxDaniel678511
 
HMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdf
HMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdfHMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdf
HMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdfRaviShankar269655
 
Forced Convection in laminar and Turbulent flows over flate plates and in the...
Forced Convection in laminar and Turbulent flows over flate plates and in the...Forced Convection in laminar and Turbulent flows over flate plates and in the...
Forced Convection in laminar and Turbulent flows over flate plates and in the...Talal Ashraf
 
Groundwater movement
Groundwater movementGroundwater movement
Groundwater movementShambel Yideg
 
Qpedia apr07 understanding_heat_transfer_coefficient
Qpedia apr07 understanding_heat_transfer_coefficientQpedia apr07 understanding_heat_transfer_coefficient
Qpedia apr07 understanding_heat_transfer_coefficientTeguh Apriy
 
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...eSAT Journals
 

Similar to Dimensionless number (20)

Dimension less quantities
Dimension less quantitiesDimension less quantities
Dimension less quantities
 
Dimensionless number in chemical engineering
Dimensionless number in chemical engineering Dimensionless number in chemical engineering
Dimensionless number in chemical engineering
 
Analogies
AnalogiesAnalogies
Analogies
 
Dimension less numbers in applied fluid mechanics
Dimension less numbers in applied fluid mechanicsDimension less numbers in applied fluid mechanics
Dimension less numbers in applied fluid mechanics
 
International Journal of Engineering and Science Invention (IJESI)
International Journal of Engineering and Science Invention (IJESI)International Journal of Engineering and Science Invention (IJESI)
International Journal of Engineering and Science Invention (IJESI)
 
Me 2204 fluid mechanics and machinery
Me 2204 fluid mechanics and machineryMe 2204 fluid mechanics and machinery
Me 2204 fluid mechanics and machinery
 
Dimensionless numbers
Dimensionless numbersDimensionless numbers
Dimensionless numbers
 
Fundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docx
Fundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docxFundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docx
Fundamentals of Heat and Mass Transfer, Theodore L. Bergman,.docx
 
Free convection
Free convectionFree convection
Free convection
 
kuliah-3-fundamental-of-convection3(0).ppt
kuliah-3-fundamental-of-convection3(0).pptkuliah-3-fundamental-of-convection3(0).ppt
kuliah-3-fundamental-of-convection3(0).ppt
 
Etht grp 11(140080125009,10,11,12)
Etht grp 11(140080125009,10,11,12)Etht grp 11(140080125009,10,11,12)
Etht grp 11(140080125009,10,11,12)
 
CE6451 FLUID-MECHANICS 2 MARKS.pdf
CE6451 FLUID-MECHANICS 2 MARKS.pdfCE6451 FLUID-MECHANICS 2 MARKS.pdf
CE6451 FLUID-MECHANICS 2 MARKS.pdf
 
9-Viscous flow in ducts.pptx
9-Viscous flow in ducts.pptx9-Viscous flow in ducts.pptx
9-Viscous flow in ducts.pptx
 
HMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdf
HMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdfHMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdf
HMT CONVhdhdhdhdhdhdh hv vhvh vECTION 1.pdf
 
MET 214 Module 3
MET 214 Module 3 MET 214 Module 3
MET 214 Module 3
 
Forced Convection in laminar and Turbulent flows over flate plates and in the...
Forced Convection in laminar and Turbulent flows over flate plates and in the...Forced Convection in laminar and Turbulent flows over flate plates and in the...
Forced Convection in laminar and Turbulent flows over flate plates and in the...
 
Fm final ppt
Fm final pptFm final ppt
Fm final ppt
 
Groundwater movement
Groundwater movementGroundwater movement
Groundwater movement
 
Qpedia apr07 understanding_heat_transfer_coefficient
Qpedia apr07 understanding_heat_transfer_coefficientQpedia apr07 understanding_heat_transfer_coefficient
Qpedia apr07 understanding_heat_transfer_coefficient
 
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...
 

Recently uploaded

CS 3251 Programming in c all unit notes pdf
CS 3251 Programming in c all unit notes pdfCS 3251 Programming in c all unit notes pdf
CS 3251 Programming in c all unit notes pdfBalamuruganV28
 
Chapter 9 Mechanical Injection Systems.pdf
Chapter 9 Mechanical Injection Systems.pdfChapter 9 Mechanical Injection Systems.pdf
Chapter 9 Mechanical Injection Systems.pdfFaizanAhmed396943
 
AntColonyOptimizationManetNetworkAODV.pptx
AntColonyOptimizationManetNetworkAODV.pptxAntColonyOptimizationManetNetworkAODV.pptx
AntColonyOptimizationManetNetworkAODV.pptxLina Kadam
 
Secure Key Crypto - Tech Paper JET Tech Labs
Secure Key Crypto - Tech Paper JET Tech LabsSecure Key Crypto - Tech Paper JET Tech Labs
Secure Key Crypto - Tech Paper JET Tech Labsamber724300
 
Detection&Tracking - Thermal imaging object detection and tracking
Detection&Tracking - Thermal imaging object detection and trackingDetection&Tracking - Thermal imaging object detection and tracking
Detection&Tracking - Thermal imaging object detection and trackinghadarpinhas1
 
Triangulation survey (Basic Mine Surveying)_MI10412MI.pptx
Triangulation survey (Basic Mine Surveying)_MI10412MI.pptxTriangulation survey (Basic Mine Surveying)_MI10412MI.pptx
Triangulation survey (Basic Mine Surveying)_MI10412MI.pptxRomil Mishra
 
Ergodomus - LOD 400 Production Drawings Exampes - Copy.pdf
Ergodomus - LOD 400 Production Drawings Exampes - Copy.pdfErgodomus - LOD 400 Production Drawings Exampes - Copy.pdf
Ergodomus - LOD 400 Production Drawings Exampes - Copy.pdfgestioneergodomus
 
input buffering in lexical analysis in CD
input buffering in lexical analysis in CDinput buffering in lexical analysis in CD
input buffering in lexical analysis in CDHeadOfDepartmentComp1
 
Introduction to Machine Learning Part1.pptx
Introduction to Machine Learning Part1.pptxIntroduction to Machine Learning Part1.pptx
Introduction to Machine Learning Part1.pptxPavan Mohan Neelamraju
 
SOFTWARE ESTIMATION COCOMO AND FP CALCULATION
SOFTWARE ESTIMATION COCOMO AND FP CALCULATIONSOFTWARE ESTIMATION COCOMO AND FP CALCULATION
SOFTWARE ESTIMATION COCOMO AND FP CALCULATIONSneha Padhiar
 
Design and Analysis of Algorithms Lecture Notes
Design and Analysis of Algorithms Lecture NotesDesign and Analysis of Algorithms Lecture Notes
Design and Analysis of Algorithms Lecture NotesSreedhar Chowdam
 
March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...
March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...
March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...gerogepatton
 
22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...
22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...
22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...KrishnaveniKrishnara1
 
Substation Automation SCADA and Gateway Solutions by BRH
Substation Automation SCADA and Gateway Solutions by BRHSubstation Automation SCADA and Gateway Solutions by BRH
Substation Automation SCADA and Gateway Solutions by BRHbirinder2
 
Prach: A Feature-Rich Platform Empowering the Autism Community
Prach: A Feature-Rich Platform Empowering the Autism CommunityPrach: A Feature-Rich Platform Empowering the Autism Community
Prach: A Feature-Rich Platform Empowering the Autism Communityprachaibot
 
2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.
2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.
2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.elesangwon
 
Indian Tradition, Culture & Societies.pdf
Indian Tradition, Culture & Societies.pdfIndian Tradition, Culture & Societies.pdf
Indian Tradition, Culture & Societies.pdfalokitpathak01
 
Robotics Group 10 (Control Schemes) cse.pdf
Robotics Group 10  (Control Schemes) cse.pdfRobotics Group 10  (Control Schemes) cse.pdf
Robotics Group 10 (Control Schemes) cse.pdfsahilsajad201
 

Recently uploaded (20)

CS 3251 Programming in c all unit notes pdf
CS 3251 Programming in c all unit notes pdfCS 3251 Programming in c all unit notes pdf
CS 3251 Programming in c all unit notes pdf
 
Chapter 9 Mechanical Injection Systems.pdf
Chapter 9 Mechanical Injection Systems.pdfChapter 9 Mechanical Injection Systems.pdf
Chapter 9 Mechanical Injection Systems.pdf
 
AntColonyOptimizationManetNetworkAODV.pptx
AntColonyOptimizationManetNetworkAODV.pptxAntColonyOptimizationManetNetworkAODV.pptx
AntColonyOptimizationManetNetworkAODV.pptx
 
Secure Key Crypto - Tech Paper JET Tech Labs
Secure Key Crypto - Tech Paper JET Tech LabsSecure Key Crypto - Tech Paper JET Tech Labs
Secure Key Crypto - Tech Paper JET Tech Labs
 
Detection&Tracking - Thermal imaging object detection and tracking
Detection&Tracking - Thermal imaging object detection and trackingDetection&Tracking - Thermal imaging object detection and tracking
Detection&Tracking - Thermal imaging object detection and tracking
 
Triangulation survey (Basic Mine Surveying)_MI10412MI.pptx
Triangulation survey (Basic Mine Surveying)_MI10412MI.pptxTriangulation survey (Basic Mine Surveying)_MI10412MI.pptx
Triangulation survey (Basic Mine Surveying)_MI10412MI.pptx
 
Ergodomus - LOD 400 Production Drawings Exampes - Copy.pdf
Ergodomus - LOD 400 Production Drawings Exampes - Copy.pdfErgodomus - LOD 400 Production Drawings Exampes - Copy.pdf
Ergodomus - LOD 400 Production Drawings Exampes - Copy.pdf
 
input buffering in lexical analysis in CD
input buffering in lexical analysis in CDinput buffering in lexical analysis in CD
input buffering in lexical analysis in CD
 
Introduction to Machine Learning Part1.pptx
Introduction to Machine Learning Part1.pptxIntroduction to Machine Learning Part1.pptx
Introduction to Machine Learning Part1.pptx
 
SOFTWARE ESTIMATION COCOMO AND FP CALCULATION
SOFTWARE ESTIMATION COCOMO AND FP CALCULATIONSOFTWARE ESTIMATION COCOMO AND FP CALCULATION
SOFTWARE ESTIMATION COCOMO AND FP CALCULATION
 
Design and Analysis of Algorithms Lecture Notes
Design and Analysis of Algorithms Lecture NotesDesign and Analysis of Algorithms Lecture Notes
Design and Analysis of Algorithms Lecture Notes
 
March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...
March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...
March 2024 - Top 10 Read Articles in Artificial Intelligence and Applications...
 
22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...
22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...
22CYT12 & Chemistry for Computer Systems_Unit-II-Corrosion & its Control Meth...
 
Versatile Engineering Construction Firms
Versatile Engineering Construction FirmsVersatile Engineering Construction Firms
Versatile Engineering Construction Firms
 
ASME-B31.4-2019-estandar para diseño de ductos
ASME-B31.4-2019-estandar para diseño de ductosASME-B31.4-2019-estandar para diseño de ductos
ASME-B31.4-2019-estandar para diseño de ductos
 
Substation Automation SCADA and Gateway Solutions by BRH
Substation Automation SCADA and Gateway Solutions by BRHSubstation Automation SCADA and Gateway Solutions by BRH
Substation Automation SCADA and Gateway Solutions by BRH
 
Prach: A Feature-Rich Platform Empowering the Autism Community
Prach: A Feature-Rich Platform Empowering the Autism CommunityPrach: A Feature-Rich Platform Empowering the Autism Community
Prach: A Feature-Rich Platform Empowering the Autism Community
 
2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.
2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.
2022 AWS DNA Hackathon 장애 대응 솔루션 jarvis.
 
Indian Tradition, Culture & Societies.pdf
Indian Tradition, Culture & Societies.pdfIndian Tradition, Culture & Societies.pdf
Indian Tradition, Culture & Societies.pdf
 
Robotics Group 10 (Control Schemes) cse.pdf
Robotics Group 10  (Control Schemes) cse.pdfRobotics Group 10  (Control Schemes) cse.pdf
Robotics Group 10 (Control Schemes) cse.pdf
 

Dimensionless number

  • 2. 1.REYNOLDS NUMBER  It is the ratio of inertia force to the viscous force. Where, Re VL    is density is velocity L is linear dimension  is viscosity Significance-It is used to identify the nature of flow (Laminar or Turbulent) V
  • 3. 2.FROUDE NUMBER  It is the ratio of inertia force to the gravity force  Where , V is the velocity g is the acceleration due to gravity L is the characteristics length Significance-It is used to analyze nature of flow where free surface is present. e.g. weirs ,channels ,spillways V Fr gL 
  • 4. 3.WEBERS NUMBER  It is the ratio of inertia force to surface tension force.  Where V is the velocity L is the characteristics length Significance-It is used in analyzing formation of droplet and in capillary studies. / V We L    is the surface tension  is the density
  • 5. 4.EULER NUMBER  It is the ratio of inertia force to pressure force.  Where P is the pressure V is the velocity Significance-It is used to characterize energy losses in a flow. V Eu P    is the density
  • 6. 5.MACH NUMBER  It is the ratio of inertia force to elastic force.  Where V is the velocity of object C is the speed of sound Significance-It is used to analyze fluid flow where compressibility is a important factor. V M C 
  • 7. 6.BIOT NUMBER  It is the ratio of conductive resistance to convective resistance. Where h is the heat transfer coefficient K is the thermal conductivity Significance-It is used in the heat transfer calculation (lumped heat analysis). chL Bi K  cL is the characteristics length(volume of the body/surface area of contact)
  • 8. 7.FOURIER NUMBER  It is the ratio of heat conducted through a body to the heat stored.  Where, t is the characteristics time  Significance-It is used in transient heat analysis. 2 c t L     is the thermal diffusivity cL is the length
  • 9. 8.NUSSELT NUMBER It is the ratio of convective heat transfer to conductive heat transfer. Where h is the convective heat transfer coefficient L is the characteristics length K is the thermal conductivity Significance-It describe the enhancement of heat transfer because of convection in comparison to conduction hL Nu K 
  • 10. 9.PRANDTL NUMBER  It is the ratio of momentum diffusivity to heat diffusivity  Where K is the thermal conductivity Significance-Prandtl number is used to describe thermal boundary layer. Pr PC K    is the dynamic viscosity PC is the specific heat
  • 11. 10.GRASHOF NUMBER  It is the ratio of buoyancy force to viscous force.  Where g is acceleration due to gravity Significance-It is used in flow analysis in natural convection.  is the coefficient of thermal expansion sT is the surface temperature T is the fluid temperature far from the surface  is the kinematic viscosity of fluid 3 2 ( )s cg T T L Gr    
  • 12. 11.RAYLEIGH NUMBER  Rayleigh number is the product of Grashof number and Prandtl number. Ra= Gr . Pr Significance-It is associated with buoyancy driven flow . Its value is used to characterize laminar to turbulent transition.
  • 13. 12.STANTON NUMBER  It is defined as the ratio of heat transferred by convection to the heat capacity of fluid.  Where h is the heat transfer coefficient u is the speed of fluid Significance-It is used in heat transfer for forced convection flows. Re.Pr p Nu h St uC    is the density of fluid pC is the Specific heat capacity of the fluid
  • 14. 13.PECLET NUMBER  It is defined as the product of Reynold number and Prandtl number.  Where L is the characteristics length u is the velocity Significance-It is used in calculations including convective heat transfer rate. Re.Pr Lu Pe     is the thermal diffusivity
  • 15. 14.JAKOB NUMBER  It is the ratio of sensible energy absorbed to latent energy absorbed during liquid- vapor phase change.  Where Significance-It is used in analyzing flow pattern in process of boiling. ( )P s sat fg C T T Ja h   PC s satT T fgh is the specific heat capacity is the temperature difference Latent heat of vaporization
  • 16. 15.BOND NUMBER  It is the ratio of buoyancy force to the surface tension force.  Where g is the acceleration due to gravity Significance-It is used in analyzing the behavior of bubbles. 1 2( )g Bo      1 2( )  is the difference in density  is the surface tension
  • 17. 16.SCHIMDT NUMBER  It is the ratio of momentum diffusivity to mass diffusivity.  Where D is the mass diffusivity Significance-It is used in fluid flows where simultaneous mass and momentum diffusion occurs. Sc D    is the kinematic viscosity
  • 18. 17.LEWIS NUMBER  It is the ratio of thermal diffusivity to the mass diffusivity. Where D is the mass diffusivity K is the thermal conductivity Significance-It is used to analyze fluid flow with simultaneous heat and mass transfer by convection. p K Le D C D      is the thermal diffusivity pC is the specific heat capacity
  • 19. 18.SOMMERFELD NUMBER  Sommerfeld number is defined by the following equation Where r is the radius of the journal c is the radial clearance P is the bearing pressure Significance-It is used in hydrodynamic lubrication analysis. 2 . snr S c P         is the dynamic viscosity sn is the journal speed in r.p.s
  • 20. 19.KNUDSEN NUMBER  It is the ratio of molecular mean free path to the characteristics length.  Where L is the characteristics length Significance-It is useful in determining whether continuum mechanics formulation can be applied or not in a system. Kn L    is the mean free path
  • 21. 20.SHERWOOD NUMBER  It is the ratio of convection mass transfer to the diffusion mass transfer  Where K is the mass transfer coefficient l is the characteristics length D is the mass diffusivity Significance-It is used in mass transfer problems. Kl Sh D 