7. semester chemical engineering civil engineeringhomes.et.aau.dk/mma/transport/lek1 transport...
TRANSCRIPT
![Page 1: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/1.jpg)
Transport processes
7. Semester
Chemical Engineering
Civil Engineering
![Page 2: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/2.jpg)
Course structure
Transport ProcessesChemical engineering
3 ECTS
Fluid and wave dynamics
Civil engineering5 ECTS
![Page 3: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/3.jpg)
Course structure
Transport ProcessesChemical engineering
3 ECTS
Fluid and wave dynamics
Civil engineering5 ECTSFluid dynamics Fluid dynamics
Wave dynamicsHeat and mass transfer
6 lectures
Oral exam in Transport processes
Oral exam in Fluid and wave dynamics
![Page 4: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/4.jpg)
My background
![Page 5: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/5.jpg)
Literature
• Primary literature:– Geankoplis, Transport processes and separation Principles
• Supplementary literature:– (Brorsen, Strømningslære)
– Selected chapters from e-books
![Page 6: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/6.jpg)
Course homepage
http://homes.et.aau.dk/mma/
On the course homepage you can find… – Slides
– Supplementary literature (e-books)
– Exercises/solutions
![Page 7: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/7.jpg)
Motivation
• Why do I need to bother myself with this course? – You need to pass an exam!
– Knowledge about Fluid flow is essential for Chemical and Civil Engineers alike
– You can actually use the stuff you learn to make some practical calculations (well at least some of it…)
– This course forms the base for Numerical Fluid Dynamics (including heat and mass dynamics)
![Page 8: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/8.jpg)
Exam
• 20 min Oral Exam
• 20 min preparation time
• Examination questions will be available 2 weeks before the exam
![Page 9: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/9.jpg)
Course plan
1. Elementary Fluid Dynamics2. Fluid Kinematics3. Finite Control Volume Analysis4. Differential Analysis of Fluid Flow5. Viscous Flow and Turbulence6. Turbulent Boundary Layer Flow7. Principles of Heat Transfer8. Internal Forces Convection9. Unsteady Heat Transfer10. Boiling and Condensation11. Mass Transfer12. Porous Media Flow13. Non-Newtonian Flow
![Page 10: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/10.jpg)
Today's lecture
• Elementary Fluid Dynamics– The Bernoulli Equation
– Static and Dynamic Pressure
![Page 11: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/11.jpg)
What is a transport process?
• Momentum transfer (flow)
• Heat transfer
• Mass transfer
Diffusion
Convection
Radiation
Conduction
MomentumHeat
Mass
Truck!Goods!
![Page 12: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/12.jpg)
Transport processes
• What is transport processes really?
Diffusion
Convection
Radiation
Conduction
![Page 13: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/13.jpg)
Energy concepts
• Energy can be a lot of things, what is your understanding? – Heat
– Work
– Potential energy
– Kinetic energy
– Internal energy
– Enthalpy
PcρForce distance×
gzρ21
2 Vρ
u
h
![Page 14: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/14.jpg)
14
Flow work• Flow work
– Flow through control volumes require work
– The required force is given by F=PA
flowW FL PAL PV= = =
![Page 15: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/15.jpg)
Mechanical energy
• The mechanical energy is the flow work, the kinetic and the potential energy:
• Change in the mechanical energy:
15
[ ]2
2P Ve Pv ke pe gz J kgρ
= + + = + +
( )2 2
2 1 2 12 12
P P V Ve g z zρ− −
∆ = + + −
[ ]2
2mVE PV KE PE PV mgz J= + + = + +
![Page 16: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/16.jpg)
Energy balance
• If the mechanical energy is conserved, then:
• This can be formulated as pressure:
• or as head:
( ) ( )2 2
1 1 2 21 22 2
P V P Vg z g zρ ρ+ + = + +
Did I hear somebody say that it was a good idea to always check the units?!?
2 21 2
1 1 2 22 2V VP gz P gzρ ρ ρ ρ+ + = + +
2 21 1 2 2
1 22 2P V P Vz zg g g gρ ρ+ + = + +
![Page 17: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/17.jpg)
Example
• Fill out the blank spaces.
![Page 18: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/18.jpg)
Energy and mass conservation• Mass balance for a system:
• Energy balance for a system:
18
in out sysm m m− = ∆
Mass which enters system boundaries Mass which exits
system boundaries
Change of the system mass (accumulation)
in out sysE E E− = ∆
Energy which enters system boundaries Energy which exits
system boundaries
Change of the systems energy
![Page 19: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/19.jpg)
Conservation of Momentum
• Newtons 2 lov, momentumbalance
F ma=∑The sum of forces which act on a system Change of the
systems momentum
![Page 20: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/20.jpg)
Bernoulli
• F=ma along a streamline
• Steady, incompressible flow:
2
constant along a streamline2
F ma
P V gzρ
=
⇓
+ + =
∑
2 21 1 2 2
1 22 2P V P Vgz gzρ ρ+ + = + +
![Page 21: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/21.jpg)
Formal derivation
![Page 22: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/22.jpg)
2
cst2
VP gzρ ρ+ + =
Name game…
Static pressureDynamic Pressure Hydrostatic Pressure
![Page 23: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/23.jpg)
Name game…#2
• Stagnation Pressure :
• Total Pressure:
2
2stag static dynVP P P P ρ= + = +
2
2tot static dyn hydroVP P P P P gzρ ρ= + + = + +
![Page 24: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/24.jpg)
Pitot-tube
• Assume that the hydrostatic pressure is negligible (the fluid is a gas)
• Static Pressure:
• Stagnations pressure:
• Combine:
2
3 2stagVP P P ρ= = +
1 4P P P= =
( )
2
3 4
3 4
2
2
VP P
P PV
ρ
ρ
− =
−=
![Page 25: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/25.jpg)
Example
• Determine an expression for h as a function of the flowrate Q
Bernolli:
Conservation of mass:
equilibrium:
Combine:
2 21 2
1 1 2 22 2V VP g z P g zρ ρρ ρ+ + = + +
1 1 2 2Q AV A V= =
( )
( ) ( )
2 1 1 2
1 2 2 1
SG
SG
g z z gl gh P gl gh P
P P g z z gh
ρ ρ ρ ρ ρ
ρ ρ ρ
− + + − = + −
− = − + −
( ) ( )( )
2 22 2 1
2 SG
Q A A Ah
gρ
ρ ρ−
=−
![Page 26: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/26.jpg)
Example
• Flow from a large reservoir
P2
11 2
Vρ+ 1 2g z Pρ+ =
22
22V g zρ ρ+ +
2V gh=
![Page 27: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/27.jpg)
Example
• Aerodynamic lift of a wing profile– Using bernoilli, explain how a lift is generated
– 2min, discus with the person next to you
![Page 28: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/28.jpg)
Example
• Galloping of a stack (chimney)– http://www.youtube.com/watch?v=EgRBpeqPUEU&feature=player_e
mbedded
– http://media.efluids.com/galleries/all?medium=578
![Page 29: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/29.jpg)
losses: (non-ideal flow)- short about pipe flow- very short about drag
![Page 30: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/30.jpg)
Pipe flow
![Page 31: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/31.jpg)
Laminar and turbulent flows
• Laminar flow:– Molecular diffusion
• Turbulent flow:– Macroscopic mixing
![Page 32: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/32.jpg)
Reynolds number
• Characterization of flows
• ρ – density
• μ – viscosity
• D – diameter
• V – velocity
Re VDρµ
=Re 2300 laminar
2300 Re 10000 transitional10000 Re turbulent
≤≤ ≤≤
![Page 33: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/33.jpg)
Example
• Is the flow in a water pipe laminar or turbulent? If we assume that it takes about 30 sekunder a one liter cup. The internal pipe diameter is assmed to be around 1 cm.
• The flow is in the transition interval!
• How would you calculate the pressure loss?
3
1000 / 3 0.42 / 0.01Re 37501.12 10 /
VD kg m m s mkg s m
ρµ −
⋅ ⋅= = =
⋅ ⋅
330.001 0.000033 /
30mQ m s
sek= =
2 0.42 /4
QV Q D m sA
π = = =
![Page 34: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/34.jpg)
Loss...?
• We talk about pressure loss in pipes– Friction between fluid and wall, the fluid sticks to the wall
– The mechanical energy of the fluid is converted into heat
– A pressure difference which we cannot recover
• Pressure loss is calculate as:
• L – pipe length
• D – pipe diameter
• V – velocity
• f – friction factor
P1P2
ΔP=P1-P2
2
2L VP fDρ
∆ = ( )laminar: 64 / Returbulent: fε/D,Re
ff=
=
![Page 35: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/35.jpg)
Energy equation with loss
2 21 2
1 1 2 22 2 lossV VP g z P g z Pρ ρρ ρ+ + = + + + ∆
![Page 36: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/36.jpg)
Colebrook equation
• The relationship between roughness, Re and f:
1.111 6.91.8logRe 3.7
Df
ε = − +
![Page 37: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/37.jpg)
Moody chart
![Page 38: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/38.jpg)
Minor and major loss
• ”Minor” loss: Pressure loss in pipes
• ”Major” loss: pressure loss in pipe components
• Total pressure loss:
P1P2
ΔP=P1-P2
2
2L VP fDρ
∆ =
2
2LVP K ρ
∆ =
2 2
2 2tot LV L VP K f
Dρ ρ
∆ = +∑ ∑
![Page 39: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/39.jpg)
Indløb og udløb
KL=1.0 KL=1.0
KL=1.0KL=1.0KL=0.5
KL=0.04KL=0.2
KL=0.8
![Page 40: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/40.jpg)
Flow komponenter
![Page 41: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/41.jpg)
Eksempel
• Bestem trykket P2:
KL findes for denne diffuser til 0.133
masse bevarelse:
komponent-tryktab:
Energibevarelse:
11 1 1 2 2 2 2 1
2
3.11 /AV A V A V V m sA
ρ ρ= ⇒ = =
21 0.00326bar
2LVP K ρ
∆ = =
2 21 2
1 1 2 2 , 1.06(empirisk konstant)2 2V VP g z P g z Pρ ρα ρ α ρ α+ + = + + + ∆ =
2 21 2
2 1 1682
V VP P P kPaαρ αρ−= + −∆ =
![Page 42: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/42.jpg)
Drag
![Page 43: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/43.jpg)
Drag
• Definition: The force acting on an object in a flow
• Mechanical energy of the fluid transferred to the object
• Friction on the surface of the object heat
![Page 44: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/44.jpg)
Ideal fluid (no viscosity)
![Page 45: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/45.jpg)
Drag Concepts
• The drag coefficient, CD:
• CD for low Re (Re<<1) flow:
• General:
212drag DF C V Aρ=
Pressure loss in pipes:
2
2LVP K ρ
∆ =
Pressure loss in pipes:
( )laminar: 64 / Returbulent: fε/D,Re
ff=
=
( )f shape,ε/L,Re,Ma,FrDC =
![Page 46: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/46.jpg)
Standard drag curve
![Page 47: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/47.jpg)
Effect of surface roughness
![Page 48: 7. Semester Chemical Engineering Civil Engineeringhomes.et.aau.dk/mma/transport/lek1 Transport processer - Elementary... · 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite](https://reader035.vdocuments.net/reader035/viewer/2022062921/5f0300127e708231d4070b9f/html5/thumbnails/48.jpg)
Excercises
• Time to wake up!