che315 pressure drop and friction loss 2.10 design equations for laminar and turbulent flow in pipes
TRANSCRIPT
![Page 1: CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in Pipes](https://reader036.vdocuments.us/reader036/viewer/2022062300/56649e755503460f94b76319/html5/thumbnails/1.jpg)
CHE315 Pressure Drop and Friction Loss
2.10 Design Equations for Laminar and Turbulent Flow in Pipes
friction loss in Pipes SF
SkinFriction
Contraction
Friction
Expansion
Friction
FittingsFriction
![Page 2: CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in Pipes](https://reader036.vdocuments.us/reader036/viewer/2022062300/56649e755503460f94b76319/html5/thumbnails/2.jpg)
CHE315 Pressure Drop and Friction Loss
2.10 Design Equations for Laminar and Turbulent Flow in Pipes
0
2
1 1212
21
22
FW
ppzzgvv savav
ff
ppF 21
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CHE315 Pressure Drop and Friction Loss
2.10B PRESSURE DROP AND FRICTION LOSS IN LAMINAR FLOW
20
32D
L
ppv L
2
1221
32
D
LLvppp ff
Example.
2.10-1
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CHE315 Pressure Drop and Friction Loss
Fanning friction factor f for friction loss in laminar flow
f is defined as drag force per wetted surface unit area (ts at the surface area) divided by the product of density times the velocity head (r v2/2):
22vf s
The drag force The wetted surface unit area 2Rp f LR 2
L
Dp
L
Rp
LR
Rp fffs
422
2
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CHE315 Pressure Drop and Friction Loss
2
1
4 2vL
Dpf f
2
42v
D
Lfp f
24
2v
D
Lf
pF ff
For laminar flow only, combining equations:
24
2v
D
Lfp f
2
1232
D
LLvp f
and vDNf
1616
Re
Eq (2.10-
2)
Eq (2.10-
5)
![Page 6: CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in Pipes](https://reader036.vdocuments.us/reader036/viewer/2022062300/56649e755503460f94b76319/html5/thumbnails/6.jpg)
CHE315 Pressure Drop and Friction Loss
friction loss in Pipes SF
SkinFriction
Contraction
Friction
Expansion
Friction
FittingsFriction
24
2v
D
Lfp f
2
1232
D
LLvp f
Re
16
Nf
f fromFigure 2.10-3
Lam
inar
Turb
ule
nt
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CHE315
![Page 8: CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in Pipes](https://reader036.vdocuments.us/reader036/viewer/2022062300/56649e755503460f94b76319/html5/thumbnails/8.jpg)
CHE315
Example 2.10-
3
NOTE: If velocity and diameter are both unknown, Solution should be Trial –and-error soln. (or computerized).
Pressure Drop and Friction Loss
![Page 9: CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in Pipes](https://reader036.vdocuments.us/reader036/viewer/2022062300/56649e755503460f94b76319/html5/thumbnails/9.jpg)
CHE315
Step by step procedure for trial-and error solution
1.Assume an initial value for the velocity (or the
diameter)
2.Calculate the Reynolds number (and e/D)
3.From the figure 3.10-3, read the corresponding
friction factor f
4.Substitute f into:
5.Compare the obtained value with the initial one
6.If values are different repeat from step2 with the
obtained value
24
2v
D
LfFf
Pressure Drop and Friction Loss
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CHE315
Example 2.10-
4Example
2.10.5
Pressure Drop and Friction Loss
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CHE315 Pressure Drop and Friction Loss
For gases, the equation 24
2v
D
Lfp f
can be rewritten as
follows:
avf D
LGfpp
2
4 2
21
vG
Pressure drop and friction factor in flow of gas
RT
MpRT
MpRT
M
mnRTpV
Ideal Gas Law:
![Page 12: CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in Pipes](https://reader036.vdocuments.us/reader036/viewer/2022062300/56649e755503460f94b76319/html5/thumbnails/12.jpg)
CHE315 Pressure Drop and Friction Loss
DM
RTLGfpp
22
22
1
4
How did we arrive to this equation?
av
f D
LGfpp
2
4 2
21
RT
MpRT
MpRT
M
mnRTpV
Using Ideal Gas Law;
The following equation can be obtained
![Page 13: CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in Pipes](https://reader036.vdocuments.us/reader036/viewer/2022062300/56649e755503460f94b76319/html5/thumbnails/13.jpg)
CHE315
Contraction
Friction
Expansion
Friction
kg
JvKh s
2
2
AL AS
vL vS
2
1
L
sex A
AK
L
sc A
AK 155.0
exhhchh
FittingsFriction 2
21vKh ff
Pressure Drop and Friction Loss
Kf :Turbulent: Table
2.10-1Laminar: Table
2.10-2
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CHE315
22224
21
222 vK
vK
vK
v
D
LfF f
sc
sex
friction loss in Pipes SF
SkinFriction
Contraction
Friction
Expansion
Friction
FittingsFriction
24
2v
D
Lf
2
2s
ex
vK 2
21vK f
2
2s
c
vK
Pressure Drop and Friction Loss
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CHE315
Example
2.10.6Example
2.10.7
Pressure Drop and Friction Loss
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CHE315
FRICTION LOSSES IN NONCIRCULAR CONDUITS
The equivalent diameter D is defined as four times the hydraulic radius
rH, defined as the ratio of the cross-sectional area of the channel to the
wetted perimeter of the channel.:
channel ofperimeter wetted
channel of area sectionalcross4
HrD
Pressure Drop and Friction Loss
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CHE315
Calculate the equivalent diameter?
Pressure Drop and Friction Loss