CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in...
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Transcript of CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in...
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
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
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
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
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)
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
CHE315
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
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
CHE315
Example 2.10-
4Example
2.10.5
Pressure Drop and Friction Loss
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:
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
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
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
CHE315
Example
2.10.6Example
2.10.7
Pressure Drop and Friction Loss
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
CHE315
Calculate the equivalent diameter?
Pressure Drop and Friction Loss