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An advantage of the plug flow model is that no part of the solution of the problem can be perpetuated "upstream". This allows one to calculate the exact solution to the differential equation knowing only the initial conditions. No further iteration is required. Each "plug" can be solved
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39:. In plug flow, the velocity of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe. The plug flow model assumes there is no
484:{\displaystyle {1 \over {\sqrt {\mathit {f}}}}=-2.0\log _{10}\left({\frac {\epsilon /D}{3.7}}+{\frac {2.51}{{\text{Re}}{\sqrt {\mathit {f}}}}}\right),{\text{(turbulent flow)}}}
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that need to be integrated to find the reactor conversion and outlet temperatures. Other simplifications used are perfect radial mixing and a homogeneous bed structure.
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caused by the pipe wall is so thin that it is negligible. Plug flow will be achieved if the sublayer thickness is much less than the pipe diameter (
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Massey, Bernard; Ward-Smith, John (1999). "6.2 Steady laminar flow in circular pipes: The Hagen-Poiseuille law".
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50:. Essentially no back mixing is assumed with "plugs" of fluid passing through the reactor. This results in
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The flow model in which the velocity profile consists of the fully developed boundary layer is known as
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of the pipe. In this regime the pressure drop is a result of inertia-dominated turbulent
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The plug flow model has many practical applications. One example is in the design of
853:
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Munson, Bruce R.; Young, Donald F.; Okiishi, Theodore H. (2006). "Section 8.4".
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244:{\displaystyle u^{*}=\left({\frac {\tau _{w}}{\rho }}\right)^{1/2}}
32:
364:{\displaystyle {\frac {\Delta P}{L}}={\frac {f\rho V^{2}}{2D}}}
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independently provided the previous plug's state is known.
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rather than viscosity-dominated laminar shear stress.
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648:is the average velocity of the plug (in the pipe),
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173:{\displaystyle \delta _{s}={\frac {5\nu }{u^{*}}}}
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90:For flows in pipes, if flow is turbulent then the
298:{\displaystyle \tau _{w}={\frac {D\Delta P}{4L}}}
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43:adjacent to the inner wall of the pipe.
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628:(not an actual velocity of the fluid),
784:(7th ed.). Cheltenham: Thornes.
698:is the pressure loss down the length
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809:(5th ed.). Hoboken, NJ: Wiley.
16:Simple model of fluid flow in a pipe
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832:"Pressure Drop Along Pipe Length"
518:(from the above equation or the
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807:Fundamentals of fluid mechanics
675:is the shear on the wall, and
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542:{\displaystyle \delta _{s}}
114:{\displaystyle \delta _{s}}
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78:, the velocity profile is
731:{\displaystyle \epsilon }
668:{\displaystyle \tau _{w}}
27:is a simple model of the
691:{\displaystyle \Delta P}
761:Plug flow reactor model
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573:is the pipe diameter,
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52:differential equations
834:. Engineers Edge, LLC
756:Hagen-Poiseuille flow
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617:{\displaystyle u^{*}}
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586:{\displaystyle \rho }
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516:Darcy friction factor
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782:Mechanics of fluids
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711:{\displaystyle L}
641:{\displaystyle V}
626:friction velocity
566:{\displaystyle D}
507:{\displaystyle f}
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76:laminar pipe flow
48:chemical reactors
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29:velocity profile
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21:fluid mechanics
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41:boundary layer
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718:of the pipe.
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86:Determination
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35:flowing in a
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836:. Retrieved
825:
806:
800:
781:
775:
744:shear stress
493:
122:
89:
69:
56:
45:
24:
18:
553:thickness,
520:Moody Chart
726:ϵ
683:Δ
657:τ
610:∗
581:ρ
531:δ
426:ϵ
415:
399:−
338:ρ
317:Δ
279:Δ
261:τ
219:ρ
210:τ
194:∗
164:∗
155:ν
137:δ
103:δ
80:parabolic
72:pipe flow
25:plug flow
854:Category
838:17 April
750:See also
551:sublayer
121:<<
738:is the
624:is the
595:density
593:is the
549:is the
514:is the
813:
788:
494:where
74:. In
767:Notes
33:fluid
31:of a
840:2018
811:ISBN
786:ISBN
448:2.51
37:pipe
522:),
438:3.7
406:log
402:2.0
125:).
19:In
856::
597:,
453:Re
410:10
82:.
23:,
842:.
819:.
794:.
706:L
686:P
661:w
636:V
606:u
561:D
535:s
502:f
474:,
470:)
460:f
443:+
434:D
430:/
419:(
396:=
388:f
382:1
356:D
353:2
346:2
342:V
335:f
329:=
324:L
320:P
290:L
287:4
282:P
276:D
270:=
265:w
237:2
233:/
229:1
224:)
214:w
204:(
199:=
190:u
160:u
152:5
146:=
141:s
123:D
107:s
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
