Plug flow

 ( Fluid Dynamics ) 

In fluid mechanics, plug flow is a simple model of the velocity profile of a fluid flowing in a pipe. 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 boundary layer adjacent to the inner wall of the pipe.

The plug flow model has many practical applications. One example is in the design of . Essentially no back mixing is assumed with "plugs" of fluid passing through the reactor. This results in differential equations 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.

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 independently provided the previous plug's state is known.

The flow model in which the velocity profile consists of the fully developed boundary layer is known as pipe flow. In Laminar flow, the velocity profile is Parabola.

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Determination For flows in pipes, if flow is turbulent then the laminar sublayer 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 ($\backslash delta\_s$<< D).

$\backslash delta\_s\; =\; \backslash frac\; \{5\; \backslash nu\}\; \{u^*\}$

$u^*\; =\; \backslash left\; (\backslash frac\; \{\backslash tau\_w\}\; \{\backslash rho\}\; \backslash right\; )^\{1/2\}$

$\backslash tau\_w\; =\; \backslash frac\; \{D\; \backslash Delta\; P\}\; \{4\; L\}$

(2025). 9780471675822, Wiley. ISBN 9780471675822

$\backslash frac\; \{\backslash Delta\; P\}\; \{L\}\; =\; \backslash frac\; \{f\; \backslash rho\; V^2\}\; \{2D\}$

$\{1\; \backslash over\; \backslash sqrt\{\backslash mathit\{f\}\}\}=\; -2.0\; \backslash log\_\{10\}\; \backslash left(\backslash frac\{\backslash epsilon/D\}\{3.7\}\; +\; \{\backslash frac\{2.51\}\{\backslash text\{Re\}\; \backslash sqrt\{\backslash mathit\{f\}\; \}\; \}\; \}\; \backslash right)\; ,\; \backslash text\{(turbulent\; flow)\}$

where $f$ is the Darcy friction factor (from the above equation or the Moody Chart), $\backslash delta\_s$ is the sublayer thickness, $D$ is the pipe diameter, $\backslash rho$ is the density, $u^*$ is the friction velocity (not an actual velocity of the fluid), $V$ is the average velocity of the plug (in the pipe), $\backslash tau\_w$ is the shear on the wall, and $\backslash Delta\; P$ is the pressure loss down the length $L$ of the pipe. $\backslash epsilon$ is the relative roughness of the pipe. In this regime the pressure drop is a result of inertia-dominated turbulent shear stress rather than viscosity-dominated laminar shear stress.

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See also

• Hagen-Poiseuille flow
• Plug flow reactor model

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Notes

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