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fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...
, 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 In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary cond ...
adjacent to the inner wall of the pipe. The plug flow model has many practical applications. One example is in the design of chemical reactors. 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 In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary cond ...
is known as
pipe flow In fluid mechanics, pipe flow is a type of liquid flow within a closed conduit, such as a pipe or tube. The other type of flow within a conduit is open channel flow. These two types of flow are similar in many ways, but differ in one important as ...
. In laminar pipe flow, the velocity profile is parabolic.


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 ( \delta_s <<''D''). : \delta_s = \frac : u^* = \left (\frac \right )^ : \tau_w = \frac : \frac = \frac := -2.0 \log_ \left(\frac + \right) , \text where f is the Darcy friction factor (from the above equation or the Moody Chart), \delta_s is the sublayer thickness, D is the pipe diameter, \rho is the
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
, u^* is the friction velocity (not an actual velocity of the fluid), V is the average velocity of the plug (in the pipe), \tau_w is the shear on the wall, and \Delta P is the pressure loss down the length L of the pipe. \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.


See also

* Hagen-Poiseuille flow *
Plug flow reactor model The plug flow reactor model (PFR, sometimes called continuous tubular reactor, CTR, or piston flow reactors) is a model used to describe chemical reactions in continuous, flowing systems of cylindrical geometry. The PFR model is used to predict th ...


Notes

{{reflist Fluid dynamics