Flow profile

Undisturbed flow profiles in a pipe. Laminar flow, turbulent flow in a smooth and rough pipe.

The flow profile is a term used in fluid mechanics , especially flow measurement technology . It describes the location-dependent distribution of the flow velocity in the cross-section of a flow . If a fluid flows through a pipe (or channel or channel ), for example, the velocity distribution over the cross section is not constant , but typically zero on the pipe wall and at most in the center of the pipe.

A distinction is made between disturbed and undisturbed (or fully developed ) profiles. An undisturbed flow profile exists when it no longer changes in the direction of flow. The speed distribution is symmetrical to the pipe or duct axis. A disturbed profile is present at the inlet, outlet, behind bends, reductions, widenings and protruding elements of a flow. The flow profile can then be asymmetrical to the pipe or channel axis and changes in the direction of flow. After a length that depends on the disturbance (for pipelines about 10 to 60 diameters ), the disturbed flow profile changes into the fully developed profile.

In pipe flows, the shape of a full flow profile depends on the Reynolds number (i.e., mean flow rate, viscosity of the fluid, and diameter of the pipe) as well as the roughness of the pipe wall.

If the Reynolds number is less than approx. 2500, there is a laminar flow and the undisturbed flow profile is parabolic . In the case of a turbulent flow (Reynolds number greater than 10,000), the flow profile can be described using a power law:

{\ displaystyle v (r) = v _ {\ mathrm {max}} \ cdot (1-r / R) ^ {1 / n}}

Here, the flow velocity is at a distance from the pipe axis and the flow velocity in the center of the pipe. is the radius of the inner pipe cross-section and an exponent that is weakly dependent on the Reynolds number and the roughness of the inner pipe wall. For Reynolds numbers larger, for example , the Reynolds number dependence of the exponent disappears and converges to a value of around 10. ${\ textstyle v (r)}$ ${\ textstyle r}$ ${\ displaystyle v _ {\ mathrm {max}}}$ ${\ textstyle R = D / 2}$ ${\ displaystyle n}$ ${\ textstyle 2 \ cdot 10 ^ {6}}$

Individual evidence

^ Alfred W. Rechten: Fluidics: Fundamentals, components, circuits . Springer, 2013, ISBN 978-3-642-93042-3 , pp. 18th ff .
^ Matthias Kraume: Transport processes in process engineering: Fundamentals and implementations of apparatus . Springer-Verlag, 2012, ISBN 978-3-642-25149-8 , pp. 142 .
^ ^A ^b H. Bau, NF DeRooij, B. Kloeck: Sensors, Mechanical Sensors . John Wiley & Sons, 2008, ISBN 978-3-527-62072-2 , pp. 376-379 .

[1] Alfred W. Rechten: Fluidics: Fundamentals, components, circuits . Springer, 2013, ISBN 978-3-642-93042-3 , pp. 18th ff .

[2] Matthias Kraume: Transport processes in process engineering: Fundamentals and implementations of apparatus . Springer-Verlag, 2012, ISBN 978-3-642-25149-8 , pp. 142 .

[:0-3] A ^b H. Bau, NF DeRooij, B. Kloeck: Sensors, Mechanical Sensors . John Wiley & Sons, 2008, ISBN 978-3-527-62072-2 , pp. 376-379 .

Flow profile

See also

Individual evidence