Reynolds number and Flowprofiles

The flow profile can have a significant impact on a flow meter. Most flow meters are velocity meters. Depending on the measurement principle, the flow profile has more or less influence.

When a gas or liquid flows through a straight, closed, or round pipe, a developed flow profile occurs. This means that the flow profile, the velocity distribution of the medium over the cross-section of the pipe, no longer changes. Not even after an additional 10D or 100D pipe. The velocity pattern is also symmetrical, with no swirl or crossflow.

reynolds number (re)

Re is dimensionless and is a number used to describe the flow behavior in a round (or any other form) of piping. Re is calculated using the formula:

Re = ρ . v. D / µ

ρ = the density in kg/m³
v = the speed in m/s
D = the internal diameter of the pipe in m
µ = the dynamic viscosity expressed in kg/[m.s]

The higher the density, velocity and diameter of the pipe and the lower the viscosity, the higher is Re.

The Reynolds number is important in the selection of flowmeters and for the performance of a chosen instrument. In particular, plug-in flowmeters, but also, for example, clamp-on ultrasonic flowmeters are "Reynolds sensitive".

Vortex flowmeters for example, do not function or function very poorly at low Re. Is Re lower than 5,000 a vortex meter is not an option, between 5,000 < Re < 10,000 a correction can improve the measurement result. In this case, the flowmeter needs a decent flow rate to generate the vortices. And the vortices are also only possible if the medium is not too viscous and in larger pipe diameters this also becomes easier and with a lower mass of the medium, less energy is needed to get the medium moving to create vortices. For most measurement techniques it is desirable to look at the Re number.

laminar flow profile

When the dimensionless Reynolds number (Re) is less than 2300, there is a laminar flow profile. The profile has a parabolic appearance. It can be visualized, for example, by allowing water to flow slowly through a Plexiglas pipe and injecting ink at a certain point. A thin line of ink then forms and moves with the water through the pipe.

When the flow speed slowly increases, there is a point at which the flow behavior becomes turbulent. The stripe of ink is then strongly mixed with the water and the water discolors behind the injection point.

This turbulent behavior occurs at a Re > 4000. In the range 2300 < Re < 4000, there is a transition zone. The flow profile can be laminar there, but is not steady.

The laminar flow profile is parabolic. Another characteristic of this flow profile is that the maximum velocity at the exact center of the pipe is 2 x the average velocity in the pipe. Or:

Vmax = 2 x Vgem

Turbulent flow profile

The turbulent flow profile is flatter. The profile is characterized by the fact that the velocity of the medium at a given point can be in any direction, but on average in the direction of the flow in the pipe. The flow profile is not completely flat, and the maximum velocity is 1.1 to 1.15 times the average flow velocity, or:

Vmax = ca. 1,13 x Vgem