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That Awful Reynolds Number (Part 2 of 2)

By Walt Boyes

E-Zine December 2013

Click here to review Part 1

So, what does this do for you?

For example, you have an insertion turbine flow sensor in a 10-inch diameter pipe. The sensor is inserted to one-tenth the diameter, so it sits one inch inside the pipe wall. If the flow is in the laminar region, the velocity being read by the flow sensor is much less than the velocity at the centerline of the pipe. This can cause inaccuracy in measurement. Yet if you are using the same flowmeter in the same pipe, and the flow is in the turbulent region, the velocity being read by the meter is closer to the velocity in the pipe cross-section. How do you ensure that the flowmeter is in the turbulent region? If you can limit the minimum flow rate, maximum viscosity and minimum density, you can ensure turbulent Reynolds numbers.

Now, notice that viscosity is the one factor in liquid flows that can affect Reynolds number the most. In water, this usually isn’t a problem, because the viscosity of water is relatively constant (1 cP). But in other fluids, the viscosity is a critical factor in making judgments concerning the type and size of flow element you are going to use. Temperature changes can cause significant changes in viscosity, which can correspondingly change the Reynolds number by orders of magnitude. Remember that viscosity is on the bottom of the equation. What this means is that you need to know the viscosity and the variation of viscosity in your fluid, or you may find that you have pushed the flowmeter into a region where it is non-linear or otherwise inaccurate. The easiest way to deal with this is to upsize or downsize the flowmeter until it has an acceptable Reynolds number across all the operating flow range of the meter in the application. In gas flows, the important factors are flow and density, since viscosity change in gases is small. The same thought process applies here as it does in liquid flows.

If you do not take care to ensure that your flowmeter is operating either always in the laminar flow region, or always in the turbulent flow region, as the flow crosses through the transition zone, the flowmeter will likely become erratic and it may become non-linear and inaccurate. Some flowmeters have significant effects in the transition zone. Some flowmeters have two calibration curves -- one for laminar flow and one for turbulent flow -- and they are simply not accurate in transition.

So, Reynolds number is the ratio of flow and density to viscosity and diameter. Next time a flowmeter vendor asks you for the expected Reynolds number of the flow application you are trying to deal with, you’ll know why he’s asking … and you’ll know how to figure out the answer.

If you’d like to read more on Reynolds number, Industrial Flow Measurement by David W. Spitzer has an excellent and clear discussion with examples. You can find the book at

From Flow Control (Nov/Dec 2002)

ISSN 1538-5280

Spitzer and Boyes, LLC
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