Relationship between Reynolds and exponent n

[Superossido93]

Hi,I'm an Energy Engineer from Italy. I have a problem regarding the measurement of the volumetric rate of a pipe using a transit-time ultrasonic flowmeter clamped-on the pipe. I already know that the flow is high( about 900 m^3/h) and the Reynolds should be in the millions(about 6 mln). I found a way to calculate the velocity profile in a paper ("effect of velocity profiles on measuring accuracy of transit time ultrasonic flowmeter" by Hui Zang etc,page 5,paper attached below)in which u=um*((1-r/R)^(1/n)) where um is the mean velocity of the fluid, and n is an exponent depending on Reynolds. I can't find anywhere a value of n for really high Re (I found n=0.86 for Re=5e5) or a formula to calculate it. All of this is needed to calculate the flow rate Q explained in the same page of the paper.Could someone help me?

thanks in advance

Masis

 

[btrueblood]

Look at the trend of n vs. Re. The value will just increase with increasing Re, therefore the correction factor will improve from 0.95 to a value nearer to 1.0. Does a 5% error matter to you? Did the meter come with a calibration (and if so, at what Re?), or does it compute the correction factor internally based upon user inputs (some do)?

 

[georgeverghese]

Whilst I dont have the info you ask for, a calc on my line sizing spreadsheet tells me, in the case of water, you are running at >50m/sec for 900m3/hr on a DN80 line or smaller. This is well beyond the velocity limits permitted for any line or flow measurement device for liquid service.
Nre is approx 1.5e6 for a typical 3-5m/sec velocity range. This still doesnt help to bring Nre within the bounds of table 1 on page 5 of this document though, but you may perhaps take the risk of extrapolating to this value from Nre = 4.5e5, if you dont get any guidance for Nre = 1.5e6.

 

[hacksaw]

Your flow profile correction is only as good as the piping layout, and whether you are using flow conditioners.

What are the suppliers recommendations on fluid velocity and the fluid type you are measuring.

 

[Superossido93]

Hi, thank you for your reply.

My pipe has an internal diameter of 311.8 mm, the temperature of the water is about 180 °C and pressure about 20 bara. Thus the velocity of the fluid is roughly 3.29 m/s for the flow rate of 900 m3/h( the velocity, and therefore the flow rate, is calculated by my flowmeter). The value of the correction factor (by equation) is a number inferior than 1, but the exponential number n depends to Reynolds, and I can't find by which correlation.
Nevertheless this flowmeter (at868 by GE) requires you to decide if you want to use the Reynolds correction or not, and if so(as in my case), to specify the value of the kinetic viscosity (you can say to use a table that it should be in the software, or just give a straight value). Sad to say, but I saved the log file and it doesn't give you the correction factor, so I cannot even say what it is.

 

[btrueblood]

Have you tried contacting GE to get the user manual? Or googling for it?

Fairly easy to find -

https://www.instrumart.com/assets/GE-AT868-Manual.pdf

Pages 2-9 thru 2-12 describe how to set the meter up for internal calculation of the correction factor, or inputting your own value. I'd let the meter do it, but then...

 

[hacksaw]

For straight pipe flow with a Reynolds number greater than 6000000, the flow is turbulent with a uniform velocity profile, with boundary layer thickess 0.03mm, so no Reynolds correction is needed.

Your reference is only for Reynolds numbers less than 100000. Major corrections would only be warranted for Reynolds number much lower less than 20000, where laminar flow conditions would be encountered.

 

[hacksaw]

correction boundary layer thickness of 0.123 mm, more or less

 

[georgeverghese]

That much better now, your second post with the bigger line ID gives Nre at a much lower 1.3e6 with velocity at 3.3m/sec.