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Square root, temp compensation
flow calculation to extract square root from Dp of a orifice plate installed on natural gas pipeline

i am going to make a program that extracts square root from Dp of a orifice plate installed on natural gas pipline. so i have to calculate the actual flow in cubic meter. i have made the program for square root extraction but i don't know how to compensate the ambient temp which effect the flow (as gas expand with rise of temperature and vice versa).

Is there any relation ship for temp compensation so that to following that relation i could compensate the error (due to variation in ambient temp)?

1. Unless the pressure is constant you will also have to compensate for that as well.
2. Basic relationship is:
Q = K * SQR(2*delta-P/density)

You can simplify this all down to:
Q = K * SQR(delta-P * T1/P1)

where K is all constants combined, delta-P is measured differential pressure, T1 is absolute temperature upstream of the orifice and P1 is absolute pressure upstream of the orifice.

To determine K, look at the orifice calibration sheet and plug in the values for Q, delta-P, T1 & P1 at the design point and solve for K.
NOTE: this is volumetric flow. If you are looking for NORMAL cubic meters, which is really mass flow, then the equation is:
W = K * SQR(delta-P * P1/T1).

Thanks otised for your reply

1) what will be the units of delta P,T1 & P1 if i want to measure flow in cubic meter.

2)How to measure K because i don't have any data for it. the system installed here is almost 15 to 20 yrs old....



What you need is a known calibration point, which is what the orifice calibration data sheet provides. If you do not have this on file, you could try using information on the orifice plate to determine the manufacturer and an identification number and then go back to the supplier and request the calibration data.

If that is not possible, then the only other possibilities I can think of are:

1. Order a new orifice plate which will come with a calibration data sheet. (Depending on the fluid you are measuring, after 15-20 years the existing orifice might be somewhat worn and out of specification anyway.)

2. Remove the orifice plate and have it calibrated at a test facility.

3. If you have an alternate means of measuring the flow in the pipe with a temporary test meter, then use that to obtain a calibration point. This should be done near the maximum flow condition.

As far as units of measurement, the important thing is to use absolute scale instruments (or convert the readings to absolute units in the DCS). Then convert the calibration point readings to the same units. Then when you calculate K, it will include the units conversion factors as well.

If you are a purist, since cubic meters is SI units, use SI units for temperature (Kelvin) and pressure and differential pressure (Pascals).

By W.L. Mostia on 1 January, 2010 - 7:36 pm

The following might be of assistance:


Flow Measurement Engineering Handbook (Hardcover) ~ Richard Miller
Flow Measurement: Practical Guides for Measurement and Control (Practical Guides for Measurement and Control,) (Hardcover) - David Spitzer

You might be better served making this flow calculation using one of the multivariable transmitters such as the Rosemount 3095 or Honeywell SMV3000, which have the square root, pressure and temperature compensation built in.

William (Bill) L. Mostia, PE
Sr. Consultant
SIS-Tech Solutions

Thank you Otised, It is very useful information.

Some good information can be found in this manual here:

This is for a gas flow computer with a choice of flow element inputs including orifice plate, and it allows for density correction or PTZ.
Good evaluations in back.