Differential Pressure (Flow) Measurement

I have a water flow measurement, through orifice + Differential Pressure Transmitter (DPT). DPT's signal (Dp) is connected to DCS's AI card and square-rooted (in DCS software).

Question: Is the flow calculation completed with just the sqrt (Dp)? Or the sqrt(Dp) has to be multiplied with factors (e.g discharge coefficient, comprecibility factor) derived from the orifice calculation sheet?

If it's the latter, which is the formula that has to be implemented in the software of DCS? For information, the DPT is from Yokogawa and the orifice is from another manufacturer.

I don't refer to pressure-temperature compensation which is done nevertheless, just the sqrt(Dp)-flow calculation.

my email is [email protected]. Any help will be appreciated!!

Thanks in advance
The square root function completes the orifice measurement for the set of orifice parameters in the calculation in the orifice data sheet. If any of the orifice flow or parameters change due to density, temperature or pressure during operation, the square root function will not compensate for the changes. For that you will need a full orifice flow calculation in your DCS or in a flow computer. If you need a special orifice calculation such as AGA 3, ISO 5167, etc. (which you do not have a need for), the square root function will not be adequate. Many orifice meters that are not used for custody transfer, just use the square root function. Make sure your tech's know where the square root is done (if fact, that should be standardized in your plant).

For a simple water calculation where the temperature is relatively constant, using the square root function should be more than adequate.

William (Bill) L. Mostia, Jr. PE
ISA Fellow, FS Eng. (TUV Rheinland)
WLM Engineering Co.
Thanks a lot Bill for your time!

In the measurement, there is a factor of 6.6407833 multiplying the square-rooted Dp (e.g SQRT(Dp) * 6.6407833), in the DCS software block.

The discharge coefficient is 0.598243 and β = 0.745798.

The value (6.6407833) cannot be verified by neither combination of β or meter coefficient C (Discharge Coefficient * sqrt(1/(1-β^4)).

So this 6.6407833 seems to have fallen out of nowhere!

The orifice has been calculated based on ISO 5167 (acc. to calculation sheet).

There is no worry about temperature and pressure combination, it is done in other part of the DCS software block. There is no flow computer.

Do you have any idea of how the 6.64 has been introduced in the calculation and most basically, is it needed?

Unfortunately, I cannot upload the FBD of the measurement, through the site.

Thanks again and I hope not to bother you very much!

There are a number of factors that are combined to come up with the multiplying factor to multiply times the differential pressure to get flow rate. Some are related to the orifice plate design, to the selected base conditions that the orifice calculation uses, and unit conversions to get to your flow units (lb/hr, barrel per hour, gallons per minutes, etc.). The factors should be on your orifice calculation and specification sheet that came with your orifice. If you do not have the calculation, you should check with the orifice plate supplier as they keep their calculations for just this case. If the calculation is not available, you can redo it or you can outsource it. If you want to do it yourself, there are a lot of programs for sizing orifices available. You can find some at these links:



http://chemicalengineeringnow.com/Orifices.aspx (free but simple)


If you want to understand more about orifice calculations and measurement, the following references may be useful:

Flow Measurement Engineering Handbook 3rd Edition, R.W. Miller
Principles and Practices of Flow Meter Engineering, L.K Spinks (and oldie but a goodie)

William (Bill) L. Mostia, Jr. PE
ISA Fellow, FS Eng. (TUV Rheinland)
WLM Engineering Co.
Thanks again Bill for the valuable info,

I have checked the proposed sizing programs, especially the axwap.com program. A lot of parameters!

Both your posts are very helpful. After reading them, I came out with that the differential pressure alone is not adequate, since the specification is ISO 5167. So, based on the other documentation you mentioned, I will have the sqrt(Dp) multiplied by the product of (Coefficient of Discharge) x velocity of approach x orifice bore cross-section or Cd x 1/(sqrt(1-beta^4)) x pi x (d/2)^2.

Did I get it right? Is the product mentioned above, adequate to achieve qood accuracy for hot water (120oC, 20bar) flow measurement?

Thanks again, hope not to bother you a lot!

Arthur Mayclin

If you have the orifice plate design data, and don't want to get wrapped up in the actual calculation, you can perform a ratio adjustment just as easily, and it is sufficiently accurate for most uses (not custody transfer). To do so gather your design flow rate (Qd), design orifice differential pressure (DPd) at that flow rate, design temperature (Td) and pressure (Pd), and then perform the following using flowing conditions (temperature and pressure must be absolute values):

Qf = Qd * Sqrt((DPf*Pf*Td)/(DPd*Pd*Tf))

Negate pressure and temperature if that compensation is not required (which simplifies further).

For using a simple square root block, the design values are brought out for the bias multiplier, and flowing pressure and temperature are square rooted separately (if needed).

Also, know your square root function, since some control system square root functions actually square root the bias as well.
I believe one of the equations is given below is similar to your equation:<pre>
Q=Cd Ao Y&#8730;(2&#8710;P/(&#963;(1- &#946;^4 ))

where: Q = Volumetric Flow
Cd = Discharge Coefficient
Ao = Orifice Area
Y = Coefficient of Expansion, Y = 1 for incompressible flow
&#8710;P = Differential Pressure
&#963; = Mass Density
&#946; = Orifice Beta Ratio</pre> &#8203;&#8203;
Note that you need to be careful to get all you units correct and use the correct formula for either volumetric flow or mass flow. See:


I found these equations for Excel that might be of help (I did not look into these Excel formulas due to time constraints).



Orifice accuracy is 1%-5% depending on the installation unless you take special care then you might get a little better. Your installation probably has more to say about your accuracy that the equation used. This equation above should be adequate.

William (Bill) L. Mostia, Jr. PE
ISA Fellow, FS Eng. (TUV Rheinland)
WLM Engineering Co.

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