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Formula for calculating flow by using Orifice:
C [none]: discharge coefficient
β [none]: Diameter ratio (β=d/D, where D is Pipe diameter)
ε [none]: Expansion factor
d [mm]: Bore diameter
Δp[kPa]: Differential pressure
ρ1[kg/m3]: Up stream fluid density

For example, the spec of Orifice is found as following:

Then we will find:
C = 0.60851
β = 0.74881
ε = 1 (for water and other liquids which are considered incompressible)
d = 368.5252 mm
Δp = 14 kPa
ρ1 = 992.3992 kg/m3

Apply those number to formula, we get:
but the unit for this Qm is (10^-4)Kg/(s.10^-0.5)
Change this into Kg/s, we get: Qm=413.218 (Kg/s)
Change this into m3/s, we get: Qm=0.4163829 (m3/s)
Finally, change this into m3/h, we get Qm=1498.9786 (m3/h)

Nearlly same as spec of Orifice! (1500m3/h)

But it take me a long time to make calculation. In my plant, this flow transmitter is over range sometimes, so i want to change the range of measuring from 1500m3/h into 2100m3/h. Then i convert the formula into:
alpha is not changed.
We can get alpha from specification of Orifice: 1500m3/h=alpha*sqrt(14kPa),
then calculate deltaP for range of 2100m3/h, i get deltaP=27.44kPa.
Fortunately, the flow transmitter works well when i change from 14kPa into 27.44kP.

Useful Link
Online caculation for differential pressure flow meter
Calculation document 1
Calculation document 2
Fundamental of Orifice 1
Fundamental of Orifice 2

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