Nozzles, temperature, pressure

[PaulLag]

Hello There
Hope you are fine.

I hope to be posting my question in the right forum


Please, I’d like to ask you a clarification concerning following topic.
I am utilizing some calibrated nozzles in order to calculate the air flow on an equipment.
These nozzles are subsonic nozzles therefore governing equation is

Qm = C/(1-β^4)*ε*3.14/4*d^2*(2*DP*rho1) ^0.5 (1) kg/s
Where
d is the nozzle outlet diameter
DP is the pressure difference in the nozzle
Rho1 is the air density at the nozzle inlet
Other symbols are nozzle characteristics that won’t change for the scope of the question.

These nozzles have been provided with a calibration certificate.
The certificate provides me a mass flow (let’s call Qm) at calibration conditions, let’s say Tcal and Pcal (temperature and pressure at calibration time) , in function of different pressure differences.

Following is my question.
Let’s assume we have in test different conditions at the nozzle inlet, said Ttest and Ptest (temperature and pressure at nozzle inlet in test condition)
How can I convert the calibrated values to the test conditions ?
1) I should simply apply mass conservation therefore

​

Volume flow (Ttest,Ptest) = Qm/rho(Ttest,Ptest) m³/s

2) Since Pcal is different from Ptest, and Tcal is different from Ptest I need

​

2.1 - First to apply the correction on density at the inlet of the nozzle, since Qm is derived from conditions Tcal and Pcal instead than Ttest and Ptest, said therefore since the nozzle is the same the (1) becomes

Q2 = Qm_cal*(rho_cal/rho_test)^0.5

And then

​

2.2)

Volume flow (Ttest,Ptest)= Qm2/rho(TB,PB)
What changes with respect to 1) is that now we apply a further correction due to inlet conditions different from calibration

Thanks in advance for your help
Stay safe

 

[mk3223]

For the calibrated nozzle used in the testing, should the Vendor provide a conversion table of method to be used to calculate the real mass /volume flow rate?
Without knowing the detail of certificate testing nozzle, it's difficult to figure it out the real answer.

 

[bimr]

Have you reviewed this issue with the supplier of the nozzles?

 

[PaulLag]

Hello

I'd like to thank you for your kind answers.

@mk32323
The vendor is providing only following data
mass flow
DP
temperature
relative humidity
pressure
(therefore density)
in calibration conditions



@bimr
Unfortunately the supplier of nozzles can't help me since he asserts of not knowing in detail how to change from calibration data to other conditions.