# Does back pressure give incorrect flow reading?

1. Oct 30, 2016

I have to build a digital peak flow meter. I have two models based on calculations ( ideal). I have noticed that the flow rate on the model with a tighter constriction has a greater value than that of a much broader constriction. While testing it out, i noticed air resistance from the first model ( tighter). The second one has almost no resistance. So, does back pressure give an incorrect reading>

2. Oct 31, 2016

### CWatters

Is the airflow sensor in the constriction?

3. Oct 31, 2016

No, it is attached to nozzles present on each side of the constriction.

4. Nov 1, 2016

### CWatters

Fluid dynamics isn't my subject but...

How do you convert differential pressure to flow rate?

If two devices with different constrictions give different results that suggests to me the possibility of an error in the way the conversion is done.

5. Nov 1, 2016

flow = a2*sqrt(2*ΔP/(density*(1-pow((a2/a1),2))));

where Q is the flowrate, ΔP is the pressure difference between the two nozzles, A1 and A2 the outer and inner diameters respectively, and ρ the density.

A higher reading was observed with a smaller constriction.

6. Nov 1, 2016

### JBA

First, the above equation is clearly only for a theoretically ideal nozzle because the one factor absolutely mandatory in every real world application flow measurement nozzle equation is the nozzle coefficient (actual measured vs ideal) of each nozzle's particular design.

As to your original question, the smaller the second section diameter the higher the velocity in that section and greater the differential between the velocity in the two sections; therefore, the greater static pressure differential as well. The "a2/a1" factor in the equation varies correspondingly to normalize the measurement between the two flow velocity conditions.

With regard to relative accuracy, the effects on flow of a given nozzle design can affect the flow and pressure differential of that nozzle, for example, flow necking at the small diameter entrance, and as a result nozzle designs can not be scaled based strictly on a given configuration, the actual nozzle coefficient for each nozzle design must be established by flow testing in a calibrated flow testing system of that individual nozzle design, including its entry and small areas ratio.