Venturi Flowmeter Design
Venturis can be used in conjunction with pressure measuring instruments to calculate the flow rate passing through them. Venturis aren’t perfect but they have many advantages over other measurement methods.
Venturis have no moving parts and are relatively cheap and simple to produce.
Unlike an orifice plate, venturis can recover almost all the dynamic pressure at the throat.
With correct sizing, instrumentation, and calibration, they can be very accurate.
Fluid at the inlet of the venturi, has static pressure P1 and a dynamic pressure proportional to inverse square of the inlet flow area A1. As the fluid flows through the venturi, the flow area begins to contract to a new cross sectional area A2 and the fluid accelerates. The static pressure P2 at the throat of the venturi is now lower than P1 since the proportion of static and dynamic pressure has changed. The flow rate Q is proportional to the square root of the differential pressure P1-P2. Decreasing the ratio of throat diameter d to inlet diameter D will increase the differential pressure for the same flow rate. As the fluid continues past the throat, the flow area gradually increases back to A1, thereby returning the fluid to its original pressure and velocity. However, if the diverging angle is too high, the flow may separate, incurring losses much like an orifice plate. The trick is to size the angles such that the flow will be uniform and not separate so total/stagnation pressure changes as little as possible through the venturi.
The accuracy of the differential pressure measurement has a large influence on the trustworthiness of the venturi. Error in the measurement propagates to the calculation causing flow rate uncertainty.
It is common to use a differential pressure transducer (single instrument) to evaluate the pressure difference. Another option is to use 2 separate pressure transducers. However, this results in a worse uncertainty due to the compounding error from 2 sensors rather than 1.
For a known, fixed uncertainty in pressure, the uncertainty in flow rate is proportional to the inverse square of the differential pressure. As the flow rate and differential pressure increase, the uncertainty in pressure is a smaller percent of the total measurement which results in a more robust flow rate calculation. Decreasing the contraction ratio also has the effect of creating more differential pressure per flow rate which makes the venturi more accurate.
Example Design:
I created a really simple script to run the calculations over a known span of flow rates and evaluate the uncertainty. You can see how the error bars decrease in magnitude as the flow rate and differential pressure increase. The CFD of 0.40 L/s shows a good pressure recovery and differential pressure agrees with the calculation.
