DAVID W SPITZER'S E-ZINE (June 2023)

At no flow conditions, the frequencies of the transmitted energy and its reflected signal are the same. However, under flowing conditions, the frequency of the reflected signal will be different than that of the transmitted energy. This is due to the Doppler effect that relates how sound is perceived when reflected from objects in motion. For example, the horn of a moving car has a higher pitch moving towards a listener than it does moving away from the listener. The frequency difference between the transmitted energy and the reflected ultrasonic signal increases linearly as flow increases. The transmitter processes signals representing the transmitted energy and its reflections to determine the flow rate where the fluid velocity is proportional to the difference in their frequencies. The following equation expresses this relationship.

Some years later, the sewage flow measured by one of these two flowmeters that had been measuring approximately 50% higher than a superior flowmeter in series suddenly dropped approximately 70% and remained low for a few days. The drop in flow and its resultant revenue loss was so extreme that the lawyers and engineers from both districts were asked to attend a joint inspection of the installation.

Physical observation revealed that the second district had replaced the flowmeter and changed its transmitter technology to measure level at the correct location in the flowmeter primary element. In addition, the steel piping immediately upstream of the flowmeter was replaced with fiberglass reinforced pipe that had a considerably smaller inside diameter than that of the existing pipe it replaced, which made the sewage drop into the flowmeter instead of flowing straight into the flowmeter.

Faced with a loss of revenue, the second sewage district re-installed the fiberglass reinforced pipe with steel pipe a few days later. This action stands in stark contrast to the second sewage district's lack of interest in correcting the previous installation that had been overbilling the first sewage district for years. After making these changes, the billing flowmeter measured less than 10% higher than the first district's superior flowmeter - much less than the approximately 50% measured prior to the change.

This article originally appeared in P. I. Process Instrumentation magazine. 

1. 0.60 percent
2. 1.25 percent
3. 2.50 percent
4. 12.5 percent

For the purposes of this problem, let's assume that bar is a gauge pressure unit. In addition, one atmosphere is 1.01325 bar absolute. However, 1 bar absolute will be used in this problem to simplify the calculations. In addition, one atmosphere of pressure corresponds to approximately 10 meters of water column.

The pressure associated with the seal is approximately 1 bar. Therefore, the effect on the pressure measurement is approximately 1.25 percent (1 / 80). However, the effect on absolute pressure is important for pressure compensation. The effect on the absolute pressure measurement is approximately 1.23 percent (1 / 81). It should be evident that the steam pressure is sufficiently high such that the effect of the errors on the gauge and absolute pressures are similar. Answer B is correct.

Of particular interest is the magnitude of the error. Not accounting for the pressure head of a 10 meter high seal does not seem like a big problem when the pressure is 80 bar. However, its affect on the pressure measurement is over 1 percent of the measured pressure. Further, its affect on a differential pressure flowmeter will be approximately 0.6 percent. This error can cause the annual cost of the steam to be biased by over $100,000 in large steam headers.

Additional Complicating Factors

It is common for steam pressure to be measured in headers that are (say) 40 meters above grade. Many steam plants are designed such that the transmitter is located near the control room (say) 10 meters above grade. In such installations, the pressure measurement error will be approximately three times larger than calculated above. 

This article originally appeared in P. I. Process Instrumentation magazine.