Measuring flow without a flowmeter

May 3, 2023
Flow is typically measured using a flowmeter. However, flow can be measured by other means such as those used in flow laboratories that incorporate weight or volumetric techniques.

Forensic work in legal cases typically involves the examination of physical evidence after an event occurs to infer the conditions present prior to the event and why the event occurred. For example, examining a damaged part can provide considerable insight into why the part failed. However, there are many times when how the process operated is important and not what occurred to a physical device or artifact. Obtaining insight into the process is often a combination of having a detailed understanding of the process coupled with a few pragmatic assumptions and approximations.

One such case involved a sanitary sewage flowmeter installed upstream of a manhole located approximately one mile downstream of a plant with two sewage sumps. Billing increased slowly over time even though there was no increase in the number of people working at the plant. Then the billing mushroomed to almost 30 times of what was considered to be a normal flow. Given the sudden billing increases, it should not be surprising that this situation quickly became noticed by management. 


The existing sewage flowmeter was replaced a few weeks before I visited the plant to observe the operation of the new flowmeter. Upon arrival, the existing flowmeter was nowhere to be found even though it was removed only weeks earlier and was already the subject of a legal dispute. Interestingly, disappearing flowmeters and other artifacts that cannot be found are not uncommon in legal cases.

Water from plant wells was used to produce potable water, operate safety showers, operate eyewash stations and water lawns in addition to other process applications. The wells had recently exhibited extremely high flows due to broken pipes resulting from a recent freeze. Water leaking from broken pipes typically falls to the ground and does not get into the sewage system. Nonetheless, the sewage district alleged that an excessive amount of well water could be entering the sanitary sewage system, so this needed to be investigated as well.

In the meantime, the sewage district continued to bill the plant for its sewage based upon its own internal formula instead of the actual measurements from the new flowmeter. Billing remained high using these calculations because the existing flowmeter had measured extremely high in the months after it failed.

To get a sense of the magnitude of the problem, billing was so high that generating the billed amount of sewage would require flushing over 500 toilets every minute 24 hours a day — every day during the month. By observation, there were far fewer toilets in the plant and not nearly enough people to flush them that often.

Further, the pumps were not capable of pumping that much sewage, and if they could, high pressure in the sewage pipe would likely cause sewage to flow out of its manhole covers. My visual observation of a trickle of flow a few days after the new flowmeter was installed and plant data supporting intermittent pump operation did not stop the district from billing exorbitantly that month and beyond. 

Process description

Sewage accumulated in a maintenance shop sewage sump and a plant sewage sump. The sewage from each sump was pumped to an underground header that allowed the sewage to flow downstream via gravity, through the flowmeter, and then into the sewage district’s main sewage header for treatment. This underground pipe was designed to be partially full during operation and empty gradually after the operating sump pump turned off.

The two sump systems were independent upstream of their respective connections to the underground header. The maintenance shop generated only a small amount of sewage, primarily during the day shift on weekdays. Therefore, its contribution to the total flow was small, so focusing on the larger plant sewage sump seemed reasonable.

During typical operation, the plant sewage sump slowly accumulates liquid overnight and then fills for a time in the morning when people arrive in the plant and use the facilities. Liquid slowly accumulates again before accelerating when people take their morning break. The significant amount of liquid generated during lunch generally causes the sump pumps upstream of the plant sewage sump to operate and fill the plant sewage sump. When the plant sewage sump reaches a high level, its pump turns on and empties its sump. A similar chain of events occurs during other breaks, shift changes and when workers clean up and shower.

Upon my arrival onsite, the failed flowmeter (that somehow disappeared) had just been replaced with a new flowmeter that the sewage district did not believe. Therefore, the sewage district continued to bill based on its internal formula that produced extraordinarily large sewage flows and hence, extraordinarily large sewage bills. There was no other flowmeter in the line to check the new flowmeter… or was there? 

Problem solution

Flow is typically measured using a flowmeter. However, flow can be measured by other means such as those used in flow laboratories that incorporate weight or volumetric techniques. In this installation, the sewage was not weighed but rather controlled on a volumetric basis. In particular, each sump pump would turn on at a high level in its respective sump, turn off at a low level and then wait for the level to rise to the high level and turn on again. By neglecting contributions from the smaller maintenance shop sewage sump, the larger plant sewage sump pump flow essentially becomes the same as the total sewage flow.

If this were a flow laboratory, tank geometry and level data would be used to calculate the pump flow under controlled conditions with no liquid entering the tank. However, in this process, sewage continues to flow into the plant sewage sump while its pump is in operation emptying the same sump. In other words, unknown amounts of sewage are both entering and exiting the sump at the same time.

After some investigation, it was discovered that the sump level was recorded in the plant control system every minute. The pump flow is an unknown amount of liquid being removed from the sump by its sump pump while an unknown amount of sewage is entering the sump. Therefore, calculating the flow rate from the falling level data would not accurately reflect the pump flow.

As is often the case, much can be derived from more granular information, in this case from data obtained in the minutes before and after the minute that the plant sewage sump pump turns off. During the minute before the minute that the pump turns off, the sump level drop can be used to calculate the pump flow minus the sewage flow into the sump. During the minute after the pump turns off, the sump level rise can be used to calculate the sewage flow into the sump. The sewage pump flow can then be calculated as the flow out of the tank one minute before the sump pump turns off plus the flow into the tank one minute after the sump pump turns off.

The appropriateness of this flow calculation is predicated on the pragmatic assumption that the sewage flow into the tank remains steady between the start of the minute before the pump turns off until the end of the minute after the pump turns off. This is reasonable because during these 3 minutes, part of the inflow is gravity fed and not likely to change much. In addition, upstream sump pumps that have turned off are not likely to turn on because they have already emptied their respective sumps and are waiting for them to fill again.

However, any one of the upstream sump pumps can turn off during these 3 minutes as its sump becomes empty. The occurrence of this possibility will cause a significant error in the sewage flow calculation. Therefore, it is expected that the flow calculation described above should be valid for most of the 3-minute intervals but fully expected to exhibit a significant error for those intervals during which an upstream sump pump turned off. 

Flow calculations

The results of calculations based upon actual measurements were convincing. Five out of six flow calculations performed using a spreadsheet containing actual sump levels during appropriate 3-minute intervals resulted in sump pump flow rates that were both reasonable and within one percent of each other. My recollection is that the sixth calculated flow was off by 20 percent or more. These results are fully consistent with the above analysis and were used to support the flow measurements generated by the new flowmeter. 

Case settled

Part of my report included an expected range of sewage flow that should be generated by the plant understanding that inflow and infiltration on wet weather days contribute to the total sewage flow. The parties finally came to an agreement and the sewage district issued a credit to the plant when the sewage flow measurements using the new flowmeter remained within this range for several months. 


David W. Spitzer has written over 500 technical articles and 10 books on flow measurement, instrumentation, process control and variable speed drives. David offers consulting services, writes/edits white papers, presents seminars and provides expert witness services.

Spitzer and Boyes LLC

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