## What is flow units?

Flow rate is the volume of fluid that passes through a unit of time. In water resources, flow is often measured in cubic feet per second (cfs), cubic meters per second (cms), gallons per minute (gpm), or a variety of other units. The measurement of water resource flow is important for applications such as system control, billing, design and many other applications. There are several ways to measure flow in a water resource system. This article outlines some of the more common methods of flow measurement and provides some useful information about flow units measurement.

## Continuity of flow equation

For water flowing in a pipe under steady-state conditions (i.e., not varying with time), continuity means that water flowing into one end of the pipe must flow out of the other end. This also means that the flow in the pipe is the same at any point along the length of the pipe. The continuity equation can be expressed as

**Flow = Velocity * Area**

The concept of continuity in steady state conditions results in the product of velocity * area being equal to a constant at any point in the pipe. This is a useful principle for making flow measurements, as shown below.

This is an example of using the continuity equation to calculate flow. Velocity is measured at 10 feet per second and the cross-sectional area of the flow is measured at 10 square feet. Flow rate = 10 feet per second * 10 square feet = 100 cubic feet per second.

## Common flow unit metering methods in open channels

### Eyeball method

It is sometimes useful to estimate the flow velocity and cross-sectional area by eye and then multiply the flow velocity by the area to obtain the flow velocity (continuity equation). A ruler or tape measure can be used to improve the accuracy of cross-sectional area measurements, and a stopwatch can be used to improve velocity measurements by timing floating debris moving a set distance. The eyeball method can be used to estimate flow when only an “order of magnitude” of flow is required or when the flow rate is too low to be measured with a flow meter.

### Flow depth (Manning)

When the channel cross-sectional area and channel slope are known and uniform flow conditions exist, the Manning’s equation can be used to calculate flow by measuring depth only. The Manning’s equation is an empirical equation that describes the relationship between flow rate in an open channel under uniform flow conditions and depth, slope and channel friction coefficient (Manning’s n). Uniform flow means that depth does not vary with the length of the conduit or channel. Flow measurements using Manning’s equation for depth are not applicable to gradually changing flow conditions, such as backwater conditions upstream of a dam or weir.

The depth flow method of flow measurement is more accurate than the “eyeball” method. The main challenge with depth-only flow measurements is the potential for inaccurate Manning’s n estimates, cross-sectional areas, and non-uniform flow conditions. This method is commonly used with ultrasonic flow meters to estimate the flow of a river by measuring only the water level of the river. Often in these causes, the river level/flow relationship is developed with the help of complex river hydraulic models to account for complex channel geometry and channel friction conditions.

### Main equipment

The main device is used to measure flow in open channels, using structures such as flumes, weirs or dams, to measure flow by measuring depth. The measured depth can then be converted to a flow rate using an equation or rated curve equation.

Primary devices work by forcing the flow through a path of critical depth, for example at the top of a weir or at the throat of a flume. In technical terms, the critical depth is defined as the depth of the minimum specific energy state that results in a particular discharge. In practice, this minimum state of energy means that only one flow corresponds to the critical depth. Therefore, measuring only the depth produces a measurement of the corresponding flux and is therefore called a “primary” device.

Primary devices are a very convenient method of flow measurement because the depth can be measured from above the flow without the need to insert a sensor in the water. This makes primary flow meters more reliable and easier to maintain. A disadvantage of primary devices is that they can cause head loss and backwater in the system. Primary devices are often considered to be the most accurate method of measuring open channel flow.

#### Surface Velocity Meters

An area velocity meter is an open channel flow meter that measures flow by making two separate measurements of depth and velocity. The depth is converted to a cross-sectional area using the geometry of the pipe or channel. The flow rate is then calculated by multiplying the flow area by the velocity using the continuity equation, hence the name “AV meter”. Velocity is typically measured using a Doppler sensor, which reflects ultrasound waves back from particles in the fluid and uses the Doppler shift in the reflected sound signal to estimate velocity. Some AV meters measure surface velocity optically to estimate velocity.

AV meters are often used to measure open channel flow in sewers because the probes are relatively small and they can be installed in existing sewer pipes without causing significant head loss in the pipe. This also allows them to be used for temporary or short-term flow metering applications for sewer studies. one disadvantage of AV meters is that the sensor must be installed in the fluid. In sewers, this requires frequent maintenance to clean the sensor. AV meters are often considered less accurate than primary flow meters because primary devices only need to measure depth and depth measurements are more accurate than velocity measurements.

#### Transport time meters

Transport time meters were developed in the oil industry to accurately measure flow in large pipelines. They have been used with some success for open channel flow in water metering applications. Transport time meters also use ultrasound like Doppler meters, but instead of bouncing the sound waves off particles in the water like Doppler flow meters, they send ultrasound waves between two sensors separated from each other by a certain distance along the length of the pipe and uses the transmission time of the sound waves to calculate the velocity of the water flow. Because the speed of sound in the water is known, the speed of the water can be calculated based on the offset in ultrasonic wave transmission time that occurs due to the speed of the water.

Transmission time meters can be expensive relative to Doppler flow meters due to the many sensors and complex installation involved. They can be more accurate due to the ability to split the flow into horizontal cross sections and measure the velocity of each section.

## Flow unit measurement methods in full tube applications

### Venturi meters

Venturi flow meters use the Venturi effect to measure flow in a full or pressurized pipe by using the converging section of the pipe to restrict the flow. According to the continuity equation, the cross-sectional area of the converging section is small and therefore the velocity is higher in the throat. Due to energy conservation and Bernoulli’s principle, higher velocities in the throat result in a drop in throat pressure. The flow rate can then be determined by measuring the pressure drop in the convergent section and calculating the flow rate using Bernoulli’s equation. Venturi meters are more common in water metering applications because the pressure measurement ports can become clogged in wastewater applications.

### Magnetic flowmeter

The electromagnetic flow meter works by applying a magnetic field to the fluid passing through the pipe. This causes a small electron potential difference that can be measured by the electrode sensor (due to Faraday’s law and electromagnetic induction). The magnitude of the electron potential difference is proportional to the velocity of the water, and the continuity equation can then be used to calculate the flow rate.

An advantage of the magnetometer is that the metering section is the same diameter as the adjacent pipe, so the magnetometer causes no additional head loss. For the most part, magnetometers are used for full (pressure) pipe applications, but nowadays open channel magnetometers can also be used.

### Turbine flowmeter

A turbine flow meter is a mechanical flow meter that uses a rotating turbine in flow to measure the flow of water in a pipe. The speed of the turbine is proportional to the velocity and the flow rate can then be calculated using the continuity equation. Turbine flow meters are only used for water applications due to potential problems with wastewater solids collection and clogging turbines.

## Conclusion

There are many ways to measure flow. Each method has different advantages, disadvantages and accuracy in different applications.

It is important to understand the characteristics of various flow measurement techniques to help select the right type of flow metering for your application or to properly interpret the flow measurements of existing flow meters. Tools like Apure (IoT-based water data analysis) help to examine measurements collected by flow meters and perform diagnostics to understand flow meter performance and quickly process and analyze the data. Contact us for technical or product service support.