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How to calculate flow rate from pressure with a differential pressure transmitter?
Mar 05,2020
Differential pressure transmitters (DP transmitters) are very versatile and can be used to measure more than pressure. In fact, over the years, they became go-to solutions for measuring level and flow. New, dedicated flow meters and level sensors are beginning to edge out the old differential pressure solutions but they still have their uses. If for no other reason than the cost of transition, differential pressure level and flow meter solutions will likely stay in use for a while.

The elements of a differential pressure flow meter
A differential pressure flow meter (DP flow meter) combines three essential elements:

The primary element is something inside the pipe that creates a change in pressure.
The transmitter reads the pressure change and converts it to numbers we can read.
The third element is a structure connecting the primary element and the pressure created by it to the transmitter. This covers impulse lines, tubing, valves, and other mechanical bits.
We now have DP transmitters with primary elements, transmitters, and connections all integrated, which makes installing them easier.

How to calculate flow rate from pressure
Bernoulli’s principles for differential pressure flow measurement
First, we need to start with fluid mechanics, or to be specific, Bernouilli’s principles – the physics behind the differential pressure flow meter.

Bernoulli was a Swiss mathematician in the 1700s, studying the conservation of energy. The principle named after him says, in a nutshell, that the sum of all energies – static, potential, and kinetic – in a fluid running within a pipe remains the same throughout the pipe.

For a differential pressure meter, the sum of all these energies upstream equals the energies downstream. We can read static energy as pressure, potential energy as elevation, and kinetic energy as velocity.

Reynolds numbers for differential pressure flow measurement
This is where Osborne Reynolds comes in. He became famous for his study of flow, and Reynolds numbers can be used to predict turbulence and find out how fluid behaves on different scales.In Instrumentation, we use the Reynolds number to scale out new flow meters, finding out their range and applicability.

Differential pressure flow meter types based on primary elements
We have to select the right primary element for your differential pressure flow meter, so we’ll give you a brief overview of the most common, with pros and cons.

Before we go over the types of differential pressure flow meters, we need to understand their effects in the pipe. Basically, a primary element creates a pressure drop by restricting the flow. The DP transmitter then measures the drop and uses Bernoulli’s equation to calculate the flow. The square root of the pressure drop across the restriction is proportional to the flow.

Let’s move on to the differential pressure flow meter types.

Orifice plate DP flow meter
The most common solution to differential pressure flow measurement, orifice plates are easy to install and cover a wide range of applications, like gas, liquids, and steam. For instance, the conditioning orifice plate can resolve irregular flow profiles. It has the advantage of working in short pipes with straight runs, usually only two diameters before and after the sensor.

Pitot tube DP flow meter
Believe it or not, Henri Pitot was also an engineer. If you do your job well in this line of work, maybe you will also have some equipment equation named after you one day.

Anyway, the pitot tube (it is not capitalized for some reason) goes across the pipe. Upstream you have the total pressure, downstream the static pressure, and the output is the pressure differential.

Venturi tube
The Venturi effect (discovered by Giovanni Battista Venturi, an Italian physicist) covers the drop in pressure when fluid goes through the restricted section of the pipe. A Venturi tube creates a lower pressure downstream. When you connect your DP differential pressure transmitter to the upstream and downstream sides, you’ll get the pressure differential.

Differential pressure flow meter installation
The three main elements of a differential pressure flow meter we mentioned earlier – primary element, transmitter, and structure – can cause problems as time marches on, such as mechanical misalignment, seal pot level changes, and others. To avoid these problems, we now have ready-made DP flow meters with primary elements already integrated with the differential pressure transmitters.

Calibrating the transmitter is fairly easy on the technical side but it can be very time-consuming. Calibrating a primary element requires removing it from the pipe, which means stopping your process and taking apart the structure. Nobody likes doing that, so differential pressure flow meters often stay uncalibrated for years. One would not encounter these issues with dedicated flow devices like magnetic flow meters, coriolis flow meters, etc.

We still use differential pressure transmitters for flow measurement because they still work. However, we have a lot of new tech out there that provides better accuracy and easy installation.