Flow profile explained

There are many different factors that can influence the final choice of flowmeter for an application. Of these factors, the flow profile is one of the most important, but often least understood. This article explains how flow profiling can help you choose the best flowmeter for your application.

Flowmeter selection would certainly be a lot easier if every application behaved in the same way. Unfortunately, every fluid behaves differently when flowing through the pipeline, meaning that there is no single flowmeter suitable for every job.

Understanding how this behaviour can affect flowmeter performance is crucial to ensuring that you get a flowmeter that matches your needs.

In simple terms, the flow profile explains the way in which the flow of a fluid behaves or is likely to behave in a pipeline based on its velocity and viscosity. Once this is known, it is possible to start to decide which of the many different types of flowmeter available is best suited to the demands of the application. 

The term ‘Flow Profile’ is generally understood to refer to a vector diagram of the conditions within the pipe and an example is shown in figure 1 (see below).

The main cause of this is viscosity – an internal property of a fluid that offers resistance to flow. How much the fluid resists flow in turn affects the velocity of flow through the pipeline.

A simple illustration of how resistance can increase with viscosity is to imagine stirring a spoon in a bowl of water. With nothing to impede it, the spoon travels quickly and easily through the water. Now imagine stirring honey, honey is more difficult to stir than water because it has a higher viscosity than water.

The viscosity and velocity of a fluid can significantly affect the way in which it flows through a pipeline.

The same applies to the flow of fluid through a pipe. As the level of resistance, or shear rate, increases, the way in which the fluid behaves will change.

By profiling the flow of a fluid through a pipeline, it is possible to find out how it behaves and from there to narrow down the choice of flowmeters to those best able to cope with the conditions of the application.

What type of fluid do you have?

The viscosity and velocity of a fluid can significantly affect the way in which it flows through a pipeline. Fluids will behave differently and will flow at a different rate at the centre of the pipeline than they do at the sides, because of the resistance generated by the pipe walls.

Put simply, fluids can be categorised as either Newtonian or non-Newtonian. Most are Newtonian, and flowmeters are generally designed for Newtonian fluids. 

Newtonian fluids are those which have a tendency to ‘stick’ to the pipe walls, resulting in the liquid moving more slowly at the sides of the pipe than in the middle. These types of fluids have a directly proportional relationship between the pressure of the liquid flowing through and the resistance, or shear force, caused by the fluid sticking to the pipe walls. Examples of Newtonian fluids include milk, water, acids and mineral oils.

There are some fluids, however, which are Non-Newtonian such as paints, shampoos and yogurt. The behaviour of Non-Newtonian fluids is harder to predict, as there is no relationship between pressure and resistance. Instead, their behaviour tends to vary either with time or as a consequence of changes in the shear force inflicted by resistance from the pipe walls.

What type of flow do you have?

There are three types of flow, each of which are linked to the velocity of the fluid.

• Laminar flow - occurs at stable, low flow rates and is the most predictable type of flow. The fluid settles into streamlined tiers which are prevented from merging by the viscous forces within the liquid and move in the same direction at a constant speed. Fully Developed Laminar Profile is parabolic in form (see figure 1).
• Transitional flow - occurs when an increase in velocity causes distortions in the flow. This leads to mixing of the tiers within the fluid, resulting in the fluid exhibiting both laminar and turbulent characteristics at different points throughout the pipeline. The profile in transitional flow is unstable and complex, it may be parabolic as in laminar, flatter as in turbulent flow or a combination of both. 
• Turbulent flow – this type of flow occurs at faster flow rates. Mass distortions in flow result through the formation of eddies and whorls which themselves randomly fragment into smaller distortions, causing blending of the tiers within the fluid. Fully Developed Turbulent Profile is not fixed, but changes with the Reynolds number, approximating a flatter shape than the parabolic, as also shown in the diagram below.

Turbulent flow is the flow regime found in almost all applications, and is the preferred condition for a flowmeter installation as flowmeters are all calibrated in such conditions and it provides the best situation for the flowmeter to achieve repeatable and accurate flow measurements. 

To select the appropriate flowmeter, it is necessary to calculate the Reynolds numbers of the application, which should take into account the full range of conditions under which the flowmeter will be operating. These figures are the ratio of momentum against viscosity and can be obtained by calculating the minimum and maximum fluid flow and viscosity figures of the application using the following equation:

where:

• Re is Reynolds Number
• V is mean velocity
• ρ is flowing Density
• µ is absolute viscosity

Once the Reynolds number of the application is known, it can be matched against a flowmeter’s Reynolds range to help pick the one that is best able to meet the demands of the application. With a Reynolds number less than 2,000, the flow is laminar, a Reynolds number in the range 2,000 – 4,000 denoting transitional flow and a number of 4,000 or above denoting turbulent flow, (the most common).

Getting the most from your flowmeter

Understanding your piping system is another crucial step in making sure you get the best performance from your flowmeter. The positioning of joints, elbows and potential sources of disturbance such as pumps, valves and filters can all affect the way in which a fluid flows through the pipe, with a resultant effect on the profile and therefore the flowmeter accuracy and repeatability.

The best way to eliminate this is to ensure wherever possible that the flowmeter is situated with the requisite amount of straight pipe lengths upstream and downstream from the point of installation. Alternatively, where space is limited, flow conditioning equipment can be used to regulate the fluid stream and provide the ideal conditions required for flowmeter operation, or the manufacturer can be asked to give an estimate of the effect of the less than ideal conditions on the performance of the flowmeter. 

Summary

The array of technologies, designs, suppliers and application needs can make choosing the right flowmeter a bewildering process. Knowing how your fluid behaves in the pipeline can be an extremely useful first step in helping you to narrow down your choice of flowmeters for your application and make a more informed choice.