Overview of Flow Principles and Pressure-Based Flow Measurement

The flow of all fluids, whether liquid or gas, will have one of three states: laminar, turbulent, and transitional. This article discusses flow principles and pressure-based flow measurement.

Types of Flows

Laminar or smooth flow (Figure 1) tends to take place at lower flow rates in smaller pipes, where the fluid particles flow in cylinders where the outermost cylinder that touches the pipe wall does not move because of viscosity.

The next cylinder flows with the slowest speed against the stationary fluid cylinder, which shows less frictional “pull” compared to the pipe wall. The velocity gradually increases with the centermost cylinder exhibiting the greatest velocity.

Figure 1. Laminar flow

Turbulent flow tends to be chaotic in nature, resulting in irregular mixing of the fluid. Continuous changes in the flow behavior due to eddies, vortexes, and wakes pose challenge in measuring flow rates accurately.

Turbulent flow typically takes place at high flow rates and/or in larger diameter pipes and is generally preferred in cases where solids need to remain suspended in the fluid to avoid blockages or settling.

Figure 2. Turbulent flow

Transitional flow (Figure 3) shows characteristics of both laminar and turbulent flow. The edges of the fluid exhibit a laminar flow, while the center of the flow continues to be turbulent. Like turbulent flows, performing accurate measurement of transitional flows is a challenging task.

Figure 3. Transitional flow

Flow Principles

Reynolds Number

Reynolds Number is a dimensionless number, which helps in predicting the changes in flow type. It is defined as follows:

     (Fluid Density x Mean Velocity x Pipe Diameter) / Fluid Viscosity

If the Reynolds Number is below 2000, then the flow is laminar, while the value is between 2000 and 4000 for transitional flows and beyond 4000 for turbulent flows.

From the Reynolds’ equation, the turbulent fluid flow can be made more laminar by lowering the mean velocity, density and/or diameter. The laminar flow can also be achieved by increasing the fluid viscosity.

Pressure Drop

Pressure drop is defined as the loss in pressure due to the friction between the fluid particles and with the pipe walls during the travelling of a fluid through a pipe or channel. Pressure drop is roughly proportional to the distance the fluid travels.

Mass Flow Versus Volumetric Flow

Mass is defined as the amount of matter that makes up an object, while volume is defined as the amount of space occupied by an object. The mass of an object is assumed as a constant, while the volume is subjected to change based on factors such as temperature and pressure. The mass and volumetric flow rate will be nearly the same at low pressures and room temperature. Nevertheless, these rates can differ greatly with changes in pressure and/or temperature.

The volumetric flow rate of the fluid can be determined by measuring the differential pressure across a laminar flow element. In most applications, compared to volumetric flow measurement, measuring mass flow provides more accurate readings of gaseous flows due to their compressible nature, which causes drastic variations in volumetric flow rates compared to mass flow rates at different pressures and temperatures.

The addition of temperature and absolute pressure measurement to the differential pressure sensor of an LFE flow meter enables measuring both mass flow and volumetric flow accurately. This information enables a flow meter like Alicat Scientific’s M-Series mass flow meter to yield simultaneous readings of both mass and volumetric flow as well as temperature and absolute pressure.

This data also enables controlling Alicat’s mass flow controllers for mass flow, volumetric flow, or absolute pressure at a click of a button.

Influence of Pressure on Volumetric Flow

Alicat V and VC Series Volumetric flow devices are designed for use in low-pressure applications because the volumetric flow rate can be measured accurately only when the flow at the differential pressure sensor is in a laminar state.

The state of the flow can be identified from the Reynolds Number. Most Alicat volumetric flow devices are designed to make useful full-scale measurements with line pressures up to 10 – 15PSIG when air is used.

If line pressures are beyond 15PSIG, it is recommended to use an Alicat mass flow device due to the requirement for additional sensors to offset the increased densities.

Laminar Differential Pressure-Based Flow Measurement

Flow measurement is generally performed based on differential pressure. These flow meters physically constrict the flow in some way for creating pressure differentials. By Bernoulli’s Principle, the speed of the constricted flow will increase with loss in pressure.

Measuring the difference in pressure between a pressure tap positioned upstream of the constriction and one placed downstream of the constriction provides the fluid velocity.

Venturi tubes and Orifice plate flow meters have been used for decades. However, these instruments generally have a narrow useable range, typically down to 25% of the rated full-scale flow rate.

Since the differential pressure is proportional to the square of the flow velocity for turbulent flows, reducing the flow velocity to 10 times reduces the differential pressure to 100 times. It is not possible to make accurate measurements below a certain flow rate.

Differential pressure flow meters with laminar flow element (LFE) constrictions drive the fluid into a laminar regime. According to Poiseuille’s Equation, the differential pressure is linearly proportional to flow velocity within the laminar region.

This linear relationship yields a differential pressure signal that is greater in low flow compared to a turbulent flow meter. Hence, it is possible to maintain the measurement accuracy in differential pressure-based flow meters with LFE down to 1/200^th (0.5%) of their rated full- scale flows.

Conclusion

Differential pressure-based flow meters and controllers yield very accurate flow measurement based on linear data. Their flexibility enables end users to achieve accurate measurement and control of both mass and volumetric flow, as well as pressure.

This unique combination of accuracy and versatility provides a cost-effective and space-saving solution for use in numerous process industry applications.

This information has been sourced, reviewed and adapted from materials provided by Alicat Scientific.

For more information on this source, please visit Alicat Scientific.