# Flow metering tutorial - Part 1: Understanding the fundamentals

Mohit Arora and Prashant Bhargava, Freescale Semiconductor, Inc. -June 18, 2012

Flow Meters: Introduction
Flow meters are used to measure the rate of flow of liquids or gases, just like electric meters measure the amount of electricity consumed. However, unlike electric meters, which are either electro-mechanical or electronic meters, there are many variants in flow-meters, all with different concepts on how the flow of fluid is measured, with some even customized to measure special fluids.

A new generation of electronic flow meters provides better control and accuracy of fluid measurement, however it still leaves several choices on how fluid is measured. Part I of this series covers basic flow meter fundamentals including types of flow meters and the main considerations and challenges in selecting a flow meter.

Fluid Flow Measurement and Reynolds Number
Flow is generally measured inferentially by measuring velocity through a known area. With this indirect method, the flow measured is the volume flow rate, QV, stated in its simplest terms:

QV = A * V                                                             (1)

Where A = Cross-sectional area of the pipe
V = Fluid Velocity

A reliable flow indication is dependent upon the correct measurement of A and V. If, for example, air bubbles are present in the fluid, the area term "A" of the equation would be artificially high. Likewise, if the velocity is measured as a point velocity at the center of the pipe, and it is used as the velocity term "V" of the equation, a greater QV than actual would be calculated because "V" must reflect the average velocity of the flow as it passes a cross-section of the pipe.

The following are the major factors affecting the flow of fluid through a pipe:

• Velocity - speed at which a fluid moves through a pipe
• Density - weight per unit volume
• Viscosity - ease of flow of a fluid
• Pipe size - diameter of the pipe carrying the fluid

Velocity of the fluid and pipe size: Fluid velocity depends on the head pressure, which is forcing the fluid through the pipe. The greater the head pressure, the faster the fluid flow rate (all other factors remaining constant), and consequently, the greater the volume of flow. Pipe size also affects the flow rate. For example, doubling the diameter of a pipe increases the potential flow rate by a factor of four.

Viscosity of the fluid: Viscosity negatively affects the flow rate of fluids. Viscosity decreases the flow rate of a fluid near the walls of a pipe. Viscosity increases or decreases with changing temperature, but not always as might be expected. In liquids, viscosity typically decreases with increasing temperature. However, in some fluids viscosity can begin to increase above certain temperatures. Generally, the higher a fluid's viscosity, the lower the fluid flow rate (with other factors remaining constant).

Density of the fluid: Density of a fluid affects flow rates such that a more dense fluid requires more head pressure to maintain a desired flow rate. Also, the fact that gases are compressible, whereas liquids essentially are not, often requires that different methods be used for measuring the flow rates of liquids, gases, or liquids with gases in them.

Reynolds number: The most important flow factors mentioned above can be correlated together into a dimensionless parameter called the Reynolds number, which indicates the relative significance of the viscous effect compared to the inertia effect. The Reynolds number is proportional to inertial force divided by viscous force. The Reynolds number is proportional to fluid flow means velocity and pipe diameter and inversely proportional to fluid viscosity.

Reynolds number (Re) = ρ * D * v/µ                                                             (2)

Where D = Internal pipe diameter
v = Velocity
ρ = Density
µ = Dynamic Viscosity

At very low velocities of high viscosities, Re is low and the fluid flows in smooth layers with the highest velocity at the center of the pipe and lower velocities at the pipe wall where the viscous forces restrain it. This type of flow is called laminar flow and is represented by Reynolds numbers below 2,000.

At higher velocities or low viscosities the flow breaks up into turbulent where the majority of flow through the pipe has the same average velocity. In the "turbulent" flow the fluid viscosity is less significant and the velocity profile takes on a much more uniform shape. Turbulent flow is represented by Reynolds numbers above 4,000. Between Reynolds number values of 2,000 and 4,000, the flow is said to be in transition.

So Reynolds (Re) number is a quantity that engineers use to estimate if a fluid flow is laminar or turbulent. This is important because increased mixing and shearing occur in turbulent flow that results in increased viscous losses, which affects the efficiency of hydraulic machines. A good example of laminar and turbulent flow is the rising smoke from a cigarette. The smoke initially travels in smooth, straight lines (laminar flow) then starts to "wave" back and forth (transition flow) and finally seems to randomly mix (turbulent flow).