Measuring fluid flow is one of the most important aspects of process control. In fact, it may well be the most frequently measured process variable. This bulletin describes the nature of flow and factors affecting it. Devices commonly used to measure flow are presented, as is a discussion on accuracy and how it is typically specified. For quick reference, a table listing the primary characteristics of flow metering devices is included along with a conversion chart for the various measurement units encountered in dealing with flow.

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:

In this equation, A is the cross-sectional area of the pipe and V is the 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.

FACTORS AFFECTING FLOW RATES IN PIPES

The major factors affecting the flow of fluids through pipes are:

• the velocity of the fluid.

• the friction of the fluid in contact with the pipe.

• the viscosity of the fluid.

• the density of the fluid.

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 times. Pipe friction reduces the flow rate of fluids through pipes and is, therefore, considered a negative factor. Because of the friction of a fluid in contact with a pipe, the flow rate of the fluid is slower near the walls of the pipe than at the center. The smoother, cleaner, and larger a pipe is, the less effect pipe friction has on the overall fluid flow rate.

Viscosity (m), or the molecular friction within a fluid, negatively affects the flow rate of fluids. Viscosity and pipe friction decrease 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 (other factors remaining constant). Viscosity is measured in units of centipoise. Another type of viscosity, called kinematic viscosity, is measured in units of centistokes. It is obtained by dividing centipoise by the fluid’s specific gravity. Density (r) of a fluid affects flow rates in 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. It has been found that the most important flow factors can be correlated together into a dimensionless parameter called the Reynolds number, which describes the flow for all velocities, viscosities, and pipeline sizes. In general, it defines the ratio of velocity forces driving the fluid to the viscous forces restraining the fluid, or:

At very low velocities of high viscosities, RD is low and the fluid flows in smooth layers with the highest velocity at the center of the pipe and low 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. One significant characteristic of laminar flow is the parabolic shape of its velocity profile (Figure 1).

At higher velocities or low viscosities the flow breaks up into turbulent eddies 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.

MEASUREMENT OF FLUID FLOW IN PIPES

Of the many devices available for measuring fluid flow, the type of device used often depends on the nature of the fluid and the process conditions under which it is measured. Flow is usually measured indirectly by first measuring a differential pressure or a fluid velocity. This measurement is then related to the volume rate electronically. Flowmeters can be grouped into four generic types: positive displacement meters, head meters, velocity meters, and mass meters.

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