Theory of Fluid Flow meters ~ Learning Instrumentation And Control Engineering Learning Instrumentation And Control Engineering

### Theory of Fluid Flow meters

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The measurement of fluid flow is very important in industrial applications. Optimum performance of some equipment and operations require specific flow rates. The cost of many liquids and gases are based on the measured flow through a pipeline making it necessary to accurately measure and control the rate of flow for accounting purposes.

A Flow meter is a device used to measure the rate of fluid movement at a given point in the pipe or tube. The flow meter is usually secured to a break in the pipe and the fluid is allowed to move through it.

Types of Fluid Flow meters:
Several methods are employed to classify flowmeters. One method is to divide flowmeters into the following categories:
(a) Differential Pressure Flowmeters
(b) Mechanical Flowmeters
(c) Electronic Flowmeters
(d) Mass Flowmeters

The different types of fluid flow meters are used in many industrial applications to measure the flow of fluids. The flow of a fluid can be measured in many ways. Commonly used methods are a simple volumetric measurement or a rate measurement.

A volumetric flow measurement can be as simple as filling and emptying a container whose volume is known and counting the number of times it is done or a rate measurement which is performed by keeping track of the time period.
Flow instruments measure flow using various measurement metrics. Two of the most popular measurement metrics are:
(a) Volumetric flow rate - in cubic feet, gallons, or liters per unit of time (this is an inferred measurement)
(b) Mass flow rate - pounds, tons, grams, or kilograms per unit of time.

Volumetric flow can be determined by using:
Volume Flow = Area x Velocity

If we define Volume flow = Q
Area = A, and
Velocity = V,
Then volumetric flow can be put simply as:
Q = VA

Mass flow rate can be determined from volumetric flow as follows:
We know that, M = Volume x Density of fluid
Therefore, Mass flow = Volume flow x Density of fluid

Types of Flow

Laminar Flow
Laminar flow occurs when the average velocity is comparatively low. In laminar flow, the fluid moves smoothly in orderly layers, with little or no mixing of the fluid across the flow stream. Changes in velocity can still exist as the friction of the wall slows the layers closest to the wall, while the flow in the centre of the pipe moves at a faster pace. This velocity change produces a parabolic streamlined flow profile as shown below:

Turbulent Flow
Turbulent flow occurs when the flow velocity is high and the fluid particles no longer flow smoothly in layers. In this type of flow, the laminar flow breaks down to produce intermixing between the layers. Turbulent flow is quite random, as smaller currents flow (known as eddies) in all directions. This type of flow has a flatter flow profile, such that the velocity of forward flow in the centre of the pipe is nearly the same as that near the walls of the pipe as shown below:

Common Terms Used in Fluid Flow Measurement

Velocity
This is the speed at which a fluid moves through a pipe. The speed of particles in a fluid flow varies across the flow profile - where the fluid is in contact with the constraining walls (the boundary layer) the velocity of the liquid particles is virtually zero; in the center of the flow the liquid particles will have the maximum velocity. Thus, the average rate of flow is used in flow calculations.

Viscosity
Viscosity is a property of a gas or liquid that is a measure of its resistance to motion or flow.Simply put, it is the ease of flow of a fluid. Viscosity (dynamic) can be measured in poise or centipoise, whereas kinematic viscosity (without force) is measured in stokes or centistokes. Viscosity changes with the temperature of a fluid.

Density
Density is the weight per unit volume.

Reynolds’ Number
Reynolds’ number is a derived relationship combining the density and viscosity of a liquid with its velocity of flow and the cross-sectional dimensions. It defines the flow conditions at a particular point. It is a way of representing fluidity and is a useful indicator of laminar and turbulent flow. Mathematically, the Reynolds’ number is expressed as:

## R=VDρ/u

Where:
V = Average velocity of fluid
D = Diameter of the pipe
ρ = Density of the fluid
u = Fluid viscosity

Laminar flow exists if the Reynolds number is less than 2000, and turbulence when the number is above 4000. There is not a clear transition between laminar and turbulent flows, which does complicate flow measurement in this range of operation.