# Flow Measurement

Flow measurement of liquids is one of the serious needs of modern industrial plants since it is critical to verify the amount of material purchased and sold. Accurate measurement of flow is so much significant in a number of operations, that it can create a whole lot difference between profit making and loss taking. Imprecise flow measurements or inability to take correct measurements can lead to severe results. In addition, flows throughout the process should be maintained near their preferred values with little variability. In such applications, good reproducibility is generally sufficient. Flowing systems require energy, usually provided by pumps and compressors, to create a pressure difference as the driving force, and flow sensors should bring in a small flow resistance, escalating the process energy consumption as slight as possible. Extraordinary considerations are obligatory for concentrated slurries, flow in an open conduit, and other process situations as compared to clean fluids flowing in a pipe.

Basic Relationship

In almost all liquid flow measurement instruments, the rate of flow is calculated by measuring the liquid’s velocity or the change in kinetic energy. The velocity of liquid depends on the differential pressure which is forcing the liquid through a pipe or conduit. Since the cross-sectional area of pipe is known and it remains constant, the average velocity is an indication of the flow rate. In such cases, the basic relationship for determining the liquid’s flow rate is given by:
Q = V x A
Where Q is the liquid flow through the pipe, V is the average velocity of the flow and A is the cross-sectional area of the pipe.

Factors Affecting Flow Rate

From the basic relationship, we deduce that factors affecting liquid flow rate comprises average velocity of the flow and cross sectional area of the pipe. Apart from these, other factors which can influence liquid flow rate are:

• Liquid’s viscosity
• Density
• Friction of the liquid in contact with the pipe

Bernoulli Equation

Several facts concerning the flow of liquids and gases can be analyzed by just applying the Bernoulli equation. Bernoulli equation determines the relationship between flow rate and pressure difference for ideal fluid flow assuming that the changes in elevation, work and heat transfer are negligible. Bernoulli equation is given as:

Because of its ease, the Bernoulli equation is an excellent point to initiate, however it may not give an exact response for many situations. Undoubtedly, it can make available a first estimate of parameter values. After incorporating viscous effects in the simple Bernoulli equation, the resulting equation is referred to as “energy equation”.
Bernoulli equation is based upon following assumptions:

• Fluid is incompressible and nonviscous.
• No energy is vanished because of friction caused between the liquid and the pipe wall.
• No heat energy gets transferred across the boundaries of the pipe to the liquid as either a heat gain or loss.
• No pumps are present in the section of pipe under consideration.
• Flow of liquid is laminar and steady and is alongside the length of the stream.

Types of Flow

In general, we come across two types of flow in liquid flow Measurement operations.
Laminar flow: This type of flow occurs at very low velocities or high viscosities. In this, the liquid flows in smooth layers with the highest velocity at the center of the pipe and low velocities at the boundary (wall) of the pipe where the viscous forces hold it back.
Turbulent flow: It takes place at high velocities or low viscosities. In this, the liquid flow breaks up into turbulent eddies which flow through the pipe with the identical average velocity. In this type of flow, fluid velocity is not much significant, and the velocity profile is a lot more uniform in shape.

Reynolds Numbers

Reynolds Number (Re) is a dimensionless unit which can affect the performance of flowmeters. It is defined as the ratio of the liquid’s inertial forces to its drag forces (viscous forces). The flow rate and the specific gravity are inertia forces, and the pipe diameter and viscosity are viscous forces. The pipe diameter and the specific gravity remain constant for the majority of liquid applications.
According to the definition, if Re number is high i.e. inertia forces are superior as compared to viscosity forces then the flow is turbulent and if Re number is low i.e. viscosity forces are superior then the flow is laminar. With R values more than 3000, nearly all applications involve turbulent flow whereas with R values less than 2000, liquids typically show laminar flow. Between these two levels, there is a transition zone which may be either laminar or turbulent depending upon the piping configuration and other installation conditions.
While selecting a good flowmeter, one of the initial steps is to find out both the minimum and the maximum Reynolds numbers for the application.

Types of Flowmeters

Following are the various types of flowmeters available for closed-piping systems:
Differential Pressure Flowmeters: These are also known as Head meters. Most common differential pressure devices consist of

• Orifices
• Venturi tubes
• Flow tubes
• Flow nozzles
• Pitot tubes
• Elbow-tap meters
• Target meters
• Variable-area meters

Velocity Flowmeters: Velocity meters consist of

• Turbine
• Vortex shedding
• Electromagnetic & Sonic designs

Positive Displacement Flowmeters: Positive displacement meters include piston, oval-gear, nutating-disk, and rotary-vane types.

Mass Flowmeters: Mass meters include Coriolis and thermal types.

Open Channel Flowmeters: In general, the measurement of liquid flows in open channels involves weirs and flumes.

Accuracy

The accuracy of flowmeters can be stated in two ways. It can be expressed either as

1. percent of full span or
2. percent of rate

Sources

Omega

PC Education

Google Books

ac.wwu