Flow Meters – Measurement Principles and Flow Measurement Methods

Flow meters measure the volumetric or mass flow rate of liquids, gases or steam.
Different measurement principles are used depending on the medium, flow range, required accuracy and operating conditions.

What is flow rate?

Flow rate is the quantity of a medium transported per unit of time.
The fluid (gas or liquid) may flow through closed pipes, ducts or open channels such as rivers or waterways.
The term flow rate is also used.

The following quantities are distinguished:

• Volumetric flow rate
  Volumetric flow rate = volume per unit time
  q_V=V/t
  The SI unit is [m³/s], although it is relatively rarely used in engineering.
  Common units are L/h, L/min and m³/h, or GPH, GPM and SCFM in the US customary system. Because volumetric flow rate is the easiest quantity to determine, it is the most commonly used in engineering.
  One disadvantage, particularly for gases, is its dependence on pressure and temperature.
  Volumetric flow rate can be converted to mass flow rate using density.
  
  
• Mass flow rate
  Mass flow rate = mass per unit time
  q_m=m/t
  The SI unit is [kg/s].
  Because it is independent of pressure and temperature, mass flow rate is an ideal measurement quantity. However, direct measurement often requires costly methods, such as Coriolis or thermal mass flow meters. Mass flow rate can be converted to volumetric flow rate using density.
  
  
• Flow velocity
  Flow velocity describes how fast a medium (e.g. water, air or gas) moves through a pipe.
  Flow velocity is directly related to flow rate and is determined by the flow velocity and the pipe cross-sectional area:
  The SI unit is [m/s].
  Flow rate = flow velocity × cross-sectional area
  [m³/s] = [m/s] x [m²]
  Why is flow velocity important?
  
  • Excessive flow velocity can cause pressure losses, noise, increased wear or cavitation.
  • Too low a velocity can encourage deposits or reduce system efficiency. Recommended velocity ranges therefore depend on the application.

Laminar and Turbulent flow

Flow refers to the movement of a liquid or gaseous medium.
It describes the state of motion of the medium within a piping system or an open flow space.
Flow rate, by contrast, is the volume or mass passing through per unit of time. Depending on the flow behaviour, a distinction is made between Laminar and Turbulent flow.
Flow direction, pressure distribution and velocity distribution can also describe flow characteristics.
The flow regime affects the velocity profile, pressure loss and accuracy of various flow measurement methods.

Laminar flow

In Laminar flow, the medium moves in largely orderly, parallel layers.
The individual fluid layers mix very little.
In Laminar pipe flow, the velocity profile is approximately parabolic. Due to friction, velocity is nearly zero at the pipe wall and reaches its maximum at the centre of the pipe.
Laminar flow occurs particularly with:

• low flow velocities
• small pipe diameters
• high-viscosity liquids
• low Reynolds numbers

Turbulent flow

In turbulent flow, the motion of the fluid is irregular.
Vortices and velocity fluctuations occur, resulting in intense mixing of the fluid.
The velocity profile of a turbulent flow in a pipe is significantly flatter than that of a laminar flow.
In industrial piping systems, the flow is often turbulent.
Turbulent flow occurs particularly with:

• high flow velocities
• large pipe diameters
• low viscosity
• high Reynolds numbers

Transition from laminar to turbulent flow

There is no sharply defined, abrupt transition between laminar and turbulent flow under all conditions.
In pipe flow in particular, there is a transition region in which the flow becomes increasingly unstable and both laminar and turbulent structures may occur. As the Reynolds number increases further, fully turbulent flow develops.

In pipe flow, whether flow is laminar or turbulent is usually assessed using the Reynolds number (Re).

Difference between laminar and turbulent flow

The main difference lies in the movement and mixing of the medium.
In laminar flow, the fluid layers move in a largely orderly manner, whereas in turbulent flow, vortices and significant fluctuations in velocity occur. The desired flow pattern depends on the specific application.
The flow pattern is highly important for flow measurement. Pipe bends, valves, tees and pumps can change the velocity profile and thereby affect measurement accuracy.
For this reason, many flow meters require defined upstream and downstream straight lengths.
Flow that is as stable and repeatable as possible is an important prerequisite for accurate flow measurement.

Reynolds Number – A Key Parameter for Flow

The Reynolds number (Re) is a dimensionless quantity used to assess the flow behaviour of a medium.
It is particularly important in flow measurement because it indicates whether flow is predominantly laminar or turbulent.
The Reynolds number describes the ratio of inertial forces to viscous forces in a flow. It depends, among other things, on flow velocity, characteristic length, density and the dynamic viscosity of the medium.
For flow in a pipe, the Reynolds number is usually calculated using the following formula:
Re = Reynolds number [dimensionless]
ρ = Medium density [kg/m³]
v = Mean flow velocity [m/s]
d = Internal pipe diameter [m]
η = Dynamic viscosity [Pa·s]

Typical guide values for flow in a straight pipe are:


Because flow velocity is directly related to flow rate, the following applies when the pipe cross-sectional area is known: Q = Flow rate [m³/s]
v = Mean flow velocity [m/s]
A = Internal pipe diameter [m²]

As flow rate increases, flow velocity and therefore the Reynolds number also increase.
At low Reynolds numbers, viscous forces dominate. The liquid or gas then flows predominantly in laminar, largely orderly layers.
At high Reynolds numbers, inertial forces dominate, resulting in turbulent flow with greater velocity and pressure fluctuations.

Calculator for the Reynolds number in pipes
Note: The Reynolds number is not used solely to assess flow conditions in pipes. In fluid mechanics, it generally describes the ratio of inertial to viscous forces and is therefore an important parameter for characterising flows.
For pipe flow, the internal pipe diameter is generally used as the characteristic length.
For other flow problems, another characteristic length appropriate to the geometry may be used instead of the pipe diameter, such as the length of a body aligned with the flow.
Because geometrically similar flows have comparable behaviour at the same Reynolds number, flow phenomena can also be investigated using scaled models. This is used, for example, in wind-tunnel testing in automotive and aircraft engineering. The relevant similarity conditions, especially a comparable Reynolds number, must be taken into account for both the model and the original.

Upstream and downstream straight lengths

When installing a flow meter, specific straight pipe lengths often need to be provided before and after the meter.
These are called the upstream straight length and downstream straight length.
They help ensure that the meter operates under defined and reproducible flow conditions.
The required upstream and downstream lengths can vary considerably depending on the measuring method, pipe geometry and type of disturbance.
Flow meter manufacturers therefore often specify the minimum upstream and downstream lengths themselves.

• Upstream straight length

  The upstream straight length is the straight pipe section before the flow meter.
  Its purpose is to reduce flow disturbances upstream of the flow meter and to ensure the most suitable flow profile possible.
  Piping components such as elbows, T-fittings, valves, reducers, expanders, or pumps can alter the flow profile and lead to vortices, swirl, or asymmetric velocity distribution. If a flow meter is installed immediately downstream of such a fitting, this can result in measurement errors.
  The required upstream length is often specified as a multiple of the internal pipe diameter (D).
  Common rule of thumb:10 x D
  D = Internal pipe diameter
  Example: for a pipe with an internal diameter of 100 mm, an upstream straight length of 1000 mm should be provided.
  

• Downstream straight length

  The downstream straight length is the straight pipe section after the flow meter.
  It may be necessary to prevent or reduce the influence of downstream piping elements on the measuring device.
  The required outlet run is often significantly shorter than the inlet run, since disturbances upstream of the measuring device are often much more critical.
  Common rule of thumb:5 x D
  D = Internal pipe diameter

Guide values for required upstream and downstream lengths after pipe fittings

The flow meter manufacturer’s installation instructions always take precedence.

How can flow rate be measured?

A wide range of instruments is available for measuring flow rate in engineering.
The appropriate flow meter is selected based on:

• Type of fluid (gas, liquid, solids)
• Flow rate
• Fluid properties (e.g. viscosity, conductivity, contamination, colour)
• Chemical compatibility with the fluid
• Operating temperature and pressure
• Required accuracy and repeatability
• Connection type (thread, flange, hygienic/sanitary connection)
• Required indication (local mechanical display, remote transmission outputs, contacts)
• Installation location (environmental conditions, indoor/outdoor, mining, vehicles, etc.)
• Certificates/approvals (ATEX, IECEx, SIL, HART®, Fieldbus®, Modbus)
• Cost