Flow Rate
Processes consist of a series of operations, each with an input and output. Materials flow between operations, and in modern factories this flow is often continuous.
A high rate of flow is usually desired because it helps ensure high productivity.
Changes in flow-rate — especially decreases — can indicate a problem, such as equipment blockage or material supply issues.
The flow of liquids is complex and involves an interplay between equipment properties (pipe geometry), food characteristics (viscosity) and flow dynamics (turbulence).
Quantities
Volumetric Flow-rate
The flow-rate of a liquid is conventionally given the symbol $Q$ and is defined as:
$$Q = \frac{V}{t}$$
The units are most commonly $L \ h^{-1}$ or $m^3 \ h^{-1}$.
A common method of measuring flow-rate in a laboratory is to periodically measure the volume of liquid collected over a certain period of time.
This quantity is known sometimes as the “volumetric flow-rate”. If units for mass (e.g., kg) are used instead it is the “mass flow rate”.
Velocity of flow
The volumetric flow-rate ($Q$) has the units $m^3 \ s^{-1}$.
We can calculate velocity of flow by dividing the volumetric flow rate ($Q$) by the area of flow $A$:
$$v = \frac{Q}{A}$$
This is usually the area of a disc because pipes are widely used in the transport of liquids.
The velocity here represents an average value, meaning that it represents the statistical average of a range of individual velocities. This is normally visualised as a moving fluid consisting of individual stream-lines, each flowing in a specific direction and with a specific velocity. In laminar (non-turbulent) flow the maximum velocity occurs towards the centre of the flowing liquid and the velocity close to the pipe wall approaches $0$. This means that liquids flows in a “curved” fashion. Velocity decreases from center to wall.
Turbulence
A high degree of turbulence is often preferred because of useful effects, including:
- Decreasing the tendency of deposits to form on equipment surfaces
- Increasing the rate of heat transfer during thermal processing
- Accelerating the disintegration of agglomerated particles
Turbulence is calculated using the Re(ynold’s) number:
$$Re = \frac{v \rho D}{\mu}$$
Turbulence increases with velocity and decreases with viscosity.
Related: Stokes’ Law