Transport phenomena in chemical processes part V Michał Araszkiewicz PhD

Momentum transport Fluid dynamics Mass balance of flow Energy balance of flow Flow resistance Flow through chokepoints, offsets, valves Non-newton fluid flow Two phase processes: solid - fluid

Fluid dynamics

There are two kinds of flow inside the pipe. If the fluid layers do not mix together we call that flow as: The flow profile is parabolic then.

The fluid velocity - laminar Fluid velocity at radius „r” can be described according to the equation:

When the fluid elements mix together during the flow with the rotational movement, such flow we call: The velocity profile is oblate

The fluid velocity - turbulent Fluid velocity at radius „r” can be described according to the equation:

Reynolds number In industrial practice, the turbulent flow can be defined with Reynolds number : As a matter of fact there is a possibility to obtain the laminar flow for, but only in very smooth pipes.

Mass balance of flow

The average fluid velocity can be definied as: Where A – is the area perpendicular to the direction of flow.

Average linear fluid velocity, mass rate of flow, fluid density and area are connected with equation:

Using the mass conservation law we can write: or

There is also volumetric rate of flow which we can define as:

Energy balance of flow Usin the law of energy conservation for the control volume:

Previous equation can be written in a developed form: A

Flow resistance During the real movement of fluid in a pipe, there is intermolecular friction process which consumes irreversibly some of the fluid energy. The pressure lost is proportional to the kinetic energy of fluid, length of pipe and inversely proportional to the internal diameter of a pipe. That dependence can be written by Darcy – Weisbach equation: D