Reading Material 12
Principles of Momentum transfer
1. Introduction
The flow and behavior of fluid is important in many of the unit operations in process engineering. A fluid may be defined as a substance that does not permanently resist distortion and, hence, will change its shape. In this text gas, liquids, and vapors are considered to have the characteristics of fluids and to obey many of the same laws.
2. Fluid Flow
The principles of the statics of fluids are almost an exact science. On the other hand, the principles of the motions of fluids are quite complex. The basic relations describing the motions of a fluid are the equations for the overall balances of mass, energy, and momentum, which will be covered in the following ctions.
The study of momentum transfer, or fluids mechanics as it is often called, can be divided into tow branches: fluid statics, or fluid at rest, and fluid dynamics, or fluids in motion. In other ctions we treat fluid statics; in the remaining ctions, fluid dynamics. Since in fluid dynamics momentum is being transferred, the term “momentum transfer” or “transfer” is usually ud.
In momentum transfer we treat the fluid as a continuous distribution of matter or as a “continuum”. This treatment as a continuum is valid when the smallest volume of fluid contains a large enough number of molecules so that a statistical average is meaningful and the macroscopic properties of the fluid such as density, pressure, and so on, vary smoothly or continuously from point to point.
Like all physical matter, a fluid is compod of an extremely large number of molecules per unit volume. A theory such as the kinetic theory of gas or statistical mechanics treats the motions of molecules in terms of statistical groups and not in terms of individual molecules. In engineering we are mainly concerned with the bulk or macroscopic behavior of a fluid rather than with the individual molecular or microscopic behavior.
In the process industries, many of the materials are in fluid form and must be stored, handled, pumped, and procesd, so it is necessary that we become familiar with the principles that govern the flow of fluids and also with the equipment ud. Typical fluids encountered include water, air, CO2, oil, slurries, and thick syrups.If a fluid is inappreciably affected by change in pressure, it is said to be incompressible. Most liquids are incompressible. Gas are considered to be compressible fluids. However, if gas are subjected to small percentage changes in pressure and temperature, their density changes will be small and they can be considered to be incompressible.
3. Laminar and Turbulent Flow
The type of flow occurring in a fluid in a channel is important in fluid dynamics problems. When fluids move through a clod channel of any cross ction, either of tow distinct types of flow can be obrved according to the conditions prent. The two types of flow can be commonly en in a flowing open stream or river. When the velocity of flow is slow, the flow patterns are smooth. However, when the velocity is quite high, an unstable
pattern is obrved in which eddies or small packets of fluid particles are prent moving in all directions and at all angles to the normal line of flow.
The first type of flow at low velocities where the layers of fluid em to slide by one another without eddies or swirls being prent is called laminar flow and Newton’s law of viscosity holds. The cond type of flow at higher velocities where eddies are prent giving the fluid a fluctuating nature is called turbulent flow.
The existence of laminar and turbulent flow is most easily visualized by the experiments of Reynolds. Water was allowed to flow at steady state through a transparent pipe with the flow rate controlled by a valve at the end of the pipe. A fine steady stream of dye-colored water was introduced from a fine jet as shown and its flow pattern obrved. At low rates of water flow, the dye pattern was regular and formed a single line or stream similar to a thread. There was no lateral of the fluid, and it flowed in streamlines down the tube. By putting in additional jets at other points in the pipe cross ction, it was shown that there was no mixing in any parts of the tube and the fluid flowed in straight parallel lines. This type of flow is called laminar or viscous flow.
As the velocity was incread, it was found that at a define velocity the thread of dye become disperd and the pattern was very erratic. This type of flow is known as turbulent flow. The velocity at which the flow changes is known as the critical velocity.
4. Reynolds Number
Studies have shown that the transition from laminar to turbulent flow in tubes is not only a function of velocity but also of density and viscosity of the fluid and the tube diameter. The variables are combined into the Reynolds number, which is dimensionless.
R=
Where Re is the Reynolds number, D the diameter in m, ρ the fluid density in kg/m3,u the fluid viscosity in Pa*s, and ν the average velocity of the fluid in m/s .(where average velocity is defined as the volumetric rate of flow divided by the cross ctional area of the pipe.)
