Viscosity fluids, flow calculation

The unit of viscosity, the poise, is defined as the force in dynes cm-2 required to maintain a relative velocity of 1 cm/sec between two parallel planes 1 cm apart. The unit commonly used for milk is the centi-poise (10 2 poise). A useful quantity in fluid flow calculations is the kinematic viscosity, or viscosity divided by density. 

Reynold s number. The function DUP/p, used in fluid flow calculations to estimate whether flow through a pipe or conduit is streamline or turbulent in nature. D is the inside pipe diameter, U is the average velocity of flow, P is density, and p, is the viscosity of the fluid. Different systems of units give identical values of the Reynold s number, and values much below 2100 correspond to streamline flow, while values above 3000 correspond to turbulent flow. 

If, on the other hand, the channel section changes then tensile stresses will also be set up in the fluid and it is often necessary to determine the tensile viscosity, k, for use in flow calculations. If the tensile stress is a and the tensile strain rate is s then... 

In design considerations for Thermonized process lines, temperatures may be determined by the Stagnation Method. The calculations involved in this method are based on static conditions where process fluid flow is not present, and are independent of the viscosity, density and thermal conductivity of the process fluid. The process temperature may be calculated from the following relationship ... 

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow —the natural science of fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics offers a systematic structure that underlies these practical disciplines, that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density, viscosity and temperature, as functions of space and time. 

The pressure drop in a pipe, due to friction, is a function of the fluid flow-rate, fluid density and viscosity, pipe diameter, pipe surface roughness and the length of the pipe. It can be calculated using the following equation ... 

Runnels and Eyman [41] report a tribological analysis of CMP in which a fluid-flow-induced stress distribution across the entire wafer surface is examined. Fundamentally, the model seeks to determine if hydroplaning of the wafer occurs by consideration of the fluid film between wafer and pad, in this case on a wafer scale. The thickness of the (slurry) fluid film is a key parameter, and depends on wafer curvature, slurry viscosity, and rotation speed. The traditional Preston equation R = KPV, where R is removal rate, P is pressure, and V is relative velocity, is modified to R = k ar, where a and T are the magnitudes of normal and shear stress, respectively. Fluid mechanic calculations are undertaken to determine contributions to these stresses based on how the slurry flows macroscopically, and how pressure is distributed across the entire wafer. Navier-Stokes equations for incompressible Newtonian flow (constant viscosity) are solved on a three-dimensional mesh ... 

However, the viscosity at which this transition takes place cannot easily be calculated because many high jyiscosity fluids are non-Newtonian. This means that the viscosity varies according to the rate at which the fluid is flowing. It is therefore best to carry out a small-scale test in order to determine whether or not flow will be laminar. A possible test method is given in A2.3.3. Chapter 10 gives more information on high viscosity fluids. 

Purging a Tubular Die A red polymer is pumped through a tubular die. At time f, the inlet stream is switched over to a white polymer for purging the die. Assuming Newtonian fluids, identical viscosities and densities, and fully developed isothermal laminar flow, calculate the volume fraction of red polymer left in the die at the time the first traces of white polymer appear at the exit. 

Figure 2 demonstrates that the viscosity-temperature relationship revealed by plotting Xarj against I T-Tq) is linear for all compositions studied as well as for oligoethylsiloxane and additive. The calculations show that all the analyzed fluid flows within the analyzed temperature range with maximum relative error 2%, obeying the Falcher-Tamman equation (fiee volume concept) [3] ... 

Gas phase viscosity data, iTq, are used in the design of compressible fluid flow and unit operations. For example, the viscosity of a gas is required to determine the maximum permissible flow through a given process pipe size. Alternatively, the pressure loss of a given flowrate can be calculated. Viscosity data are needed for the design of process equipment involving heat, momentum, and mass transfer operations. The gas viscosity of mixtures is obtained from data for the individual components in the mixture. 

For laminar flow, the characteristic time of the fluid phase Tf can be deflned as the ratio between a characteristic velocity Uf and a characteristic dimension L. For example, in the case of channel flows confined within two parallel plates, L can be taken equal to the distance between the plates, whereas Uf can be the friction velocity. Another common choice is to base this calculation on the viscous scale, by dividing the kinematic viscosity of the fluid phase by the friction velocity squared. For turbulent flow, Tf is usually assumed to be the Kolmogorov time scale in the fluid phase. The dusty-gas model can be applied only when the particle relaxation time tends to zero (i.e. Stp 1). Under these conditions, Eq. (5.105) yields fluid flow. This typically happens when particles are very small and/or the continuous phase is highly viscous and/or the disperse-to-primary-phase density ratio is very small. The dusty-gas model assumes that there is only one particle velocity field, which is identical to that of the fluid. With this approach, preferential accumulation and segregation effects are clearly not predicted since particles are transported as scalars in the continuous phase. If the system is very dilute (one-way coupling), the properties of the continuous phase (i.e. density and viscosity) are assumed to be equal to those of the fluid. If the solid-particle concentration starts to have an influence on the fluid phase (two-way coupling), a modified density and viscosity for the continuous phase are generally introduced in Eq. (4.92). 

The rate at which a fluid flows through a tube depends on the dimensions (radius and length) of the tube, the viscosity of the fluid, and the pressure drop between the ends of the tube. To discover the relation between these quantities, we first calculate the volume passing any point in a circular tube in unit time. 

This definition of has the disadvantage that e is not a simple property of the fluid, such as the molecular viscosity, but is also a function of the flow rate and position in the flow. It has the advantage that it lets us easily formulate the ratio of the Reynolds stresses to viscous stresses. In addition, in calculations of heat and mass transfer, we may introduce a similar eddy thermal conductivity and eddy diffusivity. Under some circumstances these three eddy properties are identical, and under all circumstances they are at least of the same order of nagnitude. So this approach helps to apply fluid flow data to the solution of... 

From a measured average velocity profile versus y or r) in a flow and information on the viscosity and density of the fluid, we can calculate the eddy viscosity for any point in the flow. A typical plot of vjelocity versus position is shown in Fig. 11.7. Figure 16.8 shows the eddy viscosity divided by the kinematic viscosity for flow in smooth pipes, calculated from a figure like Fig. 11.7. 

---