Fluid flow friction parameter

The theory of pressure losses can be established by developing Bernoulli s theorem for the case of a pipe in which the work done in overcoming frictional losses is derived from the pressure available. For a fluid flowing in a pipe, the pressure loss will depend on various parameters. If... 

The pressure drop across the cyclone is an important parameter in the evaluation of cyclone performance. It is a measure of the amount of work that is required to operate the cyclone at given conditions, which is important for operational and economical reasons. The total pressure drop over a cyclone consists of losses at the inlet, outlet and within the cyclone body. The main part of the pressure drop, i.e. about 80%, is considered to be pressure losses inside the cyclone due to the energy dissipation by the viscous stress of the turbulent rotational flow [9], The remaining 20% of the pressure drop are caused by the contraction of the fluid flow at the outlet, expansion at the inlet and by fluid friction on the cyclone wall surface. 

The two main non-dimensional parameters used to characterize the fluid flow are the Re and the Darcy friction factor (f). The Re depends on four quantities the diameter of the flow, viscosity, density and average liner velocity of the fluid (Equation [5.3]). 

Turbulence. A number of dimensionless parameters have been developed for the study of fluid dynamics that are used to categorize different flow regimes. These parameters, or numbers, are used to classify fluids as well as flow characteristics. One of the most common of these is the Reynolds number, defined as the ratio of inertial forces, or those that give rise to motion of the fluid, to frictional forces, or those that tend to slow the fluid down. In geometrically similar domains, two fluids with the same Reynolds number should behave in the same manner. For simple pipe flow, the Reynolds number is defined as... 

The Fanning friction factor is a dimensionless number used in fluid flow calculations. It is a common parameter used in laminar and especially in turbulent flow. It is defined as the drag force per wetted unit surface area (i.e., shear stress), divided by the product of density times velocity head or Vipo. The force is Apf, times the cross-sectional area and the wetted surface area 2xRAL. 

Thus, in laminar flow with fluid slip, the friction factor is a function of not only the Reynolds number Re, but also the non-dimensional parameter jx/a ). If the flow does not exhibit fluid slip, Eq. (3.43) gives A = 64/Re on substituting /3 —> <=o into the equation. 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

All models for turbulent flows are semiempirical in nature, so it is necessary to rely upon empirical observations (e.g., data) for a quantitative description of friction loss in such flows. For Newtonian fluids in long tubes, we have shown from dimensional analysis that the friction factor should be a unique function of the Reynolds number and the relative roughness of the tube wall. This result has been used to correlate a wide range of measurements for a range of tube sizes, with a variety of fluids, and for a wide range of flow rates in terms of a generalized plot of/ versus /VRe- with e/D as a parameter. This correlation, shown in Fig. 6-4, is called a Moody diagram. 

Corresponding expressions for the friction loss in laminar and turbulent flow for non-Newtonian fluids in pipes, for the two simplest (two-parameter) models—the power law and Bingham plastic—can be evaluated in a similar manner. The power law model is very popular for representing the viscosity of a wide variety of non-Newtonian fluids because of its simplicity and versatility. However, extreme care should be exercised in its application, because any application involving extrapolation beyond the range of shear stress (or shear rate) represented by the data used to determine the model parameters can lead to misleading or erroneous results. 

Turbulent flow of Newtonian fluids is described in terms of the Fanning friction factor, which is correlated against the Reynolds number with the relative roughness of the pipe wall as a parameter. The same approach is adopted for non-Newtonian flow but the generalized Reynolds number is used. 

Consider the fully developed steady flow of an incompressible fluid through an annular channel, which has an inner radius of r, and an outer radius of r0 (Fig. 4.27). The objective is to derive a general relationship for the friction factor as a function of flow parameters (i.e., Reynolds number) and channel geometry (i.e., hydraulic diameter Dh and the ratio f A friction factor /, which is a nondimensional measure of the wall... 

Whitaker [234] (chap 8) explains the convention normally used to distinguish between these two types of parameters. The friction factors for dispersed bodies immersed in a flowing fluid is traditionally referred to as dimensionless drag coefficients, whereas the drag force for flow inside closed conducts is generally expressed in terms of a dimensionless friction factor. 

Parameters such as impeller speed and shaft power (in a stirred bioreactor) and fluid velocity are indicators of the degree of mixing and thus play an important role in the control of mass transfer. Impeller speed is easily monitored with a tachometer (electronic or mechanical) [39], but the measurement of shaft power input is not as straightforward. The most common method utilizes a torsion dynamometer attached to the impeller drive however, this technique includes losses due to friction in the drive shaft. Better data can be obtained from balanced strain gauges mounted on the impeller [37]. On-line measurement of the liquid velocity in a flowing or stirred system can be obtained by a heat-pulse method in which a resistance thermometer is used to measure a brief temperature increase caused by an upstream pair of electrodes [43]. Use of this sensor system has been limited to laboratory applications. 

Third, the conditions for scale-up from lab to process plant are constant figures for the dimensionless parameters. But in practice it is not certain that the packing of the columns is always identical. Slight variations of the void fraction and HETP may occur. Additionally, differences in the fluid dynamics, especially at the column inlet and outlet, have to be taken into account. The theoretical scale-up strategy ignores these deviations. But in order to make sure that real numbers of plates of both plants are really the same, it is recommended to determine the Van Deemter plot, void fraction, and friction number for the new packing and to correct the interstitial velocity, the flow rate, and the injection volume. 

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