Friction factor total

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

This equation gives values that are half of those calculated as total gas flow for the shell side by using friction factors from Figure 10-140. (Note that f for plain or bare tubes = f/1.2 (with f from Figure 10-140)). 

In Table 6.7, C is the Martinelli-Chisholm constant, / is the friction factor, /f is the friction factor based on local liquid flow rate, / is the friction factor based on total flow rate as a liquid, G is the mass velocity in the micro-channel, L is the length of micro-channel, P is the pressure, AP is the pressure drop, Ptp,a is the acceleration component of two-phase pressure drop, APtp f is the frictional component of two-phase pressure drop, v is the specific volume, JCe is the thermodynamic equilibrium quality, Xvt is the Martinelli parameter based on laminar liquid-turbulent vapor flow, Xvv is the Martinelli parameter based on laminar liquid-laminar vapor flow, a is the void fraction, ji is the viscosity, p is the density, is the two-phase frictional... 

The friction factor, which is plotted against the modified Reynolds number, is Pi/pu, where R is the component of the drag force per unit area of particle surface in the direction of motion. R can be related to the properties of the bed and pressure gradient as follows. Considering the forces acting on the fluid in a bed of unit cross-sectional area and thickness /, the volume of particles in the bed is /(I — e) and therefore the total surface is 5/(1 — e). Thus the resistance force is R SH — e). This force on the fluid must be equal to that produced by a pressure difference of AP across the bed. Then, since the free cross-section of fluid is equal to e ... 

Wallis states that if bubbles were uniformly dispersed, and nonrigid, then their effect at a constant total mass-flow rate would be simply to increase the stream velocity, and at a constant friction factor, the pressure-drop would be,... 

The total number of openings N affects the flow rate, velocity, and Ret) in the region of the last opening, which is determined to (1/AO of the opening at the entrance of the distributor. So, ReD at die first and the last opening of the distributor can be calculated, and in turn, the corresponding values of the fanning friction factors can be estimated. The mean value of these two factors should be used in the calculations in diis procedure. 

III) In dilute solution, the friction factor / is equal to tj0a where rj0 is the viscosity of the solvent in which the polymer molecules are dissolved. If rj0 is 0.01 poises, / is 9.4 x 10 9 dyne sec/cm. For bulk polymer or intermediate concentrations, r)0 is usually replaced by the sample total viscosity. [The Stokes law form / was not specifically introduced by Rouse (/) and Bueche (2). It is however, a component of one of the simplest expressions of their basic idea (5,23)]. 

It is immediately noticed that the tp s do not depend on the number of subchains chosen [cf. Ferry (96)). In the first place the friction factor f of the single bead must be inversely proportional to the number of beads chosen per unit of chain length, in order to keep the frictional resistance per unit of chain length constant. This means that ffV must be proportional to the molecular weight. In the second place, b2N is equal to the mean square end-to-end distance of the total chain in a solution at rest. Also this value must be proportional to the molecular weight and independent of the number of subchains chosen. This is in agreement with Section 2.6.3. According to eqs. (3.37) and (3.50) one obtains for the contribution of the macro-molecules to the viscosity of the solution ... 

Relative roughness factor and friction factor are again taken to be 0.0006 and 0.004, respectively. Assuming the total transport line as 600 ft, frictional loss in fluid transport is... 

Equation (67) is the basis of practical heat transfer calculations. In order to use it to solve problems, additional information is required about the total heat transfer rate Q and the production rate QfCR. The first is usually expressed in terms of a heat transfer coefficient analogous to the friction factor,... 

APf = total pressure drop for intermediate baffle sections, in lb/in2 A Pfi = total pressure drop for inlet and outlet baffle sections, in lb/in2 A Pw = total pressure drop for baffle windows, in lb/in2 / = friction factor (dimensionless)... 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibility effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM ,/RT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant friction factor/over a length L of a channel of constant cross section and hydraulic diameter Du, yields,... 

Friction Factors for Total Turbulence in New Commerical Steel... 

Because of strong interactions in polyelectrolyte solutions without added salt, the use of the well-known Stokes-Einstein relation for free particle diffusion D = kBT/6Trr)Rh, where 17 is viscosity and Rh is hydrodynamic radius, is rather limited. Even at very low concentrations, where intermo-lecular interactions can be neglected due to large intermolecular separations, the friction factor contains in addition to the Stokes-Einstein contribution /SE = 67717/4 also a contribution from electrolyte dissipation, so that the total friction factor / = /SE + /eidiS, where the electrolyte dissipation term reflects the retardation of the polyion motion due to the instantaneous distortion of the surrounding ion atmosphere as the polyion moves through the solvent [27,28],... 

The friction factor is a function of the Reynolds number and pipe roughness. The mass velocity, G. is constant along the length of the pipe. Replacing u with G/p, and combining with Equation (4-23) for the case of constant temperature, T, and total molar flow rate. Fj, Equation (4-35) becomes... 

In this hydrodynamic entrance region, the apparent friction factor /app is employed to incorporate the combined effects of wall shear and the change in momentum flow rate due to the developing velocity profile. Based on the total axial pressure drop from the duct inlet (x = 0) to the point of interest, the apparent friction factor is defined as follows ... 

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