Friction factor, estimation frictional pressure drop

Use equation 12.18 for estimating the pressure drop, taking the friction factor from Figure 12.24. As the hydraulic mean diameter will be large compared to the roughness of the jacket surface, the relative roughness will be comparable with that for heat exchanger... 

A method of interpolation for the two-phase friction factor was developed by Martinelli and Nelson [ ]. No considerable improvement over this technique has heretofore been developed and there is a need for better estimates of pressure drop for two-phase systems at pressures above 1 atm. This paper presents a solution to the problem for para-hydrogen for flow with both phases turbulent, based upon the pressure drop for liquid as the single phase. 

Now that we have required that the stagnation pressure be at the location Zmi, the question of just how far upstream of the nozzle entrance the pressure can be measured without loss of accuracy needs to be addressed. Using the deflnition of the Fanning friction factor to estimate the pressure drop for fully developed, turbulent flow (22), one can show that Po will increase by less than 0.10 bar as much as 100 inner tubing diameters upstream of the nozzle entrance as long as the flow speed inside the tubing does not markedly exceed 3 m/s (Figure 3 a). 

A correct value of friction factor is required for the estimation of pressure drop. The value of the friction factor depends upon the flow characteristics. For laminar flow less than 2100), the friction factor varies inversely with the Re5molds number, whereas for turbulent flow, the friction factor has a complex relationship with the pipe diameter, roughness of the pipe, and the Reynolds number. 

On occasion one will find that heat-transfer-rate data are available for a system in which mass-transfer-rate data are not readily available. The Chilton-Colburn analogy provides a procedure for developing estimates of the mass-transfer rates based on heat-transfer data. Extrapolation of experimental or Jh data obtained with gases to predict hquid systems (and vice versa) should be approached with caution, however. When pressure-drop or friction-factor data are available, one may be able to place an upper bound on the rates of heat and mass transfer, according to Eq. (5-308). 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

For condensing vapor in vertical downflow, in which the hquid flows as a thin annular film, the frictional contribution to the pressure drop may be estimated based on the gas flow alone, using the friction factor plotted in Fig. 6-31, where Re is the Reynolds number for the gas flowing alone (Bergelin, et al., Proc. Heat Transfer Fluid Mech. Inst., ASME, June 22-24, 1949, pp. 19-28). 

Probably the most widely used method for estimating the drop in pressure due to friction is that proposed by LOCKHART and Martinelli(,5) and later modified by Chisholm(,8 . This is based on the physical model of separated flow in which each phase is considered separately and then a combined effect formulated. The two-phase pressure drop due to friction — APtpf is taken as the pressure drop — AP/, or — APG that would arise for either phase flowing alone in the pipe at the stated rate, multiplied by some factor 2L or . This factor is presented as a function of the ratio of the individual single-phase pressure drops and ... 

From the friction factor chart, the estimated friction factor is 0.0052. Finally the pressure drop per unit length is... 

Figure 8-3 illustrates the friction frictor versus GRe relationship for power law fluids under laminar flow conditions. It can also be used for Newtonian fluids in laminar flow with the Reynolds number being used in place of GRe. In fact, the Newtonian/ versus Re relationship was established much earlier than extension to non-Newtonian fluids. Once the magnitude of the friction factor is known, the pressure drop in a pipe can be estimated from Equation 12. 

In both BSR modules, the Sherwood number lies between the two Chilton-Colbum predictions, as expected. The most important conclusion to be drawn from these graphs, is that the Sherwood number for turbulent flow in a BSR can be predicted with an accuracy of ca. 30% (which is usually acceptable) on the basis of one single pressure drop experiment in the turbulent-flow regime. From this pressure experiment the empirical roughness function can be fitted, with which the friction factor can be adequately predicted as a function of Re, as discussed in the previous section from these an upper estimate of Sh... 

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