Frictional pressure drop

Assume a fluid is flowing through a pipe of uniform cross section area (diameter d), upstream pressure of pi, and downstream pressure of p2, for a pipe length of L. 

Process engineering and design using Visual Basic 

Let q be frictional resistance per unit surface area at unit velocity and the frictional resistance vary as xP. 

The constant 2gq/p is called the resistance coefficient and is denoted by / (called friction factor). Equation 2.34 can be modified as 

Equation 2.35 is the Darcy formula for the loss of head in a pipeline. The friction factor / is called the Fanning friction factor. Another friction factor commonly used is called the Moody friction factor and is equal to 4/. 

Generally, methods for determining the frictional pressiue drop begin by using a physical model of the two-phase system, and then applying an approach similar to that for single phase flow. Thus, in the so-called separated flow model, the two phases are first considered to be flowing separately and 

For upward flow of gas-liquid mixtures, an additional term (—Apg) attributable to the hydrostatic pressme, must be included on the right hand side of equation (4.16), and this depends on the liquid holdup which therefore must be estimated. 

complete analytical solutions for the equations of motion are not possible (even for Newtonian liquids) because of the difficulty of defining the flow pattern and of quantifying the precise nature of the interactions between the phases. Furthermore, rapid fluctuations in flow frequently occur and these cannot be readily incorporated into analysis. Consequently, most developments in this field are based on dimensional considerations aided by data obtained from experimental measmements. Great care must be exercised, however, when using these methods outside the limits of the experimental work. 

Good accounts of idealised theoretical developments in this field are available for mixtures of gas and Newtonian liquids [Govier and Aziz, 1982 Hetsroni, 1982 Chisholm, 1983] and the limited literature on mixtures of gas and non-Newtonian liquids has also been reviewed elsewhere [Mahalingam, 1980 Chhabra and Richardson, 1986 Bishop and Deshpande, 1986]. 

Over the years, several empirical correlations have been developed for the estimation of the two-phase pressure drop for the flow of gas-liquid mixtures, with and without heat transfer. Most of these, however, relate to Newtonian liquids, though some have been extended to include shear-thinning liquid behaviour. As the pertinent literature for Newtonian fluids and for non-Newtonian fluids has been reviewed extensively [see references above], attention here will be confined to the methods which have proved to be most reliable and have therefore gained wide acceptance. 

As noted in Section 4.3, the frictional pressure drop is given by the Fanning equation  

We will define the average value of the specific volume, v ,, along the pipe-length by 

We may substitute from equation (4.39) into equation (4.38), and, since from Section 4.4 we may assume that the friction factor, /, is constant along the pipe, this integration yields 

This may be rewritten in terms of the inlet specific volume as  

Equation (4.41) may be rearranged to give mass flow in terms of frictional pressure drop  

---

The PIF estimate is only a qualitative check on the potential benefit of a horizontal well. There is actually a diminishing return of production rate on the length of well drilled, due to increasing friction pressure drops with increasing well length, shown schematically in Figure 9.6. 

Frictiona.1 Pressure Drop. The frictional pressure drop inside a heat exchanger results when fluid particles move at different velocities because of the presence of stmctural walls such as tubes, shell, channels, etc. It is calculated from a weU-known expression of... 

Heat exchangers use energy two ways as frictional pressure drop, and as the loss in ability to do work when heat is degraded. 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

The fluid dehvery in an air-spray system can be pressure or suction fed. In a pressure-fed system, the fluid is brought to the atomizer under positive pressure generated with an external pump, a gas pressure over the coating material in a tank, or an elevation head. In a suction system, the annular flow of air around the fluid tip generates sufficient vacuum to aspirate the coating material from a container through a fluid tube and into the air stream. In this case, the paint supply is normally located in a small cup attached to the spray device to keep the elevation differential and frictional pressure drop in the fluid-supply tube small. 

Friction Factor and Reynolds Number For a Newtonian fluid in a smooth pipe, dimensional analysis relates the frictional pressure drop per unit length AP/L to the pipe diameter D, density p, and average velocity V through two dimensionless groups, the Fanning friction factor/and the Reynolds number Re. 

Ap Frictional pressure drop Pa CO Characteristic frequency or reciprocal time scale of flow 1/s... 

Frictional Pressure Drop Usually this does not have a significant effect on the reaclor size, except perhaps when the flow is two-phase. Some approximate relations fbe cited that are adequate for pressure-drop calculations of homogeneous flow reactions in pipelines. The pressure drop is given by... 

Combining both expressions gives a simple relation for estimating the frictional pressure drop in straight run pipe. 

Built-up Back Pressure - Is the frictional pressure drop that develops as a result of flow through the discharge system after the pressure relief valve opens. 

The quantity of material to be relieved should be determined at conditions corresponding to the PR valve set pressure plus overpressure, not at normal operating conditions. Frequently, there is an appreciable reduction in required PR valve capacity when this difference in conditions is considerable. The effect of friction pressure drop in the connecting line between the source of overpressure and the system being protected should also be considered in determining the capacity requirement. If the valve passes a liquid which flashes or the heat content causes vaporization of liquid, this should be considered in determining PR valve size. 

Set Pressure - The set pressure (the pressure at whieh the PR valve is designed to open) is speeified in accordance with Code requirements. In most vessel apphcations, the set pressure of at least one PR valve is equal to the design pressure. However, this set pressure is adjusted (up or down) for any effect of static pressure and friction pressure drop that may apply when the valve is installed elsewhere than directly on the vessel. For example, if a PR valve is installed in a non-flowing line above a liquid-filled vessel, the PR valve set pressure would be reduced sufficiently to allow for the liquid static head between the vessel and the valve. 

When a PR valve is relieving at rated capacity, the total frictional pressure drop between a vessel and the inlet of the valve should be less than 3% of the set pressure (kPa). In this calculation, the effect on static pressure of fluid acceleration is ignored rather, only friction loss is considered. 

For a special fan situation, a straight air duct of uniform cross-sectional area is used on the leaving side. The outgoing velocity Cj is the same as the fan leaving velocity C2. The only minor loss is the outgoing loss = pcT Another part of the pressure drop is the frictional pressure drop Ap, . Equation (9.127) gives... 

Fji = friction pressure drop at maximum flow rate... 

APc = pressure drop across control valve F i = friction pressure drop at maximum flow rate, psi... 

Friction Pressure Drop For Compressible Fluid Flow... 

Keep friction pressure drop very low, not over 1 to 2 percent of allow able pressure for capacity relief [1, 10, 25, 28, 33]. 

Allowing 10% factor of safety, expected maximum increase in friction pressure drop allowance ... 

Dukler, A. E. et al., Frictional Pressure Drop in Two-Phase Flow1 B—An Approach Through Similarity Analysis, A.I.Ch.E.J. 10,... 

---