Loss coefficient fittings

Table 13.4 gives some typical values of the loss coefficient for various fittings9. It should be noted that values for loss coefficient will vary for the same fitting, but from different manufacturers, as a result of differences in geometry. Table 13.5 gives head losses for sudden contractions, sudden expansions and orifice plates. Note that the relationship for orifice plates in Table 13.5 relates to the overall pressure drop and not the pressure drop between the pressure tappings used to determine the flowrate. 

Table 13.4 Loss coefficients for various pipe fittings. ...

Ordinarily, any numerical quantities that appear in equations that have a theoretical basis (such as that for ke above) are dimensionless and hence universal. However, many valuable engineering relations have an empirical rather than a theoretical basis, in which case this conclusion does not always hold. For example, a very useful expression for the (dimensionless) friction loss coefficient ( A) ) for valves and fittings is... 

A loss coefficient can be defined for any element that offers resistance to flow (i.e., in which energy is dissipated), such as a length of conduit, a valve, a pipe fitting, a contraction, or an expansion. The total friction loss can thus be expressed in terms of the sum of the losses in each element, i.e., ef = JT K-nVf/7). This will be discussed further in Chapter 6. 

The loss coefficient is seen to be a function only of the geometry of the system (note that the assumption of plug flow implies that the flow is highly turbulent). For most systems (i.e., flow in valves, fittings, etc.), the loss coefficient cannot be determined accurately from simple theoretical concepts (as in this case) but must be determined empirically. For example, the friction loss in a sudden contraction cannot be calculated by this simple method due to the occurrence of the vena contracta just downstream of the contraction (see Table 7-5 in Chapter 7 and the discussion in Section IV of Chapter 10). For a sharp 90° contraction, the contraction loss coefficient is given by... 

Evaluation of the friction loss in valves and fittings involves the determination of the appropriate loss coefficient (Af), which in turn defines the energy loss per unit mass of fluid ... 

The 2-K method was published by Hooper (1981, 1988) and is based on experimental data in a variety of valves and fittings, over a wide range of Reynolds numbers. The effect of both the Reynolds number and scale (fitting size) is reflected in the expression for the loss coefficient ... 

Table 7-3 3-K Constants for Loss Coefficients for Valves and Fittings... 

Flow of Liquids through Pipes Table 4-2 2-K Constants for Loss Coefficients in Fittings and Valves1 125... 

In the velocity head method of accounting for fitting losses, a multiplicative coefficient is found empirically by which the velocity head term (v)2/2g is multiplied to obtain the fitting loss. This term is then added to the regular velocity head losses in Eq. (63). Extensive tables and charts of both equivalent lengths and loss coefficients and formulas for the effect of flow rate on loss coefficients... 

The flow in pipe fittings, e.g. bends and valves, is generally too complex to determine theoretically. For turbulent flow, these minor losses are approximately equal to the square of the flow velocity. Thus, we define a loss coefficient, K,... 

Similar to the energy loss of flow gas in case of sudden changes as discussed in Section 3.4.4, various types of valves and fittings in the CVD vacuum pipehnes also produce a head loss, a so-called minor loss. As hsted in Table 3.6, the head loss (hj) associated with these parts and fittings can be expressed in terms of the head loss coefficient (K)... 

EKf (pipe fittings + valves) is the sum of the pressure loss coefficient for all the fittings and valves in the line. Expressing the maximum fluid rate in pounds per hour, Equation 3-46 becomes... 

The model assumed adiabatic conditions in the experiment. Because of heat loss, the fitted parameters may be biased. An estimate of the overall heat transfer coefficient, h, is given by ... 

A loss coefficient can be defined for any element in which energy is dissipated (pipe, fittings, valves, etc.), although the friction factor is defined only for pipe flow. All that is necessary to describe the pressure-flow relation for pipe flows is Bernoulli s equation and a knowledge of the friction factor, which depends upon flow conditions, pipe size, and fluid properties. 

Hooper (1981, 1988) correlated loss coefficients for a variety of fittings as a function of Reynolds number and diameter by the equation... 

If the system contains fittings as well as straight pipe, the term (2fLID) is replaced by E(A y/2), where represents the sum of all the loss coefficients in the system. 

Contraction-loss coefficient, dimensionless Expansion-loss coefficient, dimensionless Loss factor for fitting or valve, dimensionless Flow consistency index, kg/m-s -" or lb/ft-s " ... 

To illustrate the sizing of a flare header, an example is given in Figure 6-14. Header I is to be sized for 220,000 lb. /hr. of vapor, which includes 12,000 Ib./hr. from header II, with M = 50 and T = 300° F. Knockout drum pressure at P-1 is 17 psia. Header I length, L = 2,000 ft. loss coefficients of fittings and exit, XK = 5. Header II L = 100 ft. XK = 3. Maximum allowable back pressure downstream of valve at P-3 is 40 psia (safety valve set pressure 60 psig). 

Besides the pressure drop inside the columns there can be an additional pressure loss due to the piping and the valves between the columns. In experiments, a large pressure drop was found in an SMB-SFC apparatus due to these flow resistances [55]. Taking into account the pressure drop as a function of mass flow rates, a pressure-loss coefficient f for the total flow resistance (analogous to pipeline construction) between two columns is determined by fitting to experimental pressure drops. Then the pressure drop can be calculated from ... 

Table 7.1 Loss coefficients for bends and fittings in turbulent How...

The terms in the sum consist of the channel friction factor Xi and the pressure loss coefficient of channel internals or fittings j. For laminar flow in straight channels, the charmel fnction factor Xi is inversely proportional to the Reynolds number in the charmel ... 

Edwards et al. studied the frictional head loss for different pipe fittings for flow of Newtonian and non-Newtonian liquids in laminar flow condition [14]. They proposed generalized correlation with loss coefficient and Reynolds number (Re = VpD/p for Newtonian liquid and Re = Re for non-Newtonian liquid) of individual fittings. 

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