## K v2

The value of fT can be calculated from the Colebrook equation, fx = °.°625 2 (7-36)

in which £ is the pipe roughness (0.0018 in. for commercial steel). This is a two-constant model [fT and (L/D)eq], and values of these constants are tabulated in the Crane paper for a wide variety of fittings, valves, etc. This method gives satisfactory results for high turbulence levels (high Reynolds numbers) but is less accurate at low Reynolds numbers.

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: K V 2 K 1

Here, IDin is the internal diameter (in inches) of the pipe that contains the fitting. This method is valid over a much wider range of Reynolds numbers than the other methods. However. the effect of pipe size (e.g., 1/IDin) in Eq. (7-37) does not accurately refect observations, as discussed below.

Although the 2-K method applies over a wide range of Reynolds numbers, the scaling term (1/ID) does not accurately reflect data over a wide range of sizes for valves and fittings, as reported in a variety of sources (Crane, 1988, Darby, 2001, Perry and Green, 1998, CCPS, 1998 and references therein). Specifically, all preceding methods tend to underpredict the friction loss for pipes of larger diameters. Darby (2001) evaluated data from the literature for various valves, tees, and elbows and found that they can be represented more accurately by the following "3-K" equation:

Values of the 3 K's (Kj, Ki, and Kd) are given in Table 7-3 (along with represesentative values of [L/D]eq) for various valves and fittings. These values were determined from combinations of literature values from the references listed above, and were all found to accurately follows the scaling law given in Eq. (7-38). The values of Kj are mostly those of the Hooper 2-K method, and the values of Ki were mostly determined from the Crane data. However, since there is no single comprehensive data set set for many fittings over a wide range of sizes and Reynolds numbers, some estimation was necessary for some values. Note that the values of Kd are all very close to 4.0, and this can be used to scale known values of Kf for a given pipe size to apply to other sizes. This method is the most accurate of the methods described for all Reynolds numbers and fitting sizes. Tables 7-4 and 7-5 list values for Kf for Expansions and Contractions, and Entrance and Exit conditions, respectively, from Hooper (1988).

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

Ki = Ki/NRe + K|(1 + Kd/Dn) where Dn is the nominal diameter in inches

Fitting

Elbows 90°

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