Fitting head loss

Figure 20 shows the fittings head losses in both laminar and turbulent flow. Figure 20 shows three principal differences between the fittings head losses in both laminar and turbulent flow ... 

Figure 20 shows that there are considerable differences in the magnitude of the fittings Head losses in laminar and turbulent flow. A direct comparison of these magnitudes is shown in... 

In this example, the fittings head losses in laminar flow shown in Figure 20 and Figure 21 exceed those in turbulent flow by several orders of magnitude. 

Fig. 20. Fittings Head Losses in Laminar and Turbulent flow...

Equation 3.10 can be rearranged to express the fitting head loss as feet of straight pipe having the same head loss as the fitting. 

The flow resistance of pipe fittings (elbows, tees, etc) and valves is expressed in terms of either an equivalent length of straight pipe or velocity head loss (head loss = Kv /2g ). Most handbooks and manufacturers pubHcations dealing with fluid flow incorporate either tables of equivalent lengths for fittings and valves or K values for velocity head loss. Inasmuch as the velocity in the equipment is generally much lower than in the pipe, a pressure loss equal to at least one velocity head occurs when the fluid is accelerated to the pipe velocity. 

Friction Head Loss (Resistance) in Pipe, Fittings, and Connections... 

Equation 2-25 is valid for calculating the head loss due to valves and fittings for all conditions of flows laminar, transition, and turbulent [3], The K values are a related function of the pipe system component internal diameter and the velocity of flow for v-/2g. The values in the standard tables are developed using standard ANSI pipe, valves, and fittings dimensions for each schedule or class [3]. The K value is for the size/type of pipe, fitting, or valve and not for the fluid, regardless of whether it is liquid or gas/vapor. 

Hooper, W. B., The Two-K Method Predicts Head Losses in Pipe Fittings, Chemical Engineering, Aug. 24, 1981, p. 96. 

The loss in terms of velocity heads can be estimated by counting the number of flow contractions, expansions and reversals, and using the factors for pipe fittings to estimate the number of velocity heads lost. For two tube passes, there will be two contractions, two expansions and one flow reversal. The head loss for each of these effects (see Volume 1, Chapter 3) is contraction 0.5, expansion 1.0, 180° bend 1.5 so for two passes the maximum loss will be... 

Figure 5-1 illustrates a method that will produce a system in which the parts fit together to accomplish the common goal of good control. Control valve share of total system flowing pressure drop will be 60% at normal flow. The system will still achieve maximum flow as long as the control valve trim selected can pass maximum flow at operating head loss (line 23 of Figure 5-1). The procedure described in Figure 5-1 is intended as a stand-alone device for guiding the calculations, and worksheets can be prepared from it.

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. 

Kf is the excess head loss due to the pipe or pipe fitting (dimensionless) and u is the fluid velocity (length/time). 

For pipe fittings, valves, and other flow obstructions the traditional method has been to use an equivalent pipe length Lequiv in Equation 4-30. The problem with this method is that the specified length is coupled to the friction factor. An improved approach is to use the 2-K method,s-6 which uses the actual flow path length in Equation 4-30 — equivalent lengths are not used — and provides a more detailed approach for pipe fittings, inlets, and outlets. The 2-K method defines the excess head loss in terms of two constants, the Reynolds number and the pipe internal diameter ... 

Determine the excess head loss terms for the pipe (using Equation 4-30), for the fittings (using Equation 4-38), and for any entrance and exit effects (using Equation 4-39). Sum the head loss terms, and compute the net frictional loss term using Equation 4-29. Use the velocity at point 2. 

K are the excess head loss terms, including pipe entrances and exits, pipe lengths, and fittings (unitless). 

The excess head loss terms 2 Kt are found using the 2-K method presented earlier in section 4-4. For most accidental discharges of gases the flow is fully developed turbulent flow. This means that for pipes the friction factor is independent of the Reynolds number and that for fittings Kf = and the solution is direct. 

Assume fully developed turbulent flow to determine the friction factor for the pipe and the excess head loss terms for the fittings and pipe entrances and exits. The Reynolds number can be calculated at the completion of the calculation to check this assumption. Sum the individual excess head loss terms to get 2 Kf. 

If the frictional losses were expressed as the head loss, hf= APf/pg, then the quantity 4fLJdi would multiply u2/2g. Thus 4/Le/d, is the total number of velocity heads lost. Consequently, an alternative presentation of frictional losses for fittings is in terms of the number of velocity heads K lost for each fitting. In this case, the total frictional pressure drop may be calculated as... 

If relief is via a bursting disc, the flow capacity of the relief system will normally depend on friction and choke points in the relief system. The only exception is where friction is not important (LE/D less than about 40), where equation (A6.4) can be used.) Where friction is significant, an isometric sketch of the route of the relief system will be required to determine the capacity. If the system is to be of constant diameter, then using the sketch, the total equivalent length, LE, of the route, including the frictional resistance of bends and fittings can be determined111. This can also be expressed in terms of total frictional velocity head loss, K ... 

The additional frictional losses due to pipeline fittings such as elbows may be added to the velocity head loss N = 4fL/DH using the same velocity head loss values as for incompressible flow. This works well for fittings which do not significantly reduce the channel cross-sectional area, but may cause large errors when the flow area is greatly... 

There are four fitting K factors in Eq. (6.11). Each of these factors represents a specific valve or pipe-fitting pressure head loss, fLID. Notice that this term is not a K term, but rather represents L, the actual straight length of pipe. The reason it is not a K term is that it represents a straight section of pipe. The/factor in Eq. (6.11), including the / factor in each of the K terms, is calculated using Eqs. (6.3), (6.4), or (6.5). Derivation of the K resistance coefficients is reviewed in the next section. 

From Eq. (63), the mechanical energy equation in head form, it is seen that, in the absence of a pump head, losses in a pipe system consist of pressure head changes, potential head changes, and velocity head changes. When fittings or changes in pipe geometry are encountered, additional losses occur. 

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... 

Therefore, the total pressure or head loss due to friction in pipework due to the pipe and fittings is given by... 

What is the maximum capacity of a double-suction condensate pump operating at 1750 r/min if it handles 100°F (311 K) water from a hot well in a condenser having an absolute pressure of 2.0 in Hg (6.8 kPa) if the pump centerline is 10 ft (3.05 m) below the hot-well liquid level and the friction-head loss in the suction piping and fitting is 5 ft (1.5 m) of water ... 

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