Turbulent flow fittings, frictional losses

TABLE 6-4 Additional Frictional Loss for Turbulent Flow through Fittings and Valves ... 

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... 

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. 

The preceding analysis clearly neglects a number of factors that may have an influence on the optimum economic pipe diameter, such as cost of capital or return on investment, cost of pumping equipment, taxes, and the time value of money. If the preceding development of Eq. (39) for turbulent flow is refined to include the effects of taxes and the cost of capital (or return on investment) plus a more accurate expression for the frictional loss due to fittings and bends, the result is t... 

Some representative figures are given in Table 3.2 for the friction losses in various pipe fittings for turbulent flow of fluid, and are expressed in terms of the equivalent length of straight pipe with the same resistance, and as the number of velocity heads (M /2g) lost. Considerable variation occurs according to the exact construction of the fittings-... 

This is the mechanical-energy loss due to skin friction for the pipe in N m/kg of fluid and is part of the F term for frictional losses in the mechanical-energy-balance equation (2.7-28). This term (Pi—Pz)/ for skin friction loss is different from the (p, — Pz) term, owing to velocity head or potential head changes in Eq. (2.7-28). That part of F which arises from friction within the channel itself by laminar or turbulent flow is discussed in Sections 2.10B and in 2. IOC. The part of friction loss due to fittings (valves, elbows, etc.), bends, and the like, which sometimes constitute a large part of the friction, is discussed in Section 2.10F. Note that if Eq. (2.7-28) is applied to steady flow in a straight, horizontal tube, we obtain (pi — Pz)/p = F. 

Table 2.10-1. Friction Loss for Turbulent Flow Through Valves and Fittings...

TABLE 2-13 Equivalent Length of Fittings for Friction Loss of Calculations for Single-Phase Turbulent Flow ... 

Figure 48.2 Frictional losses due to fittings for fluid in turbulent flow.

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