FRICTION LOSS IN VALVES AND FITTINGS

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 basis for the equivalent L/D method is the assumption that there is some length of pipe (Leq) that has the same friction loss as that which occurs in the fitting, at a given (pipe) Reynolds number. Thus, the fittings are 

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Newtonian fluids can be correlated by this method that is, the same correlation applies to both Newtonian and non-Newtonian fluids when the Newtonian Reynolds number is replaced by either Eq. (7-40) for the power law fluid model or Eq. (7-41) for the Bingham plastic fluid model. As a first approximation, therefore, we may assume that the same result would apply to friction loss in valves and fittings as described by the 2-K or 3-K models [Eq. 7-38)]. 

Darby, R. Friction loss in valves and fittings—Part IF Chem Eng 2001 (in press). Darby R, J Forsyth. Can J Chem Eng 70 97-103, 1992. 

You must specify a pump to be used to transport water at a rate of 5000 gpm through 10 mi of 18 in. sch 40 pipe. The friction loss in valves and fittings is equivalent to 10% of the pipe length, and the pump is 70% efficient. If a 1200 rpm motor is used to drive the pump, determine ... 

There are insufhcient data in the literature to enable reliable correlation or prediction of friction loss in valves and fittings for non-Newtonian fluids. As a first approximation, however, it may be assumed that a correlation analogous to the 2-K or 3-K method should apply to non-Newtonian... 

Two-phase friction loss in valves and fittings can be estimated using the no-slip velocity, v s, the single-phase head Coefficients. K, and the no-slip density ... 

For laminar flow, data for the frictional loss of valves and fittings are meager. (Beck and Miller,y. Am. Soc. Nav. Eng., 56, 62-83 [194fl Beck, ibid., 56, 235-271, 366-388, 389-395 [1944] De Craene, Heat. Piping Air Cond., 27[10], 90-95 [1955] Karr and Schutz, j. Am. Soc. Nav. Eng., 52, 239-256 [1940] and Kittredge and Rowley, Trans. ASME, 79, 1759-1766 [1957]). The data of Kittredge and Rowley indicate that K is constant for Reynolds numbers above 500 to 2,000, but increases rapidly as Re decreases below 500. Typical values for K for laminar flow Reynolds numbers are shown in Table 6-5. 

The selection of the pump cannot be separated from the design of the complete piping system. The total head required will be the sum of the dynamic head due to friction losses in the piping, fittings, valves and process equipment, and any static head due to differences in elevation. 

The velocities at the entrance and exit of the system can be calculated from the respective diameters of the tanks or pipes and the volumetric flow rate of the food. The energy loss term E/ consists of losses due to friction in pipe and that due to friction in valves and fittings ... 

Friction losses in straight pipe, valves, and fittings... 

The total piping system pressure drop for a particular pipe installation is the sum of the friction drop in pipe valves and fittings, plus other pressure losses (drops) through control valves, plus drop through equipment in the system, plus static drop due to elevation or pressure level. For example, see Figure 2-2. 

The friction losses for fluid flow in pipe valves and fittings are determined as presented in Chapter 2. Entrance and exit losses must be considered in these determinations, but are not to be determined for the pump entrance or discharge connections into the casing. 

The absolute pressure at the inlet to the pump is usually the atmospheric pressure in the receiver, plus the static head from the water surface to the pump inlet and minus the friction loss through the pipes, valves and fittings joining the pump to the receiver. If his absolute pressure exceeds the vapor pressure of water at the temperature at which it enters the pump, then a net positive suction hand (NPSH) exists. If this NPSH is above the value specified by the pump manufacturer, the water does not begin to boil as it enters the pump suction and cavitation is avoided. If the water entering the pump is at a higher temperature, its vapor pressure is increased and a greater hydrostatic head over the pump suction is needed to ensure that the necessary NPSH is obtained. 

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... 

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... 

Pumping Head—The energy required to raise water to the distribution elevation and overcome friction losses through pipe, valves, fittings and nozzles. It is expressed in feet of liquid the pump must move and is equal to the total friction loss, static head and pressure drop through the distribution system. 

We might now well inquire for the purpose of purchasing a pump-motor, say, as to what the work would be for a real process, instead of the fictitious reversible process assumed above. First, you would need to know the efficiency of the combined pump and motor so that the actual input from the surroundings (the electric connection) to the system would be known. Second, the friction losses in the pipe, valves, and fittings must be estimated so that... 

So far all the discussion has been about steady flow well downstream of the pipe entrance in straight circular pipe. This is the simplest and one of the most important cases of fluid friction. However, in many fluid systems we must take into account the effect of valves, elbows, etc. They are much more complex to analyze than the one-dimensional flows we have considered so far. (The student is advised to take apart an ordinary household faucet and study its flow path it is much more complicated than that of a straight pipe.) Efforts have been made to calculate the friction losses in such fittings, and the results have been correlated in several convenient ways which allow us to treat them as if they were one-dimensional problems. 

Fluid friction is covered by information on pressure losses in pipes, ducts, orifices, valves, and fittings in pt 5 of reference 51. 

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. 

Frictional losses in mechanical-energy-balance equation. The frictional losses from the friction in the straight pipe (Fanning friction), enlargement losses, contraction losses, and losses in fittings and valves are all incorporated in the F term of Eq. (2.7-28) for the mechanical-energy balance, so that... 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

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