Pipes, defined

Mote The friction factor jr is the same as the friction factor for pipes (= defined in Chapter ... 

Let / b be the radius of curvature of the pipe axis and R4 be the radius of the circular cross section of the pipe. Define U as the axial velocity component and (=/ d — r) as the distance normal to the wall. Denote 0 as the angle in the transverse plane with respect to the outward direction of the symmetry line and 4> as the angle measured in the plane of the curved pipe axis, as shown in Figs. 11.9(a) and (c). Assume that the changes of the flow pattern along the axis of the bend can be neglected. Thus, the momentum integral equations... 

For each tube or channel the variation with the magnetic field intensitj of the pressure drop between the tw o sockets was determined for a number of values of the volume velocity F or of the Reynolds number R. The latter is, in the case of a cylindrical pipe, defined by... 

The fifth type of tap is unique in that the downstream tap location varies depending of the orifice P ratio. This tap is located at the vena contracta the location where the stream issuing from the orifice attains its minimum cross section. The location of this tap is defined from the upstream face of the orifice as is the D/2 tap. The downstream tap for corner, flange, and pipe taps is measured from the downstream face of the orifice. Vena contracta taps maximize the measured differential pressure. For modem transmitters this is not an important consideration and this type of tap is no longer widely used. 

Although it has been common practice to specify the pressure loss in ordinary valves in terms of either equivalent length of straight pipe of the same size or velocity head loss, it is becoming more common to specify flow rate and pressure drop characteristics in the same terms as has been the practice for valves designed specifically for control service, namely, in terms of the valve coefficient, C. The flow coefficient of a valve is defined as the volume of Hquid at a specified density that flows through the fully opened valve with a unit pressure drop, eg, = 1 when 3.79 L/min (1 gal /min) pass through the valve... 

For most nonmetallic pipes ANSI/ASME B31.3 prescribes a somewhat similar formula for calculating the pipe thickness under internal pressure where the terms are as previously defined ... 

Restraints. A restraint limits thermal reactions at equipment and line stresses or expansion movement at specifically desired locations. It may be defined as a device preventing, resisting, or limiting the free thermal movement of a piping system. Because the appHcation of a restraint reduces the inherent flexibiHty of the piping, its effect on the system is estabHshed through calculation. 

Flexibility and Stress-Intensification Factors. The flexibihty factor k (>1.0) is defined as the ratio between the rotation per unit length of the part in question produced by a given moment to the rotation of a straight pipe (of the same size and schedule) produced by the same moment. A close approximation of the flexibiUty factor that agrees quite well with theory and experiment for bends is as follows ... 

Standard Chemical Pump. In 1961, the American National Standards Institute (ANSI) iatroduced a chemical pump standard (29), known as ANSI B73.1, that defined common pump envelope dimensions, connections for the auxiUary piping and gauges, seal chamber dimensions, parts mnout limits, and baseplate dimensions. This definition was to ensure the user of the availabiUty of iaterchangeable pumps produced by different manufacturers, as well as to provide plant designers with standard equipment. A typical ANSI chemical pump, known as of the mid-1990s as ASME B73.1M-1991, is shown ia Figure 6. 

Experimental techniques to visualize flows have been extensively used to define fluid flow in pipes and air flow over lift and control surface of airplanes. More recently this technology has been appHed to the coating process and it is now possible to visualize the flow patterns (16,17). The dimensions of the flow field are small, and the flow patterns both along the flow and inside the flow are important. Specialized techniques such as utilizing small hydrogen bubbles, dye injection, and optional sectioning, are required to visualize these flows. 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

For fully developed incompressible horizontal gas/hquid flow, a quick estimate for Ri may be obtained from Fig. 6-27, as a function of the Lockhart-MartineUi parameter X defined by Eq. (6-131). Indications are that liquid volume fractious may be overpredicled for liquids more viscous than water (Alves, Chem. Eng. Prog., 50, 449-4.56 [19.54]), and uuderpredicted for pipes larger than 25 mm diameter (Baker, Oil Gas]., 53[12], 185-190, 192-195 [1954]). 

Ri = effective radius of miter bend, defined as the shortest distance from the pipe centerhne to the intersection of the planes of adjacent miter joints 0 = angle of miter cut, °... 

In calculating the flexibihty of a piping system between anchor points, the system shah be treated as a whole. The significance of all parts of the hne and of all restraints introduced for the purpose of reducing moments and forces on equipment or small branch hnes and also the restraint introduced by support friction shall be recognized. Consider all displacements over the temperature range defined by operating and shutdown conditions. 

Table 10-56 gives values for the modulus of elasticity for nonmetals however, no specific stress-limiting criteria or methods of stress analysis are presented. Stress-strain behavior of most nonmetals differs considerably from that of metals and is less well-defined for mathematic analysis. The piping system should be designed and laid out so that flexural stresses resulting from displacement due to expansion, contraction, and other movement are minimized. This concept requires special attention to supports, terminals, and other restraints. 

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