Fluid flow equivalent length

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. 

Clearly, the maximum degree of simplification of the problem is achieved by using the greatest possible number of fundamentals since each yields a simultaneous equation of its own. In certain problems, force may be used as a fundamental in addition to mass, length, and time, provided that at no stage in the problem is force defined in terms of mass and acceleration. In heat transfer problems, temperature is usually an additional fundamental, and heat can also be used as a fundamental provided it is not defined in terms of mass and temperature and provided that the equivalence of mechanical and thermal energy is not utilised. Considerable experience is needed in the proper use of dimensional analysis, and its application in a number of areas of fluid flow and heat transfer is seen in the relevant chapters of this Volume. 

Some representative figures are given in Table 3.2 for the friction losses in various pipe fittings for mrbulent 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 ( 2/2g) lost. Considerable variation occurs according to the exact construction of the fittings. 

Heat is to be transferred from one process stream to another by means of a double pipe heat exchanger. The hot fluid flows in a 1 in. sch 40 tube, which is inside (concentric with) a 2 in. sch 40 tube, with the cold fluid flowing in the annulus between the tubes. If both fluids are to flow at a velocity of 8 ft/s and the total equivalent length of the tubes is 1300 ft, what pump power is required to circulate the colder fluid Properties at average temperature p = 55 lbm/ft3, p = 8 cP. 

Note that the Nusselt number is equivalent to the dimensionless tcmperalure gradient at the sniface, and thus it is properly referred to as the dimensionless heat transfer coefficient (Fig. 6-33). Also, the Nusselt number for a given geometry can be expressed in terms of the Reynolds number Re, the Prandtl number Pr, and the space variable. v, and such a relation can be used for different fluids flowing at different velocities over similar geometries of different lengths. 

It is clear that all the end effects are not caused by the seal friction and cylinder end surfaces alone. A 40mm long rotor with a 5mm annular gap has an end effect equivalent length of 58mm. Approximately half of this can be explained as due to the radial surfaces at the sides of the rotor and the likely losses in the thick fluid films on the seal faces. The remaining end effects are probably due to three dimensional flow effects which may be unique to the test rig or may be generally applicable. 

Any engineering or fluid-flow handbook contains tables of equivalent lengths of straight pipe for piping designs. These are based on the type of bend, its radius of curvature, and, often, the conditions of the inner surfaces of the pipe. Table 5-1 shows a suggested set of factors for bend and curve designs (Perry, 1950). More recently, a tremendous amount of work has been carried out by Ito (1959) to determine pressure losses in pipe bends. A typical pressure-loss curve as seen by Ito when... 

If fully developed turbulent flow is assumed, the friction factor, f, is constant. For process changes involving the same fluid, the density remains constant, and if the pipe is unchanged, the equivalent length and diameter are unchanged. 

The definitions for the mass transfer coefficients can be used to theoretically predict them using the diffiisivity, concentrations, length scales, and fluid flow characteristics, thus rendering the two mass transfer approaches equivalent. This can easily be done in the cases of equimolar counterdiffusion (Maz + A bz = 0) and diffusion of A through a stagnant film (Ab = 0) (Hines and Maddox, 1985, p. 140). Also, the theoretical models of film, penetration, surface renewal, and film penetration have been proposed for the estimation of the mass transfer coefficients at a fluid-fluid interface (Hines and Maddox, 1985, pp. 146-151). 

The specific heat of water is approximately four times the specific heat of NaK-55 meaning that the mass flow rate of NaK will be approximately four times the mass flow rate of water for a fixed heat duty and fixed terminal fluid temperatures. The ratio of volumetric flow rates will be also be approximately four as water and NaK densities are similar. For a fixed flow area, NaK velocity will be approximately four times water velocity while the Reynolds Number with NaK will be approximately 1.6 to 1.7 times the Reynolds Number with water for a given equivalent diameter. While the higher Reynolds Number will reduce the friction factor with NaK, the higher NaK velocity will still result in increased pressure drop due to friction relative to water for a given equivalent diameter and flow path length. 

---