Document ppLV3Y58p0bGYw8VnJgpkR4KB

70 CHAPTER 4 1956 Guide where NE. *= Reynolds number. p = the density in pounds per cubic, foot, p = the absolute viscosity in pounds per foot-second. Both / and the Reynolds number are dimensionless. To aid in comput ing the Reynolds number, values of -, the kinematic viscosity, are shown as a function of temperature for air in Fig. 2, and for water in Fig. 3. Fig. 4 shows the relation between / and the Reynolds number, adapted from a review by Moody.1 The straight line sloping downward at the left of the chart supplies, the values of / for laminar flow determined by the formula: Fluid Flow 71 unstable region where the flow changes from laminar to turbulent, or vice versa. .The actual value is impossible of prediction for any condi tions of flow, though in general it may be said that the prevailing type of flow persists into the unstable region; however, once the change starts, it proceeds very rapidly. When the flow is turbulent, the velocity profile is essentially parabolic over four-fifths of the pipe diameter, but near the pipe walls, the effect of friction becomes evident, and in the boundary layer at the pipe wall the flow is laminar. Fig. 5 compares the velocity profiles for three different Reynolds numbers, but for the same average velocity. The lower curve in the turbulent region in Fig. 4 represents the relation of / to the Reynolds number for smooth pipe, such as drawn brass tubipg Fio. 3. Relation of Kinematic Viscosity to Temperature op Water 64 f Nr. (10) With laminar flow, the velocity profile is a .parabola, having the formula: V - ^; (f* T V) 4pi (11) where r = the radius of the pipe in feet. L = distance perpendicularly from the axis of the pipe, in feet. Accordingly, the:maximum velocity occurs at the center of the pipe and is twice the average velocity; the average velocity is found when L -- 0.707 r. It is worth noting that roughness, of the pipe wall has no effect on the loss in head for laminar flow. Between values of the Reynolds number of 2000 and 4000, there is an * Superior number* refer, to the. references at the end of chapter. Fio. 4. Relation Between Friction Factor and Reynolds Number Note: The straight line at left shows values of Friction Factor for laminar flow. Reprinted by permission from ASMB Transaction*. or glass tubing. The effect of roughness on/, an effect which is considerable in turbulent flow, is open to some conjecture; artificially roughened pipes, for instance, give results at variance with actual tests. The curves above the smooth pipe curve of Fig. 4 represent a summary of tests on rough pipe, each of them identified by a value of e/d, with e signifying theabsolute roughness in feet. Values of e for different pipes are given in Table 1. To find the friction loss for any pipe, follow the curve with the proper value of e/d, to the pertinent value of NRta and from this' point proceed horizontally to left margin to find the value of / for use in Equation 8.