Document ZBJmJJ5pK5zDzMKeDJDVxDO3L

78 CHAPTER 4 1949 Guide where Ns. 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 com puting the Reynolds number, values of'-, the kinematic viscosity, are p shown as a function of temperature for air in Fig. 2 and for water in Fig. 3. Fluid Flow 79 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, pnce 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 tubing Fig. 3. Relation of Kinematic Viscosity to Tempehature of Water Fig. 4 shows the relation between / and the Reynolds number, adapted from a review by Moody'. The straight line sloping downward at the left of the chart supplies the values of/.for laminar, flow; it represents the formula: 64 / IVro (10) With laminar flow, the velocity profile is a parabola, having the formula. where v = 4pt ") ' .- (ID 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 foundwhen 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 1 Superior numbers refer to the references at the end of the chapter. Fig. 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 AJ2.MJ2. Transactions. or glass tubing. The effect of roughness on /, which is a considerable factor 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 sig nifying the absolute roughness in feet. Values of e/d 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 VRO; and from this point proceed horizontally to left margin to find the value of / to use in Equation 8. /