Document zdmEgNbgQ0BD50yRp8pVDEE0B

78 CHAPTER 4 1950 Guide where Nn, = 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 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, 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 .A. r>,,--iris n,,mhw for smooth Dme. such as drawn brass tubing Fig. 3. Relation op Kinematic Viscosity to Temperature of Water 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; it represents the formula: With laminar flow, the velocity profile is a parabola, having the formula where V - r4pil (** ~ W <U> 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 1 Superior number* 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 AJSJfJS. 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 VR0; and from this point proceed horizontally to left margin to find the value of f to use in Equation 8.