Document 6wK7ODK1Rd3gGrK8RvoyY0En6

76 where CHAPTER 4 1951 Guide' Na. * Raynolds number. P = the density in pounds per cubic foot. m = the absoitite viscosity in pounds per foot-fiecond Both / and the Reynolds number are dimensionless. To aid in com. pitting 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. .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. How 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 - , *i.,, Remolds number for smooth pipe, such as drawn brass tubing Viscosity to Temperature op Water With laminar flow, the velocity profile is a parabola, having the formula where . an 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 numbers refer to the references at the end of chapter. To find the friction loss for any pipe, follow the curve with the proper value of e/d, to the pertinent value of NRe, and from this point proceed horizontally to left margin to find the value of / for use in Equation 8.