Document om91x70X2aR4aGMYmn4Qmm4EE

-76 CHAPTER 4_______________ _________ 1948 Guide ^ = 0(r*-i*) - (8) where r = the radius of the pipe in feet. h~ ~ 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 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 A Transactions. 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, blit 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 or glass tubing. The effect of roughness on /.. which is a considerable Fluid FUrw 77 Fig. 5. Comparison of Velocity Profiles for 3 Different Reynolds Numbers but for Same Average Velocity 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 signifying 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 and from this point proceed horizontally to left margin to find the value of / to use in Equation 5. Equation 5 is applicable to all liquids, and to gases when the pressure loss is less than 10 per cent of the initial pressure.. When the loss in head is high, the formula to,be used for gases is ** ->* = pi* gd pit* (9) which may be rearranged to give the loss in pressure ' <,o> Pressure Loss in Non-Circular Pipes The formulas for flow in pipes are based upon the use of pipes of circular cross-section. The formulas may be used with conduits of other shapes, and in conduits not flowing full, when the flow is turbulent, by using the hydraulic radius, Rh, which is really a ratio: ,, area of cross-section. = ---------- --------:------------- 7----- :----------- :---wetted perimeter oi cross-section /11N (11) Table 1. Values of ejd for Different Kinds of Pipe Type of pipe Commercial steel or wrought iron. .............................................. Asphalted cast-iron :-- ---------- Wood stave. .......... -- .......... -.................... -----....... --- e/d. . 0.000005 0.00015 0.0004 0.0005 0.00085 0.0006 to 0.003 0.001 to 0.01 0.003 to 0-03