4 but hagen did not realize that the constant was

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Unformatted text preview: as proportional to the fluid viscosity. The formula broke down as Hagen increased Q beyond a certain limit, i.e., past the critical Reynolds number, and he stated in his paper that there must be a second mode of flow characterized by “strong movements of water for which p varies as the second power of the discharge. . . .” He admitted that he could not clarify the reasons for the change. A typical example of Hagen’s data is shown in Fig. 6.4. The pressure drop varies linearly with V Q/A up to about 1.1 ft/s, where there is a sharp change. Above about V 2.2 ft/s the pressure drop is nearly quadratic with V. The actual power p V1.75 seems impossible on dimensional grounds but is easily explained when the dimensionless pipe-flow data (Fig. 5.10) are displayed. In 1883 Osborne Reynolds, a British engineering professor, showed that the change depended upon the parameter Vd/ , now named in his honor. By introducing a dye 120 Turbulent flow ∆p α V 1.75 100 Pressure drop ∆p, lbf/ft2 80 60...
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