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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
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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- Spring '08