Fluid Mechanics Studies—Isothermal Skin Friction in Flow through Annular Sections

Fluid friction in noncircular ducts

“…Rothfus and coworkers (9) have found that r, is greater than the computed value a t the lower critical Reynolds number. Therefore, the actual lower critical value is somewhat smaller than shown in Figure 3.…”

Laminar, transitional and turbulent annular flow of drag-reducing polymer solutions

“…Early investigations for the flow of Newtonian fluids by Knudsen and Katz [17], Rothfus et al [1,18], Walker and Rothfus [19] and Brighton and Jones [20] assumed coincidence of the position of zero shear stress and maximum velocity. Lawn and Elliott [21] were the first to show, using hot-wire anemometry, that the positions of zero shear stress and maximum velocity for fully-developed turbulent flow are non-coincident.…”

Simplified flow calculations for tubes and parallel plates

“…The same upper limit has been found to exist a t the outer walls of annuli by Rothfus, Monrad, Sikchi, and Heideger (10). If it is desired to calculate the pressure drop caused by fluid friction between parallel plates, the friction factor obtained from Figure 4 a t the parallel-plate Reynolds number can be inserted directly into Equation ( 5 ) .…”

“…This fact does not, in itself, detract from utility and accuracy if a truly equivalent tube can be found. The results of recent experimental investigations of pressure drop and velocity distribution in annuli (3,9,10) have indicated, however, that the tube postulated in the usual hydraulic-radius concept is not the correct one, although its use often yields a good approximation to the actual friction head. It is therefore reasonable to believe that the hydraulicradius method is based on an empiricism which in many cases is not far removed from the true situation.…”