Reply by Authors to R. H. Cramer

Abstract

the body and the virtual origin the observed wake converged, but at approximately 4 body-diameters downstream of the base the self-preservation or similarity region can be imagined to originate.Unfortunately, it appears likely that the entire selfpreservation and similarity concept does not represent closely what occurs in the wake in physical actuality. A recent paper by Ermshaus 4 gives very convincing proof that the supposed axially-symmetric wake-spreading behavior that would follow the jc 173 law is not found to be confirmed by experiments, nor does the ratio remain constant that expresses the comparison between the maximum shear stress, represented by the quantityand v f are the fluctuations of velocity in the x and r directions, respectively) to the square of the velocity defect at the middle of the wake. In the mixing-length theory used to derive the expressions given above there is implicit the hypothesis that r m /(UL^Os 2 must remain constant (where the s subscript denotes conditions at the centerline). The surprising result obtained by Ermshaus is that two-dimensional configurations (cylinders and narrow bands or beams) and axially symmetric configurations, as well, have to all intents and purposes the same exponent in the law describing the downstream spread of the wake. For all such configurations, to be precise, the width of the wake appears to grow approximately according to jc 0 -44 = # 1/2 -25 , not the jc 1/2 law predicted on basis of similarity theory for two-dimensional bodies, nor according to the x 1 / 3 law, predicted according to classic theory, for axially symmetric bodies. Consequently, even though Eqs. (6) and (7) appear to be well-substantiated by the faired data-plots given by Chevray, some caution should be exercised in trying to apply to quite different situations these particular results that have come from one kind of body shape and for which the asymptotic state apparently was not yet attained (if it ever would be).IN the case of axially-symmetric turbulent wake flow, the following equations for the velocity profile and the wake width were formulated simply from available information: and where = uv(cX)r l/3 b=B(C D dx) r] =y/b D1 /3(D

Systematic Approach for Calculating the Concentrations of Chemical Species in Multiequilibrium Problems: Inclusion of the Ionic Strength Effects

“…The numerical calculation of concentrations in chemical equilibrium problems is of great importance in a wide range of areas related to chemistry, as its teaching in several science courses, such as general chemistry, analytical chemistry, pharmacy, chemical engineering, and environmental science attests. − For the sake of simplicity, ideal conditions are usually assumed where activities and concentrations coincide. This means that the effects of the electrostatic interaction of ions are disregarded; however, the deviations from ideality can be significant.…”