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For several days during the spring of 1955, wind-speed profiles were measured from an oil drilling platform in the Gulf of Mexico. Various standard parameters such as the friction velocity, roughness parameter, surface stress, and resistance coefficient are computed from these profiles. Functional relationships are derived between the various computed parameters and the wind speed at ten meters. A re-analysis of data obtained by Wiist in 1919 shows that it is in very good agreement with the present data. An attempt is made to relate the roughness parameter with the root-mean-square of the water-level fluctuations, and though some indication of a dependence can be inferred, there is too much scatter of the plotted points to arrive at a unique functional relationship.

In the formulas in present use the resistance coefficient has been considered constant for a particular type of material in a particular state of upkeep. The resistance coefficient, however, is not a constant for a given channel but varies with both velocity and depth. From the nature of these formulas in present use it may be seen that the variable influence of viscosity is not taken into consideration. Because of the need for more accurately determining the discharges in open channels a standard for roughness for open channels such as that which exists for pipes is desirable. The problem of developing a reproducible standard for roughness in open channels has previously received very little systematic study. Although several investigations have been made, each was made with a different type of roughness. This study was conducted for the purpose of determining whether an artificial roughness standard could be established for a channel with a boundary so rough that the viscous effects were negligible. The equation Figure 1. was established and is applicable over at least a fourfold variation in d/a and nearly a twofold variation in the resistance coefficient.

Calculations have been made covering the predictions of a model re presenting the vi s­ coelastic behavior of rubberlike polymers for molecular weights greater than 1\11., M. being the lower limit of t he range in which the viscosity is proportional to 1\113.4. A pronounced diff erence in the character of G" is predicted for polymers with molecu lar we ights between five and ten times 1 11. as compared with those whose molecular weights are outside this range. In a recent publication [1]1 we presented the steady state and transient behavior predicted by a model designed to repl'~sent the mechani~al behav:ior, in shear, of rubberhke polymers. ThIs model IS very similar to the molecular theor:v of Rouse [2], except that it includes directly the effect of entanglements found in long polymer chains. Our model assumes an entropy-type elasticity as the origin of t he relaxing force observed in it stress­ relaxation experiment. It involves a resistance coefficient per unit segment of a polymer chain which is evalu ated from the steady state viscous be­ havior, and the molecular weight of the polymer, expressed as the ratio of molecular weight to critical molecular weight, Me, defined as the lower limit of the range in which the viscosity is proportional to M 3. 4. For the particular example we presented in reference 1 this ratio was 60, and at the time we prepared this previous paper we did not have system­ atic calculations showing the predictions of the model for a range of molecular wei ghts. I'Ve made an effort (sec. 3, p . 176 of reference (1)) to relate the extrema of G" and J" to the molecular weight through the use of various approximate relationships, since the full expressions can only be treated numeril cally. We have now carried out further numerical calculations covering a range of molecular weights, and find that our previous approximate relations were completely inadequate to represent t he posi­ tions of these extrema as functions of molecular weight. In addition, we have found certain quite unexpected qualitative features of the predicted curves when the molecular weight is varied between one and ten times the critical molecular weight. I Since these quabtative features ma~T present the possibility of a rather critical test of the validity of this model, we pres en t the results here in some I detail. The results of our previous paper may be rep­ rf'sentf'd in terms of normalized functions. the

The resistance coefficient of flow through granular media depends on the porosity of the medium as well as the Reynolds number of the flow. There is disagreement as to the functional relationship between porosity and resistance coefficient, hence a series of carefully conducted permeability tests was made on randomly packed and systematically packed media using a variable head permeameter. The test results indicated that the relationship between porosity and resistance coefficient for laminar flow through granular media is represented best by the Fair-Hatch expression (l-a)2/a3 when compared with other factors that appear in the literature.