Slowly moving hull forms in short waves

The purpose of this paper is to provide a mathematical tool to improve the optimal design of ship forms. It is common practice that hull forms are designed such that they have minimum wave resistance in calm water. In this paper a theory is described by which the effect of short waves may be incorporated.The basic tool we use is the ray theory. First, the appropriate free-surface condition is shown. Then, the standard ray method, well-known in geometric optics, is formulated in the fluid region and at the free surface. After an elimination process the eiconal equation and the transport equation are obtained. The characteristic equation for the nonlinear eiconal equation is derived, keeping in mind that the characteristics are not perpendicular to the wave fronts, due to the effect of the double-body potential due to the forward speed of the ship, which is assumed to be a good approximation for the steady potential.Numerical computations are carried out by means of the RK4 method to obtain the ray pattern. After some manipulations the amplitude may be computed just as well. Finally, the nonlinear added-resistance force is calculated. Pictures of ray patterns for several angles of incidence are shown. Also the forces are shown.     

Calculation of the molar volume of liquid hydrocarbons

Equations are proposed for calculating the molar volume of liquid hydrocarbons used in production of surfactants. With such data, it will be possible to calculate most of the physicochemical properties of these hydrocarbons to solve many process problems. __________ Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 6, pp. 39–41, Novemmber–December, 2006.     

Nucleation of solidification in liquid droplets

Analytical and numerical methods have been developed to analyze the solidification kinetics of a mass of liquid droplets dispersed in a fluid or solid matrix using classical nucleation theory. The resulting analytical expressions and numerical calculations can be compared directly with calorimetric measurements of the droplet solidification exotherms to obtain information about the nucleation mechanism. With increasing contact angle at the solid-liquid-matrix triple point, the solidification onset, peak, and end temperatures and exothermic peak height all decrease sharply and the droplet solidification exotherms become broader. Decreasing either the droplet radius or the number of potential catalytic nucleation sites produces a similar but smaller effect. Distributions in droplet radius, contact angle, and nucleation sites have no effect on the solidification peak temperature, but the droplet solidification exotherms become broader and more symmetric. The solidification onset temperature is independent of cooling rate in the calorimeter, but the solidification peak and end temperatures decrease and the exothermic peak height increases with increasing cooling rate. Predicted droplet solidification exotherms are in excellent agreement with detailed experimental measurements on 10-nm-radius Cd droplets embedded in a solid Al matrix. Analytical predictions give best-fit values of 43 deg and 430 for the contact angle and the number of potential catalytic nucleation sites per droplet, respectively; numerical predictions give best-fit values of 43 deg and 750 for the contact angle and the number of potential catalytic nucleation sites per droplet, respectively.     

Towards real CAD

Present-day computer-aided design (CAD) packages play only a small part in the area of mechanical engineering design, which involves the synthesis and embodiment of physical components to perform a pre-determined function without unwanted side effects. The computer cannot properly help the designer in this task until it is able to capture and process the function requirements of the design. This paper describes the computer system being developed for this purpose at the Engineering Design Centre at Cambridge University Engineering Department. The paper also explores some of the geometrical and programming implications raised.     

Developing and fully developed turbulent flow of drag reducing fluids in an annular duct

Velocity profiles for the inner and outer flow regions of annuli are proposed for the turbulent flow of drag reducing fluids. Theoretical expressions for friction factors are developed. From the shear stress equations and the velocity profiles, estimates for the entrance lengths are given.     

Empirical equations for the perforation of mild steel plates

The experimental results for the perforation energy of mild steel plate struck by flat-ended, non-deforming, cylindrical penetrators have been correlated using the principles of dimensional analysis. A correlation is presented for long penetrators. It is shown that for short penetrators a different response of the target is observed and that, at present, there are insufficient published data to produce a unifying correlation.