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Subsea cable laying process is a difficult task for an engineer due to many uncertain situations which occur during the operation. It is very often that the cable being laid out is not perfectly fit on the route being planned, which results in the formation of slack. In order to control wastages during installation, the slack needs to be minimized and the movement of a ship/vessel needs to be synchronized with the cable being laid out. The current problem was addressed using a mathematical model by considering a number of defining parameters such as the external forces, the cable properties and geometry. Due to the complexity, the model is developed for a steady-state problem assuming velocity of the vessel is constant, seabed is flat and the effect of wind and wave is insignificant. Non-dimensional system is used to scale the engineering parameters and grouped them into only two main parameters which are the hydrodynamic drag of the fluid and the bending stiffness of the cable. There are two solutions generated in this article; numerical and asymptotic solutions. The result of these solutions suggests that the percentage of slack can be reduced by the increase of the prescribed cable tension, and also the increase in either the drag coefficient of the sea water or the bending stiffness of the cable, similarly will result in lower slack percentage.

Riverbank filtration (RBF) technology is applied in several countries around the world as one of the main sources of drinking water supply both from quantitative and qualitative point of view. Consequently, several analytical modelling methods, mostly based on the transformation techniques, are developed in literature to describe different processes which occur in RBF system. An extensive overview of these analytical methods, their uses and limitations are discussed. The review disclosed that most analytical models usually are concerned in evaluating stream depletion rate rather than contaminants transport especially the transportation of pesticides and pathogens. Laplace and Fourier methods are more popular methods used by researchers to solve the system of partial differential equation that developed to simulate the RBF problem.

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